Maverick Philosopher

The Holy Roman Empire and the Ground Zero Mosque

Somewhere in Saul Kripke's Naming and Necessity he employs the example of the Holy Roman Empire which was neither holy, Roman, nor an empire.  Well, I heard the Ground Zero mosque described this morning by a Muslim on C-Span as neither at Ground Zero nor a mosque.  As for the first claim, take a gander at this aerial shot (image credit):

 

The mosque site appears to be about two and a half city blocks from GZ.  That should count as close enough to justify the moniker 'GZM.'  After all, it couldn't be built right at GZ!  As for the second point, that the GZM is not a mosque,  is  true in part: it will be a mosque enveloped by an Islamic center -- which is arguably worse.

But judgments on these matters differ wildly, don't they?  Meanwhile, it turns out that the GZM developer, Sharif el-Gamal has quite a rap sheet.

 

 

 

 

The Eliminativist/Reductivist Distinction: Three Further Examples

For Part I of this discussion, and the first six examples, see here.  Recall that my concern is to show via a variety of examples that the eliminativist-reductivist distinction is useful and important and indeed indispensable for clear thinking about a number of topics.

7. Truth is warranted assertibility.   Someone who makes this claim presumably intends to inform us about the nature of truth on the presupposition that there is truth.  He is saying: there is truth all right; and what it is is warranted assertibility.  But I say:  if truth is warranted assertibility, then there is no truth.  The italicized claim, no matter what the intentions of a person who makes it, amounts to a denial of truth.  This example, as it seems to me, is 'on all fours'  (as the Brits say) with the Feuerbach example and the 'properties are sets' example.  Just as a property is not the sort of entity that could be identified with a set, truth is not the sort of property that could be identified with warranted assertibility (even at the Peircean ideal limit of inquiry.)  These three claims are all of them eliminativist.

8. Truth is relative.  Ditto.  Truth is not the sort of property that could be relative: if you know what truth is then you know that truth is absolute.  So if you say that truth is relative, then you are either confusing truth with some other property (e.g. the property of being believed by someone) or you are willy-nilly denying the very existence of truth.  If you understand the concept of God, then you understand that God cannot be an anthropomorphic projection. And if you understand the concept of truth, then you understand that truth cannot be relative to anything, whatever your favorite index of relativization might be, whether individuals, social classes, historical epochs . . . .

See Truth is Absolute! Part One.   Part Two.

9. The morally obligatory is that which God commands.  In stark contrast to the two foregoing examples, this example cannot be given an eliminativist reading.  The very concept of truth disallows truth's relativization. But there is nothing in the concept of moral obligation to disallow the identification of the morally obligatory with that which God commands.  But here we need to make a distinction.

You will have noticed that identity is a symmetrical relation:  if x = y, then y = x.  But reduction is asymmetrical: if x reduces to y, then y does not reduce to x.  Therefore, an identification is not the same as a reductive identification or reduction.  'Hesperus = Phosphorus' is an identity claim but not a reductive claim: the claim is not that Hesperus reduces to Phosphorus, as if Phosphorus were the fundamental reality and Hesperus the less fundamental, or perhaps a mere appearance of Phosphorus.  But 'Table salt = NaCl' is a reduction of what is less fundamental to what is more fundamental.

Now what about our italicized claim?  There are problems with reading it as a left-to-right reduction.  The morally obligatory is what we morally ought to do; but what we ought to do cannot be reduced to what anyone commands, not even if the commander is morally perfect.  The normative oughtness of an act or act-ommission cannot be reduced the mere fact that someone commands it, even if the commander always commands all and only what one ought to do. So one could argue that the italicized claim, if construed as a reduction of the morally obligatory to what God commands, collapses into an elimination of the morally obligatory.  Be we needn't take it as a reduction; we can take it as a nonreductive identification.  Accordingly, being morally obligatory and being commanded by God are the same property in reality even though they are conceptually distinct.

But even if you don't agree with the details of my analysis, I think you must agree to distinguish among eliminative claims, reductive identity claims, and nonreductive identity claims.

 

The Liberal Debating Manual

From the The Liberal Debating Manual (San Francisco: PeeCee Publishers, 2010):

No matter what position your conservative opponent takes on any issue, choose one or more epithets from the following list and label him with it:

Racist, bigot, fascist, sexist, intolerant, homophobic, Islamophobic, xenophobic.

Mix and match, and repeat as necessary.  Never ever engage conservative arguments.  To do so is to admit that your enemy is a rational being with a point of view worth considering.  Never credit a conservative with reason, moral decency or intellectual insight.  The smear is extremely effective if repeated often enough.   Never miss an opportunity to play the race card.  Insult and demean.  Tea-Partiers are 'teabaggers.'  If they reply in kind, act shocked and insist on the double-standard: we are morally and intellectually superior people while you are scum.  How can you object when we call you what you are: bigots, racists, scumbags?

Keep your eye on the prize and never forget that winning is all that counts.  The end justifies the means.  Example here.

On the Utility of the Eliminativist/Reductivist Distinction

If we think carefully about examples such as the following, I think we can come to agree that it is useful to make a distinction between eliminativist and reductivist claims.  The distinction is useful because it allows us to disambiguate claims that otherwise would be ambiguous.  Roughly, the distinction is between claims of the form There are no Fs and of the form There are Fs but Fs are Gs.

1. God is an anthropomorphic projection. (Feuerbach)  This could be construed as implying that there is an x such that x = God and x is an anthropomorphic projection.  This would be a reductivist construal.  It has absolutely nothing going for it given that the concept of God is the concept of a being that exists a se, and thus independently of human beings and their thoughts and projections.  If you think that God could be an anthropomorphic projection, then you simply do not understand the concept of God -- whether or not anything instantiates the concept.The Feuerbachian claim is to be read eliminatively as  implying that there is no x such that x is God.

So here we have a very clear example of a sentence which, though it appears to be predicating something of God, and thus presupposing the existence of God, is really a negative existential in disguise. 

2. The self is a bundle of perceptions. (Hume)  This example, unlike the first, can be read either way with some plausibility.  I would argue that a mere bundle of perceptions (or of other mental data) cannot constitute a self because a self is that which supports and unifies and is aware of such data. But other philosophers will disagree.  So for present purposes I judge this example to be susceptible of both readings.

3. Causation is regular succession. Someone who claims that events e1, e2 are such that e1 causes e2 iff the e1-e2 event sequence instantiates a regularity is arguably leaving out something so fundamental -- the notion that the cause produces or brings into existence the effect --  that the claim is tantamount to a denial of causation.  Or so I would argue.  But regularity theorists will vigorously disagree.  They will take the dictum (suitably expanded and qualified) to express the nature of causation.  They will insist that there is causation but that what it is is regular succession.  So, in an irenic spirit, I will classify this example as open to both readings.

4. Properties are sets.  (David Lewis)  Accordingly, the property of being red is the set of all actual and possible red things.  A cruder form of the theory is that the property of being red, e.g., is the set of all red things.  The theory in either form is hopeless, but that is not the question.  The question is whether it is eliminativist or reductivist.  Is it tantamount to a denial of properties, or does it imply that there are properties but that what they are are sets?  I say the former, but David Lewis is one formidable opponent!  Here is a quick little argument:  Properties are instantiable entities by definition; no set is instantiable; ergo, no property is a set!  My considered opinion is that 'Properties are sets' boils down to a denial of properties.  If you understand the concept property, then you know no property could be a set.  It is just like #1 above: if you understand the concept God, then you know that God could not be an anthropological projection.

5. Mental events are brain  events.  I suddenly remember an evening spent on the banks of the River Charles with a pretty girl . . . . That sudden remembering is a mental event token.  There are those who want to say that it is identical to a brain event token. These philosophers speak of 'token-token identity theory.'  The philosophers who maintain this do not intend to deny the existence of mental events; their intention is to inform us as to the nature of mental events on the presupposition that  they exist.

But although their intention is reductive identification and not elimination, one can reasonably wonder whether the reduction does not collapse into an elimination.  Indeed, that is what I would maintain.  For if every mental state is identical to some brain state, and if the identification is supposed to be a reduction  of the mental to the physical, then what you have in the final analysis is just the brain state: the mental state has been eliminated.

Even if you disagree with me that in this case the reduction collapses into an elimination, to even understand what the debate is about you must understand the distinction between elimination and reduction.

6. The tree in the quad is a cluster of ideas in the mind of God. (Berkeley)  The good bishop is not denying that there are physical things; he is telling us what he thinks physical things are.  They reduce to clusters or bundles of divine ideas.  It shows a complete lack of understanding to think that stone-kicking is so much as relevant to the idealist thesis.  So this is a clear case of a reduction.

Could one argue that in this case too the reduction collapses into an elimination?  If the mind-brain identity thesis collapses into an elimination of the mind (as was claimed in #5), then why shouldn't the Berkeleyan identity thesis (Physical objects are a clusters of divine ideas) collapse into an elimination of physical objects?  Perhaps we can say the following.  That the existence of a tree is its existence for the divine mind is consistent with everything we know about trees. (We do not know about trees that they can exist independently of any mind.)  But that a mental state is identical to a brain state is not consistent with what we know about mental states.  Thus we know that they exhibit intentionality while physical states do not.  Mental states cannot be identical to brain states; therefore, a materialist about the mind must be an eliminativist.  But an idealist about physical objects needn't be an eliminativist.

The Midas Touch

Whatever King Midas touched turned into gold.  The philosophers have something akin to it: whatever they touch turns into a puzzle.  (I borrow the thought from Wilfrid Sellars.)

Saturday Night at the Oldies: A Half Dozen Dedications

To Horace Jeffery Hodges who describes himself thusly:

I've gone from the Arkansas Ozarks through Texas, California, Switzerland, Germany, Australia, and Israel to South Korea. I've traveled to Mexico, Belgium, Holland, East Germany, England, France, Denmark, Austria, Czechoslovakia (before it split into the Czech Republic and Slovakia), Russia, Italy, Japan, Singapore, and Scotland. Hence: "Gypsy Scholar."

I've Been Everywhere.

To Peter Lupu, Forty Cups of Coffee and Smoke Smoke That Cigarette.

To Mike Valle, Ghost Riders in the Sky.

To Philoponus the Impecunious, Money.

To William the Nominalist, The Name Game.

To David Brightly, Heartaches by the Numbers.

Oikophobia

Here.

Fist and Hand, Statue and Lump: The Aporetics of Composition

1. Some maintain that a hand, and that same hand made into a fist, are identical. And there are those who would say the same about a piece of bronze and the statue made out of it, namely, that they are identical at every time at which both exist. This is not an unreasonable thing to say. After all, fist and hand, statue and bronze, are spatially coincident and neither has a physical part the other doesn't have. A fist is just a certain familiar arrangement of hand-parts. There is no part of the fist that is not part of the hand, and vice versa. So at looks as if first and hand are identical.  But we need to be clear as to what identity is.

2. Identity is standardly taken to be an equivalence relation (reflexive, symmetrical, transitive) governed by the Indiscernibility of Identicals (InId) and the Necessity of Identity (NecId). The first principle says that, if two items are numerically identical, then they share all properties. The second says that if two items are numerically identical, then this is necessarily the case.  Both principles strike me as beyond epistemic reproach.  'Identity' is short for 'numerical identity.'

3. Despite the considerations of #1, it looks as if fist and hand, statue and hunk of bronze, cannot be identical since they differ in their persistence conditions. The hunk of bronze can, while the statue cannot, survive being melted down and recast in some other form. The hand can, while the fist cannot, survive adoption of a different 'posture.'  In both cases, something is true of the one that is not true of the other.  So even at the times at which the fist is the hand, and the bronze is the statue, the two are not identical: the 'is' is not the 'is' of identity.  It is the 'is' of composition and what you have are two things, not one.

What I have just given is a modal discernibility argument.  Let me spell it out.  Consider a time t at which the hand is in the shape of a fist.  At t, the hand, but not the fist, has the modal property of being possibly such as to to be unfisted.  So the hand cannot be identical to the fist given that, for any x, y, if x = y, then x, y share all properties.

But there is also this nonmodal discernibility argument.  The hunk of bronze existed long before the statue came into existence, and the hunk of bronze exists while the form of a statue.  So the hunk of bronze exists at more times that the statues does, which implies the the hunk of bronze is not identical to the statue.

There is also this consideration.  Identity is symmetrical.  So we can say either fist = hand or hand = fist.  But is it the fist or the hand that both are?  Intuitively, it is the hand.  The hand is the fundamental reality here, not the fist.  So how can fist and hand be identical?  It seems that fist and hand are numerically distinct, albeit spatially coincident, concrete individuals.

4.  The Law of Excluded Middle seems very secure indeed, especially in application to presently existing things.  So either the fist is identical to the hand, and there is just one thing, a fisted hand, or the fist is not identical to the hand and there are two spatially coincident things, a fist and a hand.  So which is it?

5. If you say that the fist = the hand, then when you make a fist nothing new comes into existence, and when the potter makes a pot out of clay, nothing new comes into existence.  And when a mason makes a wall out of stones, nothing new comes into existence.  He started with some stones and he ended with some stones.  Given that the stones exist, and that the mason's work did not cause anything new to come into existence, must we not say that the single composite entity, the wall, does not exist?  (For if it did exist, then there would be an existent in addition to the stones.)  But it sounds crazy to say that the wall the mason has just finished constructing does not exist.

6. If, on the other hand, you say that the fist is not identical to the hand, then you can say that the making of a fist causes a new thing to come into existence, the fist.  And similarly with the statue and the wall.  After the mason stacks n stones into a wall, he has as a result of his efforts n +1 objects, the original n stones and the wall. 

But this is also counterintuitive.  Consider the potter at his wheel.  As the lump of clay spins, the potter shapes the lump into a series of many (continuum-many?) intermediate shapes before he stops with one that satisfies him.  Thus we have a series of objects (proto-pots) each of which is a concrete individual numericallt distinct from the clay yet (i) spatially conicident with it, and (ii) sharing with it every momentary property.  And that is hard to swallow, is it not?

7.  We appear to be at an impasse.  We cannot comfortably say that the fist = the hand, nor can we comfortably say that the fist is not identical to the hand. Nor can we comfortably give up LEM.  If there are no fists, statues, walls, artifacts generally, then there cannot be any puzzles about their composition.  But we cannot comfortably say that there are no such things either.

Do we have here an example of a problem that is both genuine but insoluble?

Guest Post: Is There a Real Distinction Between Reductionism and Eliminativism?

What follows is a guest post by a long-standing card-carrying member of the MavPhil commentariat, William the Nominalist.  He is eager to hear any thoughtful and pertinent comments you may have. 

The distinction between reductionism and eliminativism is widely recognised in the philosophy of mind and the philosophy of science. It also seems to be very clear. Here it is, as explained by William Ramsey.

Ontologically conservative theory change occurs when the entities and posits of the replaced theory are relocated, often with some degree of revision, in the replacing theory. For example, as our theory of light was gradually replaced by our understanding of electro-magnetic radiation, our conception of light was dramatically transformed as we recognized ways in which our old conception was mistaken or incomplete. Nevertheless, at no point did we come to say that there is really no such thing as light. Rather, light was eventually identified with a form of electro-magnetic radiation.

By contrast, our notion of demons did not come to find a new home in contemporary theories of mental disorder. There is nothing in the theories of schizophrenia, Tourette's Syndrome, neuro-pathology or any of the other modern explanations for bizarre behavior, that we can sensibly identify with malevolent spirits with supernatural powers. The notion of a demon is just too far removed from anything we now posit to explain behavior that was once explained by demonology. Consequently, the transition from demonology to modern accounts of this behavior was ontologically radical. We dropped demons from our current ontology, and came to realize that the notion is empty — it refers to nothing real.

But after a moment's reflection, I find it is not very clear at all. Why?

The Last Refuge of a Liberal

The last refuge of a liberal are charges of bigotry and intolerance. Charles Krauthammer:

. . . promiscuous charges of bigotry are precisely how our current rulers and their vast media auxiliary react to an obstreperous citizenry that insists on incorrect thinking.

-- Resistance to the vast expansion of government power, intrusiveness and debt, as represented by the Tea Party movement? Why, racist resentment toward a black president.

-- Disgust and alarm with the federal government's unwillingness to curb illegal immigration, as crystallized in the Arizona law? Nativism. [and racism and xenophobia]

-- Opposition to the most radical redefinition of marriage in human history, as expressed in Proposition 8 in California? Homophobia.

-- Opposition to a 15-story Islamic center and mosque near Ground Zero? Islamophobia.

For just one example of what Krauthammer is rightly protesting, read Robert Reich's Anatomy of Intolerance.  You will note that here as elsewhere in liberal screeds there is no attempt at engaging conservative arguments.  What is offered is name-calling and psychologizing.  According to Reich,

Most Americans approve of Arizona’s new law allowing police to stop anyone who looks Hispanic and demand proof of citizenship.

This is plainly false and looks to be an outright lie.  A man as intelligent and well-informed as Robert Reich cannot possibly be unaware at this late date of the content of AZ SB 1070.  The law does not allow the the police to stop anyone who looks Hispanic to check citizenship status.  It disallows this.  See The Misrepresentations of Arizona SB 1070 Continue.

On Reconciling Creatio Ex Nihilo with Ex Nihilo Nihil Fit

This post examines Richard C. Potter's solution to the problem of reconciling creatio ex nihilo with ex nihilo nihil fit in his valuable article, "How To Create a Physical Universe Ex Nihilo," Faith and Philosophy, vol. 3, no. 1, (January 1986), pp. 16-26. (Potter appears to have dropped out of sight, philosophically speaking, so if anyone knows what became of him, please let me know. The Philosopher's Index shows only three articles by him, the last of which appeared in 1986.)

I. THE PROBLEM

We first need to get clear about the problem. On classical conceptions, God creates ex nihilo, out of nothing.  He is not a Platonic demiurge who operates upon some preexistent stuff: he creates without it being the case that there is something out of which he creates.  Nor does God create out of himself, a notion that presumbaly would give aid and comfort to pantheism.  God creates out of nothing.  Given that God creates out of nothing, how is this consistent with the apparent truth that something cannot come from nothing? The latter, the principle of ex nihilo nihil fit, seems to be an intuitively self-evident metaphysically necessary truth. Let us assume that it is.   As metaphysically necessary, it is not a truth over which God has any control. Its truth-value is not within the purview of the divine will.  Our problem is to understand, if possible, how it can be true both that God creates out of nothing, and that out of nothing nothing comes.  Potter offers an ingenious solution.

Ex nihilo nihil fit is interpreted by Potter in terms of the following Principle of Creation by Compounding:

PCC. For any object O and time t, if O comes into being at t, then there exist some objects out of which O is composed and those objects existed prior to t.

Potter sees the problem as one of reconciling (PCC) with the following principle:

ENP. God created contingent objects in such a way that there was a time t₁ at which contingent objects came into being, although there was no time prior to t₁.

On the face of it, (PCC) and (ENP) are logically inconsistent.

Robert Royal on the GZM

Here. Excerpt:

If you’re like me, you’ve probably heard enough about the mosque. But the problem for me is that what I’m hearing doesn’t seem to address the main question. When NY Mayor Bloomberg says it’s a tragedy if 9/11 results in the loss of religious liberty – as if Islam were being curtailed here – I feel like I’m listening to a political class that’s taken leave of its senses. To put the matter baldly, some of us now think America is merely a matter of legal precedents, not a human community.

Two things are clear: 1. in America, religious liberty is an unshakeable right and houses of worship may be built, allowing for local zoning laws and other reasonable restrictions; 2. there is reason for doubt whether the mosque should be built, as last week even President Obama was forced to acknowledge.

Liberals have suddenly discovered a virtual absolute right for religion – primarily Islam – to be assertive anywhere, any time. Strange, because the Left has for decades sought to minimize religion in the public square.

Latest example:  Utah crosses ruled unconstitutional. 

Hats Off to Hentoff: "Pols Clueless on Ground Zero Mosque"

Here.  Excerpts:

Imam Rauf has refused to call Hamas a terrorist organization and had no comment when, on Aug. 15, Mahmoud al-Zahar, its co-founder, strongly supported the Imam's mosque near Ground Zero, saying, Muslims "have to build everywhere" (Associated Press, Aug. 16). Sen. Charles Schumer, D-N.Y., said the support by Hamas of the Imam's mosque carried no weight because "Hamas is a terrorist organization."

How's that for bizarro reasoning? Any normal person would take Hamas support for the GZM to be worrisome indeed.  But not Schumer the liberal.  No bigot he.  He takes the fact that Hamas is a terrorist organization as somehow giving us a reason to ignore its support!

This imam - widely lauded in much of the press as "a moderate" Muslim - is not reticent, however, in his firm commitment to Sharia (Islamic law), which regards women as far less than fully human. In the Dec. 9, 2007 Arabic newspaper Hadi el-Islam, Rauf insisted:

Throughout my discussions with contemporary Muslim theologians, it is clear an Islamic state can be established in more than just a single form or mold. It can be established through a kingdom or a democracy. The important issue is to establish the general fundamentals of Sharia that are required to govern.

I would greatly appreciate it if Imam Rauf explained, maybe Pelosi will ask him, more fully what he meant in his 2004 book, "What's Right With Islam is What's Right With America." In it he declares: "American Constitution and system of governance uphold the core principles of Islamic law." Rauf says Sharia law is a core principle of Islamic law. Does that also include a core principle of our Constitution?

Gutting, Dawkins, and Russell's Celestial Teapot

In his recent NYT Opinionator piece, On Dawkins's Atheism, Notre Dame's Gary Gutting writes, describing the "no arguments argument" of some atheists:

To say that the universe was created by a good and powerful being who cares about us is an extraordinary claim, so improbable to begin with that we surely should deny it unless there are decisive arguments for it (arguments showing that it is highly probable). Even if Dawkins’ arguments against theism are faulty, can’t he cite the inconclusiveness of even the most well-worked-out theistic arguments as grounds for denying God’s existence?

He can if he has good reason to think that, apart from specific theistic arguments, God’s existence is highly unlikely. Besides what we can prove from arguments, how probable is it that God exists? Here Dawkins refers to Bertrand Russell’s example of the orbiting teapot. We would require very strong evidence before agreeing that there was a teapot in orbit around the sun, and lacking such evidence would deny and not remain merely agnostic about such a claim. This is because there is nothing in our experience suggesting that the claim might be true; it has no significant intrinsic probability.

But suppose that several astronauts reported seeing something that looked very much like a teapot and, later, a number of reputable space scientists interpreted certain satellite data as showing the presence of a teapot-shaped object, even though other space scientists questioned this interpretation. Then it would be gratuitous to reject the hypothesis out of hand, even without decisive proof that it was true. We should just remain agnostic about it.

The claim that God exists is much closer to this second case. There are sensible people who report having had some kind of direct awareness of a divine being, and there are competent philosophers who endorse arguments for God’s existence. Therefore, an agnostic stance seems preferable to atheism.

I have a serious problem with Gutting's response to the Russell-Dawkins tag team.  Gutting concedes far too much in his reply, namely, that it even makes sense to compare the claim that there is an orbiting teapot with the claim that God exists.  Instead of attacking this comparison as wrongheaded from the outset, Gutting in effect concedes its aptness when he points out that, just as there could be (inconclusive) scientific evidence of a celestial teaspot, there could be (inconclusive) experiential and argumentative evidence for the existence of God.  So let me try to explain why I think that the two existence claims ('God exists' and 'A celestial teapot exists') are radically different .

Of Dhimmitude and Derriere

Western licentiousness meets the panty jihad. Quotable:

This is a traditional tactic of the Islamic march to domination.  One fight at a time, one street at a time, one billboard at a time, one school at a time, one book at a time, one TV news report at a time. Islam must always be acknowledged to be above Christianity, Judaism, Hinduism and other ancient religions.

 

The eventual state whereby Christians and Jews acknowledge Islam’s authority and superiority is called the dhimmitude.  Dhimmis will be invited to convert to Islam, but if they do not, they will be allowed to continue to practice their own religions, although with restrictions, and they must profess submission to Islamic laws.

 

Shamefully, Sloggi is marching down that road.

Peter van Inwagen, Artifacts, and Moorean Rebuttals

Two commenters in an earlier van Inwagen thread, the illustrious William the Nominalist and the noble Philoponus of Terravita,  have raised Moore-style objections to an implication of PvI's claim that "every physical thing is either a living organism or a simple" (MB 98), namely, the implication that "there are no tables or chairs or any other visible objects except living organisms." (MB 1)  The claim that there are no inanimate objects, no tables, chairs, ships and stars will strike many as so patently absurd as to be not worth discussing.  Arguments to such a conclusion, no matter how clever, will be dismissed as unsound without  evaluation on the simple ground that the conclusion to which they lead is preposterous.  This is the essence of a Moorean objection.  If someone says that time is unreal, you say, 'I ate breakfast an hour ago.'  If someone denies the external world, you hold up your hands.  If someone denies that there are chairs, you point out that he is sitting on one.  And then you clinch your little speech by adding, 'The points I have just made are more worthy of credence than any premises you can marshall in support of their negations.' 

I myself have never been impressed with Moorean rebuttals.  To my mind they signal on the part of those who make them a failure to understand the nature of philosophical (in particular, metaphysical) claims.  See, e.g., Can One See that One is not a Brain in a Vat?

Though I disagree with van Inwagen's denial of artifacts, I think he can be quite easily defended against the charge of maintaining something 'mad' or something refutable by a facile Moorean rejoinder.

Chapter 10 of Material Beings deals with the Moorean objection.  Van Inwagen does not deny that we utter such true sentences as 'There is a wall that separates my property from my neighbor's.'  But whereas most of us would infer from this that walls exist, and thus that composite non-living things exist, van Inwagen refuses to draw this inference maintaining instead that the truth of 'There is a wall that separates my property from my neighbor's' is consistent with there being no walls.

This is not as crazy as it sounds.  For suppose that what the vulgar call a wall is (speaking with the learned) just some stacked stones, some stones arranged wall-wise.  And to simplify the discussion, suppose the stones are simples.  Then the denial that there is a wall is a denial that there is one single thing that the stones compose.  But this is consistent with the existence of the stones.  Accordingly, the sentence 'There is a wall that separates my property from my neighbor's' is true in virtue of the existence of the stones despite the fact that there is no wall as a whole composed of these stony parts.

Or consider the house built by the Wise Pig years ago out of 10, 000 blocks (which for present purposes we may consider to be honorary simples.)  (The tail tale of the Wise Pig is recounted on p. 130 of Material Beings.) At the completion of construction, did something new come into existence?  I would say 'yes.'  Van Inwagen would say 'no.'  All that has happened on PvI's account is that some blocks have been arranged house-wise.  His denial then, is that there is a y such that the xs compose y.  He is not denying the xs (the blocks construed as simples); he is denying that there is a whole that they compose.  And because there is no whole that they compose, the house does not exist.

Furthermore, because the house does not exist, there can be no question whether the house built by the Wise Pig years ago, and kept in good repair by him and his descendants by replacement of defective blocks, is the same as or is not the same as the one that his descendants live in today.  The standard puzzles about diachronic artifact identity lapse if there are no artifacts.   

Does this fly in the face of Moorean common sense?  If  madman Mel were to say that there are no houses he would not mean what the metaphysican means when he says that there are no houses.  If Mel is right, then it cannot be true that I have been living in the same house for the last ten years.  But the truth of 'I have been living in the same house for the last ten years' is consistent with, or at least not obviously inconsistent with,  PvI's denial of houses (which is of course not a special denial, but a consequence of his denial of artifacts in general). This is because PvI is not denying the existence of the simples which we mistakenly construe as parts of a nonexistent whole.

But then how are we to understand a sentence like, 'The very same house that stands here now has stood here for three hundred years'?  Van Inwagen proposes the following paraphrase:

There are bricks (or, more generally, objects) arranged housewise here now, and these bricks are the current objects of a history of maintenance that began three hundred years ago; and at no time in that period were the then-current objects of that history arranged housewise anywhere but here. (133)

I am not endorsing PvI's denial of artifacts, I am merely pointing out that it cannot be dismissed Moore-style. 

 

Hodges Weighs in on 'Suicide Bomber'

Dear Bill,

Interesting discussion on 'suicide' bombers. I prefer the expression "suicide bomber" to "homicide bomber." I think that the term "bomber" implies that the individual is aiming not solely at suicide but at other killing or destruction, too. I also like the fact that Islamists object to the term "suicide" since suicide is forbidden in Islam, so the insult is useful.

Yours,

Jeffery

See Dr. Hodges' Islamism: Radicalism at the Core of Islam?  Follow the links and use the search function to locate other of Hodges' Islam(ism) posts.  And now I note that he just posted on Christopher Hitchens' take on the Ground Zero mosque.  By the way, those who complain about this moniker, objecting that the provocation in question will not be located precisely at Ground Zero, need to be reminded that (i) there is no way that it could be located precisely there, and that (ii) debris from one of the trade towers hit the building whose demolition is to make way for the GZM.

More on 'Suicide Bomber'/'Homicide Bomber'

I have been receiving e-mail about my earlier post on this topic.  Here is one letter:

I fear you may have been a little harsh on Bill Keller in your recent post about the virtues of calling suicide bombers 'homicide bombers'. Whilst I accept the conceptual and definitional analysis of the terms, surely the simple point is that ANY bomber who kills other humans is a homicide bomber, but it is only the suicide bomber who kills himself/herself and other humans. The term 'suicide bomber', in my opinion, is perfectly apt as it emphasises that this individual was prepared to kill himself/herself in the pursuit of killing others (rather than planting a bomb and detonating it remotely, for example). It may not be conceptually neat, but it's a worthy distinction to make, and one that is obscured by the term 'homicide bomber'.

Since the point I have just made is so simple and luminous, it is reasonable to conjecture that you were blinded to its alethic luminosity by your right-wing bias, a bias that is reinforced on a quotidian basis by the crowd you run with.

I really enjoy reading the blog.

Very clever.  I see your point, but let's think about it a bit more.  There are three cases: (1) the bomber who kills himself while killing others; (2) the bomber who kills himself without killing others; (3) the bomber who kills others without killing himself.  In all three cases the bomber is a homicide bomber.  In the first two cases, the bomber is a suicide bomber.  Because 'suicide bomber' applies in both the first and the second cases, the term 'suicide bomber' does not distinguish between them.  To that extent 'suicide bomber' is not sufficiently precise. 

You write, ". . . it is only the suicide bomber who kills himself/herself and other humans."  Not so: you are ignoring case (2).  Case (2) splits into two subcases: (2a) the bomber intends to blow only himself up and succeeds; (2b) the bomber intends to blow himself and others up, but succeeds only in blowing himself up.

Consider an example.  A Palestinian Arab walks into a Tel Aviv pizza parlor and detonates his explosive belt killing himself and 100 Israelis.  It would be misleading to say that this man has committed suicide even though he assuredly has, given that suicide is the intentional taking of one's own life. It is misleading because he hasn't merely killed himself, he has killed himself in order to commit mass murder.

As a conservative, I detect left-wing bias in the use of 'suicide bomber' in a case like this.  It is biased because it plays down the element of mass murder of others. It puts the emphasis on the poor terrorist -- a product of oppressive circumstances we will be told -- instead of where it belongs, on the slaughter of civilians.  So from my conservative point of view, 'homicide bomber' seems more apt.  This is reinforced by the linguistic fact that when one hears 'suicide' one does not usually think of homicide even though suicide is a form of homicide.  The word 'homicide' in ordinary English carries the connotation of the killing of others.  If a man commits suicide we typically do not say that he committed homicide, and if a man commits homicide we do not normally think of the case in which he commits homicide by committing suicide.

I will concede to you, though, that since 'homicide bomber' covers all three cases, it fails to convey the notion that the terrorist killed himself in order to kill others.  So we may have a stand-off here: neither of us can compellingly show that the other's usage is incorrect or to avoided.

Thank You Zoe Pollock of The Daily Dish

When I logged on yesterday, I was surprised to see that my readership was way up: by the end of the day I had logged 2,698 page views for the day.  That's about double what I was getting the few days preceding.  Here is the link from Zoe Pollock. 

Hell, if I knew she was going to link to that meditation on death and Hitchens, I would have polished it.  Almost everything I post on this site is first-draftish.  That is the nature of the 'sport' of blogging.  The idea is to see if you can bang out something interesting, substantive, penetrating, muscular yet elegant, without spending the whole day doing it.

I have been blogging for over six years now on a daily basis. Something tells me I'm in it for the duration.  It has added very considerably to the quality of my life, especially because of the likeminded friends I have made.  You guys know who you are.  The social networking that the Internet makes possible solves a very nasty problem of human relations:  How can one find people one can relate to?

Chutzpah

A delightful word of Yiddish, 'chutzpah' is in the semantic vicinity of 'insolence,' 'effrontery,' 'impudence,' 'gall.'  An excellent contemporary example of chutzpah: building a mosque and huge Islamic center a couple of blocks from where nearly three thousand Americans were slaughtered in the name of Islam.   As we say in the Southwest, that takes cojones!

Emergentism

Here is a measly hunk of frangible bone and flesh out of which emerges a balloon so vast as to encompass the universe past, present, and future.  And then one day the wretched little animal dies, the air supply is cut off, and the balloon collapses, its last thought being: what the hell was that all about?

'Suicide Bomber' or 'Homicide Bomber'?

Bill Keller is the Executive Editor of the New York Times. I saw him on C-Span 1 on the morning of 1 September 2004. In response to a caller who brought up the issue of liberal bias in the NYT, Keller rightly pointed out that political opponents often try to seize control of the terminology in which debates are couched in order to gain an advantage over their adversaries. As one might expect, the examples he chose favored his liberal tilt. Thus he mentioned the Republican use of 'death tax' to refer to what is more commonly known as the estate tax, as well as the fairly recent tendency of Republicans and conservatives generally to use 'Democrat Party' instead of the more traditional 'Democratic Party.' I'll return to these examples in a moment; it is Keller's third example, however, that inspired this post. 

Keller took exception to the practice of some conservatives who label what are more commonly known as suicide bombers as 'homicide bombers,' claiming that 'suicide bombers' is the correct term. Keller claimed in effect that a person who blows himself up is a suicide bomber, not a homicide bomber.

This is a clear example of muddled thinking. Note first that anyone who commits suicide ipso facto commits homicide.* If memory serves, St. Augustine somewhere argues against suicide using this very point. The argument goes something like this: (1) Homicide is wrong; (2) Suicide is a case of homicide; ergo, (3) Suicide is wrong. One can easily see from this that every suicide bomber is a homicide bomber. Indeed, this is an analytic proposition, and so necessarily true.

More importantly, the suicide bombers with whom we are primarily concerned murder not only themselves but other people as well. As a matter of fact, almost every suicide bomber is a homicide bomber not just in the sense that he kills himself, but also in the sense that he kills others. There are two points here. As a matter of conceptual necessity, every suicide bomber is a homicide bomber. And as a matter of contingent fact, every suicide bomber, with the exception of a few solitary individuals, is a homicide bomber.

Keller missed both of these points. Had he seen them, he would have appreciated that 'homicide bomber' is a perfectly accurate expression free of ideological taint. He would have seen that every suicide bomber is a homicide bomber, though not conversely. He would have grasped that suicide bombers are a proper subset of homicide bombers. (S is a proper subset of T iff S is a subset of T but S is not identical to T.)

Since the points I have just made are so simple and luminous, it is reasonable to conjecture that Keller was blinded to their alethic luminosity by his liberal bias, a bias that is reinforced on a quotidian basis by the crowd he runs with. As to the other two examples, I am willing to concede that 'death tax' is inaccurate. It is not the event of dying that is being taxed, but the transfer of wealth that occurs on the occasion of dying when the wealth is greater than a certain amount. But calling the Democrat Party the Democrat Party is as accurate as can be. For it makes it clear that 'Democrat Party' is a proper name as opposed to a description. 'Democratic Party,' however, suggests that there is a description satisfaction of which is necessary for 'Democratic Party' to have a referent -- which is false. 'Democratic Party' refers to what it refers to even if the referent fails to be democratic.  They are a pack of elitists, scarcely democratic.  Dropping the '___ic' makes this clear.

_________________

*Since the reference class for the sake of this discussion is human beings, we needn't consider such counterexamples as that of the nonhuman extraterrestrial who commits suicide, or the terrestrial nonhuman (a dolphin perhaps) who does so. If Star Trek's Mr. Spock or Dolly the Dolphin commit suicide, they do not thereby commit homicide. 

What Explains Islamist-Leftist Collaboration?

An analysis by Daniel Pipes.  Excerpt:

Why, then, the formation of what David Horowitz calls the Left-Islamist "unholy alliance"? For four main reasons.

First, as British politician George Galloway explains, "the progressive movement around the world and the Muslims have the same enemies," namely Western civilization in general and the United States, Great Britain, and Israel in particular, plus Jews, believing Christians, and international capitalists. In Iran, according to Tehran political analyst Saeed Leylaz, "the government practically permitted the left to operate since five years ago so that they would confront religious liberals."

Listen to their interchangeable words: Harold Pinter describes America as "a country run by a bunch of criminal lunatics" and Osama bin Laden calls the country "unjust, criminal and tyrannical." Noam Chomsky terms America a "leading terrorist state" and Hafiz Hussain Ahmed, a Pakistani political leader, deems it "the biggest terrorist state." These commonalities suffice to convince the two sides to set aside their many differences in favor of cooperation.

Second, the two sides share some political goals. A mammoth 2003 joint demonstration in London to oppose war against Saddam Hussein symbolically forged their alliance. Both sides want coalition forces to lose in Iraq, the War on Terror to be closed down, anti-Americanism to spread, and the elimination of Israel. They agree on mass immigration to and multiculturalism in the West. They cooperate on these goals at meetings such as the annual Cairo Anti-War Conference, which brings leftists and Islamists together to forge "an international alliance against imperialism and Zionism."

Third, Islamism has historic and philosophic ties to Marxism-Leninism. Sayyid Qutb, the Egyptian Islamist thinker, accepted the Marxist notion of stages of history, only adding an Islamic postscript to them; he predicted that an eternal Islamic era would come after the collapse of capitalism and Communism. Ali Shariati, the key intellectual behind the Iranian revolution of 1978–79, translated Franz Fanon, Che Guevara, and Jean-Paul Sartre into Persian. More broadly, the Iranian analyst Azar Nafisi observes that Islamism "takes its language, goals, and aspirations as much from the crassest forms of Marxism as it does from religion. Its leaders are as influenced by Lenin, Sartre, Stalin, and Fanon as they are by the Prophet."

Moving from theory to reality, Marxists see in Islamists a strange fulfillment of their prophesies. Marx forecast that business profits would collapse in industrial countries, prompting the bosses to squeeze workers; the proletariat would become impoverished, rebel, and establish a socialist order. But, instead, the proletariat of industrial countries became ever more affluent, and its revolutionary potential withered. For a century and a half, author Lee Harris notes, Marxists waited in vain for the crisis in capitalism. Then came the Islamists, starting with the Iranian Revolution and following with 9/11 and other assaults on the West. Finally, the Third World had begun its revolt against the West, fulfilling Marxist predictions—even if under the wrong banner and with faulty goals. Olivier Besancenot, a French leftist, sees Islamists as "the new slaves" of capitalism and asks if it is not natural that "they should unite with the working class to destroy the capitalist system." At a time when the Communist movement is in "decay," note analyst Lorenzo Vidino and journalist Andrea Morigi, Italy's "New Red Brigades" actually acknowledge the "leading role of the reactionary clerics."

Fourth, power: Islamists and leftists can achieve more together than they can separately. In Great Britain, they jointly formed the Stop the War Coalition, whose steering committee includes representation from such organizations as the Communist party of Britain and the Muslim Association of Britain. Britain's Respect Party amalgamates radical international socialism with Islamist ideology. The two sides joined forces for the March 2008 European Parliament elections to offer common lists of candidates in France and Britain, disguised under party names that revealed little.

Immanuel Kant Versus Israel?

Old Kant man that I am, I have added a question mark to the title of an extremely interesting piece by Daniel Pipes.  In it, Pipes summarizes and comments upon an article by Yoram Hazony,  "Israel Through European Eyes."  Worth careful study.

The Aporetics of Artifacts: Puzzling Over Van Inwagen's Denial of Artifacts

This post is a sequel to Van Inwagen on the Ship of Theseus.  Peter van Inwagen, Material Beings (Cornell UP, 1990), p. 31, writes: 

The question 'In virtue of what do these n blocks compose this house of blocks?' is a question about n + 1 objects, one of them radically different from the others. But the question 'What could we do to get these n blocks to compose something? is a question about n rather similar objects. . . . . questions of the former sort turn our minds to various metaphysical and linguistic questions about the "special" n + 1st [read: n + 1th] object and our words for it: What are the identity conditions for houses of blocks?

Why does van Inwagen think that a house of blocks is an object radically different from the blocks that compose it? And why does he think that if there are, say, 1000 blocks, then in the place where the house is, there are 1001 objects? Not only do I find these notions repugnant to my philosophical sense, I suspect that it is their extremism that motivates van Inwagen to recoil from them and embrace something equally absurd, namely, that there are no such things as houses of blocks or inanimate concrete partite entities generally. 

In other words, if one begins by assuming that if a house of blocks, for example, is a whole of parts, then it is an object radically different from the objects that compose it, an object numerically additional to the objects that compose it; then, recoiling from these extreme positions, one will be tempted to embrace an equal but opposite extremism according to which there are no such inanimate partite entities as houses of blocks. What then should we say about a house of blocks?

First off, it is not identical to any one of its proper parts. Second, it is not identical to the mereological sum of its parts: the parts exist whether or not the house exists. From this it follows that there is a sense in which the house is 'something more' than its parts. But surely it is not an object "radically different" from, or numerically additional to, its proper parts. If there is a house of 1000 blocks in a place, there are not 1001 objects or entities in that place. After all, the house is composed of the blocks, and of nothing else.

So on the one hand the house is 'something more' than its constituent blocks, while on the other hand it is not a "radically different" object above and beyond them. Think of how absurd it would be for me to demand that you show me your house after you have shown me every part of it. "You've shown me every single part of your house, but where is the bloody house?"

The house, thought not identical to the blocks that compose it,  is not wholly diverse from the blocks that compose it .  The house is the blocks arranged housewise. The house is not the blocks, and the house is not some further entity "radically different" from the blocks. The house is just the blocks in a certain familiar arrangement. Should we conclude that the house exists or that it does not exist? I say it exists: the house is the blocks arranged housewise, and the existence of the house is the housewise unity of the blocks. Van Inwagen seems to think that there is no house, there are just the blocks. (Of course, he doesn't believe in the blocks either since they too are inanimate partite entities; but to keep the discussion simple, we may assume that the blocks are simples.)  

Now if it is allowed that the house exists, it seems clear that the house does not exist in the way the blocks do. But this does not strike me as a good reason for saying that the house does not exist at all. What is wrong with saying that the house is a dependent existent? And what is wrong with saying that about partite entities generally? They exist, but they do not exist in addition to their parts, but as the unity or connectedness of their parts. Saying this, we avoid van Inwagen's absurd thesis that inanimate partite entities do not exist. Of course, this commits me to saying that there are at least two modes of existence, a dependent mode and an independent mode. I suspect van Inwagen would find such a distinction incoherent. But that is a topic for a separate post.

The problem can be set forth as an aporetic pentad:

1. The house is not identical to the blocks that compose it.

2. The house is not wholly diverse from the blocks that compose it; it is not an object numerically additional to the blocks that compose it:  given that the house is composed of n blocks, the house itself is not an n + 1th object.

3. The house exists.

4. The constituent blocks exist.

5.  'Exists' is univocal as between wholes and parts: wholes and their parts exist in the same sense.

Each limb has a strong claim on our acceptance.  But they cannot all be true.  Any four of the propositions, taken together, entails the negation of the remaining one.  For example, if the first four are all true, then the fifth must be false.  To solve the problem, one of the limbs must be rejected.  But which one? 

To me it seems obvious that the first four are all true.  So I reject (5).  Rejecting (5), I can say that the house exists as the connectedness of the blocks.  Thus the mode of existence of the whole is different from the mode of existence of its simple parts.  But this solution requires us to believe in modes of existence, which is sure to inspire opposition among analytic philosophers.  Van Inwagen, if I understand him, denies (2) and (3) while accepting the others.

But van I's solution is just crazy, is it not?  Mine is less crazy.  But perhaps you, dear reader, have a better suggestion.

 

Three Things About Islam

This well-made YouTube video explains the central Islamic concepts of abrogation, Shari'a, and Taqiyya (deception). 

Which Islam Will Prevail in America?

Required reading.  Excerpts:

Most of the mosques and Islamic centers in our country are controlled, to a greater or lesser degree, by the Muslim Brotherhood and its satellites. The North American Islamic Trust (NAIT) was established in the early Seventies to buy up property for the establishment of American mosques and “Islamic centers,” the latter being what the Brotherhood calls “the axis” of the Islamist movement in America. [. . .]

The Kingdom and the Brotherhood have combined for a half-century to put American Muslim communities in a stranglehold. They proselytize a fundamentalist interpretation of Islam — an amalgam of Saudi Wahhabism and Brotherhood Salafism — that is virulently anti-Western. Its instruction to Muslims in the United States, Canada, and Europe is voluntary apartheid: Immigrate but don’t integrate, infiltrate but don’t assimilate. [. . .]

It is the Brotherhood’s objective to thread sharia through American law and culture. This mission drives imam Feisal Rauf’s [the guy behind the Ground Zero mosque provocation] work, as documented by the Center for Security Policy’s Christine Brim in an eye-popping report at Andrew Breitbart’s Big Peace website.

Hitch-22: A Memoir

Well-written but dripping with envy and pusillanimity, Terry Eagleton's review exemplifies the Left's hatred of apostasy.  Another similarity with Islamism.

Van Inwagen on the Ship of Theseus

Peter van Inwagen's Material Beings (Cornell UP, 1990) is a very strange book, but he is a brilliant man, so one can expect to learn something from it. A central claim is that artifacts such as tables and chairs and ships do not exist. One can appreciate  that if there are no ships then the ancient puzzle about identity known as the Ship of Theseus has a very quick (dis)solution. 

The Ship of Theseus is a puzzle about diachronic artifact identity. Here is one version. You have a ship, or a rowboat, or any object, composed entirely of wooden planks. You remove one of the planks and replace it with an aluminum plank of the same size. The wooden plank is placed in a warehouse. After this minor replacement, you have a ship and indeed numerically the same ship as the one you started with. It is not a numerically different ship. Now replace a second wooden plank with an aluminum plank, and place the second wooden plank in the warehouse. Again, the numerical identity of the original ship has been preserved. Continue the replacement process until all of the wooden planks have been replaced with aluminum planks. You now have a wholly aluminum ship that is presumably numerically identical to the original wholly wooden ship despite the fact that none of the original matter is to be found in the aluminum ship. After all, the aluminum ship 'grew out of' the original wooden ship by minor changes each of which is identity-preserving.

Now take the wooden planks from the warehouse and assemble them in the form of a ship and in such a way that the planks bear the same relations to one another as the planks in the original wooden ship bore to one another. You now have two ships, a wooden one and an aluminum one. The question is: which of these ships is identical to the original wooden one?

Suppose the two ships collide on the high seas, and suppose the captain of the original ship had taken a solemn vow to go down with his ship. Where does his duty lie? With the wooden ship or with the aluminum one? Is the original ship identical to the resultant aluminum ship? One will be tempted to say 'yes' since the aluminum ship 'grew out' of the original wooden ship by minor transformations each of which was identity-preserving. Or is the original ship identical to the wooden ship that resulted from the re-assembly of the wooden planks? After all, it consists of the original matter arranged in the original way. Since the resultant wooden and aluminum ships are numerically distinct, they cannot both be identical to the original ship.

Van Inwagen makes short work of the puzzle: "There are no ships, and hence there are no puzzles about the identities of ships." (128) One way van Inwagen supports this bizarre solution is by re-telling the story in language that does not make even apparent reference to ships. Here is his retelling:

Once upon a time, there were certain planks that were arranged shipwise. Call then the First Planks. . . . One of the First Planks was removed from the others and placed in a field. Then it was replaced by a new plank; that is, a carpenter caused the new plank and the remaining First Planks to be arranged shipwise, and in just such a way that the new plank was in contact with the same planks that the removed planks had been in contact with, and at exactly the same points. Call the planks that were then arranged shipwise the Second Planks. A plank that was both one of the First Planks and one of the Second Planks was removed from the others and placed in the field and replaced (according to the procedure laid down above), with the consequence that certain planks, the Third Planks, were arranged shipwise. Then a plank that was one of the First Planks and one of the Second Planks and one of the Third Planks . . . . This process was repeated till all the First Planks were in the field. Then the First Planks were caused to be arranged shipwise, and in just such a way that each of them was in contact with the same planks it had been in contact with when the First Planks had last been arranged shipwise, and was in contact with them at just the same points. (128-129)

If I understand what van Inwagen is claiming here, it is that there is nothing in the standard telling of the story, a version of which I presented above, that is not captured in his re-telling. But since there is no mention of any ships in the re-telling, no puzzle about ship-identity can arise. Perhaps van Inwagen's point could be put by saying that the puzzle about identity is an 'artifact' of a certain way of talking that can be paraphased away. Instead of talking about ships, we can talk about shipwise arrangements of planks. The planks do not then compose a ship, he thinks, and so there is no whole of which they are proper parts, and consequently no question about how this whole maintains its diachronic identity under replacement of its parts.

What are we to say about van Inwagen's dissolution of the puzzle? What I find dubious is van Inwagen's claim that ". . . at no time do two or more of these planks compose anything, and no plank is a proper part of anything." (129) This strikes me as plainly false. If the First Planks are arranged shipwise, then there is a distinction beween the First Planks and their shipwise arrangement. The latter is the whole ship and the former are its proper parts. So how can van Inwagen claim that the planks do not compose a ship? Van Inwagen seems to think that if the planks were parts of a whole, and there were n planks, then the whole would be an n + 1 th entity. Rejecting this extreme, he goes to the other extreme: there is no whole of parts. If there were ships, they would be wholes of parts, but there are no artifactual wholes of parts, so there are no ships. The idea seems to be that when we build an artifact like a ship we are not causing something new to come into existence; we are merely re-arranging what already exists. If so, then although a ship's planks exist, the ship does not exist. Consider what van Inwagen says on p. 35:

If I bring two cubes into contact so that the face of one is conterminous with the face of the other, have I thereby brought into existence a solid that is twice as long as it is wide? Or have I merely rearranged the furniture of the earth without adding to it?

Van Inwagen seems to be saying that when it comes to artifacts, there is only rearrangement, no 'addition to existence.' As a general thesis, this strikes me as false. A ship is more than its planks, and van Inwagen seems to concede as much with his talk of a shipwise arrangement of planks; but this shipwise arrangement brings something new into being, namely, a thing that has causal powers that its constituents do not have. For example, a boat made of metal planks properly arranged will float, while the planks themselves will not float.

How Far Does Religious Toleration Extend?

Suppose that there were a religion whose aim was to dominate the world and suppress every other religion.  Would we who value toleration be under any obligation to tolerate such a religion?  Of course not.  Toleration does not extend to the toleration of the intolerant.  Is there such a religion?  According to Farhad Khosrokhavar, Inside Jihadism: Understanding Jihadi Movements Worldwide (Paradigm 2009, p. 22):

In the twentieth century, one of the first to insist that Islam entails its imposition on humanity was Seyed Qutb, one of the modern forefathers of Jihadism . . . . He stated that Islam summons to worship no one else but Allah . . . . This implies the relentless fight against all idols until Allah's reign is set up on earth [ . . .]

The war on idolatry (taqut) is, in his interpretation, the most important part of Islam, taking precedence over the other principles. From this view, all of modernity is based on the worship of idols and, therefore, illegitimate, necessitating that Jihad wipe out its idolatrous tendencies. 

Jihad is not one of the five pillars of Islam.  But recent jihadists interpret the first pillar in a manner to require jihad.  "For them [recent jihadist intellectuals] the first Islamic pillar, the Unity of Allah (Tawhid) makes it compulsory for Muslims to wage the Jihad against infidels." (p. 21) 

I will be told that not all who identify as Muslims take this radical view.  True, but they are not the problem.  The Jihadists are the problem.  And we have reason to think that they represent the essence of Islam with the so-called 'moderates' being simply those who do not take the core message with full seriousness.  To the extent that Islam takes on Jihadist contours, to the extent that Islam entails its imposition on humanity, it cannot and ought not be tolerated by the West.  Indeed, no religion that attempts to suppress other religions can or ought to be  tolerated, including Christianity.  We in the West do, or at least should, believe that competition among religions in a free marketplace of ideas is a good thing. 

My own view is that no extant religion can legitimately claim to be the true religion; the true religion  has yet to be worked out.  In pursuit of that goal we need to make use of all available materials from all the best traditions.  Perhaps even Islam, as crude as it is, has something to teach us.

 

Hitchens' Hubris

Here.

Kierkegaard's Fear

Kierkegaard dreaded ending up the property and preserve of professional scholars. But who reads him apart from professors of philosophy, of religion, of divinity, of Danish literature, and their students? The professors read him for professional purposes, to make a living; the students also read him for professional purposes, to prepare for making a living. His works have become fodder for the career game, just as he feared. But there is something worse, as S. K. would be the first to point out, namely, a man's filling his belly from the fact that another man was crucified. The Kierkegaard scholar merely fills his belly from the fact that a man reflected lifelong on what it might mean to follow the one who was crucified.

Pope Benedict's Regensburg Speech and Muslim Oversensitivity

This is a slightly redacted version of a piece first posted on 18 September 2006 at the old PowerBlogs site.  I repost it not only to save it for my files, but also because it it important to remember not only the successful and unsuccessful acts of Islamist terrorism worldwide, but also the many incidents which betray the illiberal and anti-Enlightenment values of our Islamist opponents (e.g., the fatwa against Salman Rushdie, the Danish cartoon 'caper,' etc. etc. The analog to the fatwa would be the Pope putting a price on the head of Andres Serrano, the 'artist' famous notorious for his 'Piss Christ.') 

...............

People need to face the fact that Western civilization is under serious threat from militant Islamic fanaticism. (And it may be coming to a theater near you.) Yet another recent indication of the threat is the unreasoning umbrage taken by many in the Islamic world over a mere  QUOTATION Pope Benedict XVI employs in his address at the University of Regensburg entitled, "The Best of Greek Thought is an Integral Part of Christian Faith."

Benedict's talk is only tangentially about Islam; it is primarily about the role of reason in the posing and answering of the God question, and about whether Christianity should be dehellenized. The Pope begins by mentioning a dialogue "by the erudite Byzantine emperor Manuel II Paleologus and an educated Persian on the subject of Christianity and Islam, and the truth of both." Then comes the 'offending' passage (bolding added):

Dennis Miller Has Some Advice for Imam Rauf and Co.

In the war against radical Islam and its liberal-leftist enablers, all weapons must be deployed including humor and mockery. 

On a more serious note, here are two pieces you must read.  When Islam Abandoned Reason: A Conversation with Robert R. Reilly; Ayaan Hirsi Ali, How to Win the Clash of Civilizations

Google Chrome

I started using it yesterday.  It's faster but the display is not as pretty.  Must speed be purchased in the coin of a substandard display?

Christopher Hitchens on the Topic of Cancer

Here.  Via Malcolm Pollack.

Can Only the Mortalist Love?

From the mail: 

A friend of mine (a philosophy professor) and I were discussing issues of immortality, meaning, and love on Facebook. I explained to him that the love I feel for others in some sense 'seeks' immortality, as the depth of the feeling is such that without that belief, love would be almost too painful for me to bear. He expressed a diametrically opposed view, wherein love REQUIRES that we acknowledge the mortality of both the other and ourselves. This is, he said, because time is only a limited commodity and the time we spend with someone else is only valuable because there is a limited amount of it, and so spending time with someone is only really an act of love for the one for whom time is extremely limited.

 

Your friend seems to be maintaining that only a mortalist (one who maintains that bodily death spells the end of a person) can truly be said to love another person.  Your friend's argument seems to be this:

 

1. The time spent with the beloved is valuable only because it is limited; therefore,

 

2. One cannot love without acknowledging the mortality of both lover and beloved.

 

First of all, I would say that this is a non sequitur.  For even if we suppose that (1) is true, (2) is obviously false.  Gabriel Marcel did not acknowledge the mortality of himself or his wife, and yet he loved his wife.  (On this topic, Marcel is one of the people to read.)  Whether or not love is genuine cannot hinge on whether one is right or wrong about the mortalism/immortalism question.  It would be both churlish and absurd to say to Geach and Anscombe, "You two don't really love each other because you are immortalists!"

 

Your friend might respond by saying that the intensity of a love believed to be undying must be less than the intensity of a love believed to be as mortal as the lovers.  To this I have two responses.  First, the question of intensity is not the same as the question of whether the love is genuine.  The genuineness of love varies independently of its intensity.  Second, it is not obvious that a love believed to end with the lovers must be less intense. One could easily argue the opposite:  if I believe that my love cannot survive bodily death, then I am more likely to practice something like Buddhist nonattachment with respect to the beloved and with respect to my loving of the beloved in accordance with the 'truth' that all is impermanent and therefore  nothing is worthy of a full measure of commitment.  In other words, you could argue against your friend that it is precisely because love can conquer death that you value it as highly as you do, and that because he does not believe this, he ought to value it less.    You could say to him, "Look, if you believe that you and your love will soon pass away, then it is irrational of you to ascribe much value to yourself or your love. Impermanence does not intensify value; it argues lack of value!"

 

Saying this to your friend, you will not convince him ( I am quite sure of that!) but you will neutralize his argument and show that it is not compelling.  And that is about all one can accomplish in a philosophical discussion. But it is also all you need to accomplish to be able to show that your intuitions are rationally acceptable.

 

As for (1), it is arguably false, and for some of the same reasons I have just given.  If contact with the beloved ends utterly with death, then this could be taken to show that the contact was not so valuable  in the first place on the Platonic-Augustinian ground that impermanence argues (relative) unreality and unimportance.  I grant that this is not absolutely compelling, but it is as compelling as the opposite, namely, that impermanence increases value and importance.

 

I'm with you: love is a harbinger of Transcendence; it intimates of Elsewhere.  You won't be able to convince your friend of this, but don't let that bother you.  Any argument he can throw up, I can neutralize.

 

If you haven't read Augustine, you should.  I also recommend P. T. Geach, Truth. Love, and Immortality: An Introduction to McTaggart's Philosophy (University of California, 1979), esp. the last chapter.

Life's Parade

We need those who march in the parade, but we also  need those who merely observe and ask where it is going.

Infinity and Mathematics Education

A reader writes,

Regarding your post about Cantor, Morris Kline, and potentially vs. actually infinite sets: I was a math major in college, so I do know a little about math (unlike philosophy where I'm a rank newbie);
on the other hand, I didn't pursue math beyond my bachelor's degree so I don't claim to be an expert. However, I do know that we never used the terms "potentially infinite" vs. "actually infinite".

I am not surprised, but this indicates a problem with the way mathematics is taught: it is often taught in a manner that is both ahistorical and unphilosophical.  If one does not have at least a rough idea of the development of thought about infinity from Aristotle on, one cannot properly appreciate the seminal contribution of Georg Cantor (1845-1918), the creator of transfinite set theory.  Cantor sought to achieve an exact mathematics of the actually infinite.  But one cannot possibly understand the import of this project if one is unfamiliar with the distinction between potential and actual infinity and the controversies surrounding it. As it seems to me, a proper mathematical education at the college level must include:

1. Some serious attention to the history of the subject.

2. Some study of primary texts such as Euclid's Elements, David Hilbert's Foundations of Geometry, Richard Dedekind's Continuity and Irrational Numbers, Cantor's Contributions to the Founding of the Theory of Transfinite Numbers, etc.  Ideally, these would be studied in their original languages!

3. Some serious attention to the philosophical issues and controversies swirling around fundamental concepts such as set, limit, function, continuity, mathematical induction, etc.  Textbooks give the wrong impression: that there is more agreement than there is; that mathematical ideas spring forth ahistorically; that there is only one way of doing things (e.g., only one way of construction the naturals from sets); that all mathematicians agree.

Not that the foregoing ought to supplant a textbook-driven approach, but that the latter ought to be supplemented by the foregoing.  I am not advocating a 'Great Books' approach to mathematical study.

Given what I know of Cantor's work, is it possible that by "potentially infinite" Kline means "countably infinite", i.e., 1 to 1 with the natural numbers?

No! 

Such sets include the whole numbers and the rational numbers, all of which are "extensible" in the sense that you can put them into a 1 to 1 correspondence with the natural numbers; and given the Nth member, you can generate the N+1st member. The size of all such sets is the transfinite number "aleph null". The set of all real numbers, which includes the rationals and the irrationals, constitute a larger infinity denoted by the transfinite number C; it cannot be put into a 1 to 1 correspondence with the natural numbers, and hence is not generable in the same way as the rational numbers. This would seem to correspond to what Kline calls "actually infinite".

It is clear that you understand some of the basic ideas of transfinite set theory, but what you don't understand is that the distinction between the countably (denumerably) infinite and the uncountably (nondenumerably) infinite falls on the side of the actual infinite.  The countably infinite has nothing to do with the potentially infinite.  I suspect that you don't know this because your teachers taught you math in an ahistorical manner out of boring textbooks with no presentation of the philosophical issues surrounding the concept of infinity.    In so doing they took a lot of the excitement and wonder out of it.  So what did you learn?  You learned how to solve problems and pass tests.  But how much actual understanding did you come away with?

The Ground Zero Mosque: The Controversy Continues

And it seems to be heating up as the anniversary of 9/11 approaches.  I suspect dialogue with liberals on this topic is impossible due to what I call the 'two planets problem':  conservatives and liberals live on different planets.  You could cash out the metaphor by saying  that we differ radically in temperament, sense of life, values, and assumptions. But I am getting e-mail from decent and well-intentioned left-leaners who disagree with me about the GZM, so here goes one more time. 

Let's be clear about what the issue is.  To put it as crisply as possible, it is about propriety, not legality.  No one denies that Imam Rauf et al. have the legal right to build their structure on the land they have purchased.  The point is rather that the construction in that place is improper, unwise, provocative, insensitive, not conducive to comity.  To put it aphoristically, what one has a right to do is not always right to do.  But that is to put it too mildly:  the construction of a mosque on that hallowed ground is an outrage to the memories of those who died horrendous deaths on 9/11 because of the acts of Muslim terrorists, terrorists who didn't just happen to be Muslims, but whose terrorist deeds were a direct consequence of their Islamist beliefs. 

Now at this point you either get it or you don't.  A majority of the American people get it, but Obama doesn't.   Lacking the spine to address the real issue -- the issue of propriety, not legality -- he gave us a lecture on freedom of religion and the First Amendment.  Besides being b-o-r-i-n-g, his pathetic homily amounted to the logical fallacy of ignoratio elenchi.  This fallacy is committed when, mistaking the thesis your interlocutor is advancing, you respond to a distinct thesis that he is not advancing.  We who oppose the GZ mosque do not maintain that its construction is illegal; and because we do not maintain this, Obama and his leftist cohort commit ignoratio elenchi when they insist that it is legal.

Here again we note the 'two planets' problem.'  Leftists just cannot grasp what the issue is as conservatives see it.  Since they do not feel the impropriety of a mosque's being built near Ground Zero, they cannot believe that conservatives feel it either; and so they must interpret the conservative response in some sinister way: as an expression of xenophobia or 'Islamophobia' or nativism or a desire to strip Muslim citizens of their First Amendment rights. 

Supposedly, a major motive behind the construction is to advance interfaith dialogue, to build a bridge between the Muslim and non-Muslim communities.  But this reason is so patently bogus, so obviously insincere, that no intelligent person can credit it.  For it is a well-known fact that a majority of the American people vehemently oppose the GZM.  Given this fact, the construction cannot possibly achieve its stated end of advancing mutual understanding.  So if Rauf and Co. were sincere, they would move to another site.

Here is a little analogy.  Suppose you and I have a falling out, and then I make an attempt at conciliation. I extend my hand to you.  But you have no desire for reconciliation and you refuse to shake hands with me.  So I grab your hand and force you to shake hands with me.  Have I thereby patched things up with you?  Obviously not: I have made them worse.  Same with the GZM.  Once it became clear that the the American people opposed the GZM, Rauf and Co. either should have nixed the project or else had the cojones to say:  we have a legal right to build here and we will do so no matter what you say or how offended you are.

As it is, we have reason to suspect Rauf et al. of deception.

 

A Tea Party Manifesto

Here.  The authors, Dick Armey and Matt Kibbe, make it clear that fiscal responsibility and limited government are the central concerns of Tea Partiers.

The criteria for membership are straightforward: Stay true to principle even when it proves inconvenient, be assertive but respectful, add value and don't taking credit for other people's work. Our community is built on the Trader Principle: We associate by mutual consent, to further shared goals of restoring fiscal responsibility and constitutionally limited government. [. . .]

The big-government crowd is drawn to the compulsory nature of centralized authority. They can't imagine an undirected social order. Someone needs to be in charge—someone who knows better. Big government is audacious and conceited.

Note that the opposition is to big government, not to government as such.  This simple point needs to be repeated again and again in the teeth of liberal-left slander.

By definition, government is the means by which citizens are forced to do that which they would not do voluntarily. Like pay high taxes. Or redistribute tax dollars to bail out the broken, bloated pension systems of state government employees. Or purchase, by federal mandate, a government-defined health-insurance plan that is unaffordable, unnecessary or unwanted.

This is perhaps OK for a manifesto.  But surely government cannot be defined in this slanted way.    But the authors are right to point out the coercive nature of government.  They should have gone on to say that government and its coercion are necessary and legitimate when properly limited. 

For the left, and for today's Democratic Party, every solution to every perceived problem involves more government—top-down dictates from bureaucrats presumed to know better what you need. Tea partiers reject this nanny state philosophy of redistribution and control because it is bankrupting our country.

Spot on.  The main reason the Tea Partiers reject the liberal-left vision of an omnicompetent, omni-intrusive government is purely pragmatic: it is leading us to financial ruin.  This is reason enough to oppose the fiscal irresponsibility of both major parties.  We don't even need to get into the injustices of progressive taxation and redistributionism, and the  assault on individual liberty -- though these are powerful additional arguments. 

On Hitchens and Death

I just caught the last third of an interview of Christopher Hitchens by Charlie Rose.  He looks bad, the chemotherapy having done a nasty tonsorial number on him.  But his trademark intellectual incandescence appeared undiminished.  'Brilliant' is a word I don't toss around lightly, but Hitch is one to whom it unarguably applies. Public intellectuals of his caliber are rare and it will be sad to see him go.  Agree or disagree with him, it is discourse at his level that justifies the high regard we place on free speech.

In the teeth of death the man remains intransigent in his unbelief.  And why not?  He lived in unbelief and so it is only fitting that he should die in it as well.  He lived for this life alone; it is fitting that he should die without hope. As I read him, God and the soul were never Jamesian live options.  To cop out now as debility and death approach must appear to him to be utterly contemptible, a grasping for straws, a fooling himself into a palliative illusion to ease the horror of annihilation.

For what he takes to be the illusion of immortality, Hitch substitutes literary immortality.  "As an adult whose hopes lay assuredly in the intellect, not in the hereafter, he concluded, 'Literature, not scripture, sustains the mind and — since there is no other metaphor — also the soul.'" (Here) But to the clearheaded, literary immortality is little more than a joke, and itself an illusion.  Only a few read Hitch now, and soon enough he will be unread, his books remaindered, put into storage, forgotten.  This is a fate that awaits all scribblers but a tiny few.  And even they will drink the dust of oblivion in the fullness of time.

To live on in one's books is a paltry substitute for immortality, especially when one recalls Georg Christoph Lichtenberg's aphorism: Ein Buch ist ein Spiegel, aus dem kein Apostel herausgucken kann, wenn ein Affe hineinguckt. "A book is a mirror:  if an ape peers in, no apostle will look out."  Most readers are more apish than apostolic.

To live on in one's books is only marginally better than to live on in the flickering and mainly indifferent memories of a few friends and relatives. And how can reduction to the status of a merely intentional object count as living on?

The besetting sin of powerful intellects is pride.  Lucifer, as his name indicates, is or was the light-bearer.  Blinded by his own light, he could see nothing beyond himself.  Such is the peril of intellectual incandescence.  Otherworldly light simply can't get through.  One thinks of Nietzsche, Russell, Sartre, and to a lesser extent Hitchens.  A mortal man with a huge ego -- one which is soon to pop like an overinflated balloon.

The contemplation of death must be horrifying for those who pin all on the frail reed of the ego.  The dimming of the light, the loss of control, the feeling of helplessly and hopelessly slipping away into an abyss of nonbeing.  And all of this without the trust of the child who ceases his struggling to be borne by Another.  "Unless you become as little children, you cannot enter the kingdom of heaven."  But this of course is what the Luciferian intellect cannot do. It cannot relax, it must hold on and stay in control.  It must struggle helplessly as the ego implodes in upon itself.  The ego, having gone supernova, collapses into a black hole.  What we fear when we fear death is not  so much the destruction of the body, but the dissolution of the ego.  That is the true horror and evil of death.  And without religion you are going to have to take it straight.

Have you read Philip Larkin's Aubade?

What would Hitch lose by believing?  Of course, he can't bring himself to believe, it is not a Jamesian live option, but suppose he could.  Would he lose 'the truth'?  But nobody knows what the truth is about death and the hereafter.  People only think they do. Well, suppose 'the truth' is that we are nothing but complex physical systems slated for annihilation.  Why would knowing this 'truth' be a value?  Even if one is facing reality by believing that death is the utter end of the self, what is the good of facing reality in a situation in which one is but a material system? 

If materialism is true, then I think Nietzsche is right: truth is not a value; life-enhancing illusions are to be preferred.  If truth is out of all relation to human flourishing, why should we value it?

Islam's Role in the Etiology of Terrorism

WARNING:  Free speech and political incorrectness  up ahead!

Our man on the ground in Afghanistan, Spencer Case, writes:

Here at Forward Operating Base Thunder, the captain has recently returned from leave, bringing with him his propensity for political debate. One hot subject in the office, the Ground Zero mosque, has led to a genuine philosophical question which I’d like to see you take up. The question is this: at what point is it appropriate to credit/blame an “-ism” for the deeds/misdeeds of professed adherents?

To me it seems perfectly correct to say that Islam causes terrorism, that 9/11 was an Islamic attack, and that Islam as an overarching worldview is responsible for certain evils. The captain thinks 9/11 was simply a crazy or evil attack. The fact that the attackers happened to be Muslim, rather than Christian, Buddhist, Communist or what-have-you is purely accidental (Allahu Akbar! notwithstanding).

First of all, the 9/11 hijackers were not 'crazy' or insane or irrational.  They displayed a high degree of instrumental rationality in planning and carrying out their mission.  It is a big mistake to think that evil actions are eo ipso crazy actions.  People who say or suggest this (typically liberals) simply do not take evil seriously or the free will that makes it possible.  They think that people who commit mass murder must be out of their minds.  No! Mass murder can be an entirely rational means for the furtherance of one's (evil) goals.  The 9/11 terrorists knew exactly what they were doing, did it deliberately and freely and consciously and rationally (in terms of instrumental rationality), and they dealt us a severe blow from which we are still reeling.  It is also a mistake to call Muhammad Atta and the boys 'cowards' as Bill O'Reilly and others have done.  On the contrary!  They displayed great courage in carrying out their evil deeds.  The fact that courage is a virtue is consistent with an exercise of courage having an evil upshot.

And your captain is certainly wrong if he thinks that it is an accidental fact about the 9/11 hijackers that they are Muslims.  Intentional actions derive from and reflect beliefs.  People do not act  in a doxastic vacuum.  And what they believe cannot help but influence their actions. A convinced pacifist is highly unlikely to be a suicide bomber.  Compare the number of Buddhist terrorists to the number of Muslim terrorists.  There are many more of the latter than of the former, to put it in the form of an understatement.   Obviously, the content of Buddhist/Muslim beliefs plays an important role in the etiology of pacifist/terrorist acts.

Don't Mess With Texas: After 9th DWI, Texas Man Gets Life

News accounts like this one give me hope that there is still some common sense left  in this crazy country dominated as it is by the politically correct.  The sentence is just.  Think about it.  This is the miscreant's 9th conviction.  The road to conviction is long.  First there must be an apprehension, then a trial, then a conviction.  How many times was this dude tried without being convicted?  How many times did he drive drunk without being caught? Perhaps hundreds. 

Kline on Cantor on the Square Root of 2

Morris Kline, Mathematics: The Loss of Certainty, Oxford 1980, p. 200:

. . . when Cantor introduced actually infinite sets, he had to advance his creation against conceptions held by the greatest mathematicians of the past. He argued that the potentially infinite in fact depends on a logically prior actually infinite. He also gave the argument that the irrational numbers, such as the square root of 2, when expressed as decimals involved actually infinite sets because any finite decimal could only be an approximation.

Here may be one answer to the question that got me going on this series of posts. The question was whether one could prove the existence of actually infinite sets. Note, however, that Kline's talk of actually infinite sets is pleonastic since an infinite set cannot be anything other than actually infinite as I have already explained more than once.  Pleonasm, however, is but a peccadillo. But let me explain it once more.  A potentially infinite set would be a set whose membership is finite but subject to increase.  But by the Axiom of Extensionality, a set is determined by its membership: two sets are the same iff their members are the same.  It follows that a set cannot gain or lose members.  Since no set can increase its membership, while a potentially infinite totality can, it follows that that there are no potentially infinite sets.  Kline therefore blunders when he writes,

However, most mathematicians -- Galileo, Leibniz, Cauchy, Gauss, and others -- were clear about the the distinction between a potentially infinite set and an actually infinite one and rejected consideration of the latter. (p. 220)

Kline is being sloppy in his use of 'set.'  Now to the main point.  Suppose you have a right triangle. If two of the sides are one unit in length, then, by the theorem of Pythagoras, the length of the hypotenuse is the sqr rt of 2 = 1.4142136. . . . Despite the nonterminating decimal expansion, the length of the hypotenuse is perfectly definite, perfectly determinate. If the points in the line segment that constitutes the hypotenuse did not form an infinite set, then how could the length of the hypotenuse be perfectly definite? This is not an argument, of course, but a gesture in the direction of a possible argument.

If someone can put the argument rigorously, have at it.

Does Potential Infinity Rule Out Mathematical Induction?

In an earlier thread David Brightly states that "The position on potential infinity that he [BV] is defending is equivalent to the denial of the principle of mathematical induction."  Well, let's see.

1.  To avoid lupine controversy over 'potential' and 'actual,' let us see if we can avoid these words.  And to keep it simple, let's confine ourselves to the natural numbers (0 plus the positive integers).  The issue is whether or not the naturals form a set.  I hope it is clear that if the naturals form a set, that set will not have a finite cardinality!  Were someone to claim that there are 463 natural numbers, he would not be mistaken so much as completely clueless as to the very sense of 'natural number.'  But from the fact that there is no finite number which is the number of natural numbers, it does not follow that there is a set of natural numbers.

2.  So the dispute is between the Platonists -- to give them a name -- who claim that the naturals form a set and the Aristotelians -- to give them a name -- who claim that the naturals do not form a set.  Both hold of course that the naturals are in some sense infinite since both deny that the number of naturals is finite.  But whereas the Platonists claim that the infinity of naturals is completed, the Aristotelians claim that it is incomplete.  To put it another way, the Platonists -- good Cantorians that they are -- claim that  the naturals, though infinite,  are a definite totality whereas the Aristoteleans claim that the naturals are infinite in the sense of indefinite.  The Platonists are claiming that there are definite infinities, finite infinities -- which has an oxymoronic ring to it.  The Aristotelians stick closer to ordinary language.  To illustrate, consider the odds and evens.  For the Platonists, they are infinite disjoint subsets of the naturals.  Their being disjoint from each other and non-identical to their superset shows that for the Platonists there are definite infinities.

3.  Suppose 0 has a property P.  Suppose further that if some arbitrary natural number n has P, then n + 1 has P.  From these two premises one concludes by mathematical induction that all n have P.  For example, we know that 0 has a successor, and we know that if  arbitrary n has a successor, then n +1 has a successor.  From these premises we conclude by mathematical induction that all n have a successor.

4.  Brightly claims in effect that to champion the Aristotelean position is to deny mathematical induction.  But I don't see it.  Note that 'all' can be taken either distributively or collectively.  It is entirely natural to read 'all n have a successor' as 'each n has a successor' or 'any n has a successor.'  These distributivist readings do not commit us to the existence of a set of naturals.  Thus we needn't take 'all n have a successor' to mean that the set of naturals is such that each member of it has a successor.

5. Brightly writes, "My understanding of 'there is' and 'for all' requires a pre-existing domain of objects, which is why, perhaps, I have to think of the natural numbers as forming a set."  Suppose that the human race will never come to an end.  Then we can say, truly, 'For every generation, there will be a successor generation.'  But it doesn't follow that there is a set of all these generations, most of which have not yet come into existence.  Now if, in this example, the universal quantification does not require an actually infinite set as its domain, why is there a need for an actually infinite set  as the domain for the universal quantification, 'Each n has a successor'?

6.  When we say that each human generation has a successor, we do not mean that each generation now has a successor; so why must we mean by 'every n has a successor' that each n now has a successor?  We could mean that each n is such that a successor for it can be constructed or computed.  And wouldn't that be enough to justify mathematical induction?

Addendum 8/15/2010  11:45 AM.  I see that I forgot to activate Comments before posting last night.  They are on now. 

It occurred to me this morning that  I might be able to turn the tables on Brightly by arguing that actual infinity poses a problem for mathematical induction.  If  the naturals are actually infinite, then each of them enjoys a splendid Platonic preexistence vis-a-vis our computational activities.  They are all 'out there' in Plato's heaven/Cantor's paradise.  Now consider some stretch of the natural number series so far out that it will never be reached by any computational process before the Big Crunch or the Gnab Gib, or whatever brings the whole shootin' match crashing down.  How do we know that the naturals don't get crazy way out there?   How can we be sure that the inductive conclusion For all n, P(n) holds?  Ex hypothesi, no constructive procedure can reach out that far.  So if the numbers exist out there, but we cannot reach them by computation, how do we know they behave themselves, i.e. behave as they behave closer to home?  This won't be a problem for the constructivist, but it appears to be a problem for the Platonist.

On Strictu Dictu and Holus Bolus

If memory serves, I picked up strictu dictu from an article by the philosopher C. B. Martin. It struck me as a bit odd, but having found it in use by other good writers, I started using it myself. Using it, I am in good company. But classicist Mike Gilleland, who knows Latin much, much better than I do, considers it not a proper Latin phrase at all. See An Odd Use of the Second Supine and More on Strictu Dictu.

So I am inclined to drop strictu dictu. I should take the advice I myself give in On Throwing Latin ( a most excellent post that I cannot at the moment locate). I do strive to practice what I preach. But I will continue to pepper my prose with the unexceptionable mirabile dictu, horribile dictu, difficile dictu, and the like, ceteris paribus of course. And I will not apologize for my use of 'big words' such as ambisinistrous, animadversion, preternatural, desueteude, incarnadine, inconcinnity, unexceptionable, et cetera.   Am I writing for a pack of idiots?

"Why not forget the foreign ornamentation and just say what you want to say clearly and simply and in plain English?"

Well, sometimes I do exactly that. But I refuse to be bound by any one style of writing, or to pander to the appallingly limited vocabularies of my fellow citizens. George Orwell and others who reacted against the serpentine and baroque sentences of their Victorian fathers and grandfathers went too far in the opposite direction.  And now look what we have.  For a poke at Orwell, see here.  Zinnser I criticize here and here.   

It just now occurs to me that it wasn't strictu dictu that I picked up from C. B. Martin but holus bolus.  Holy moly, that too looks like bogus Latin. Perhaps the estimable Dr. Gilleland will render his verdict on this construction as well.

My Angelic Wife

One indicator of her angelicity is her support of my chess activities -- in stark contrast to the wives of two acquaintances both of whose 'better' halves destroyed their chess libraries in fits of rage at time spent sporting with Caissa. "Hell hath no fury like a woman scorned," wrote old Will.

I'm no bard, but here's my ditty in remembrance of my two long lost Ohio chess friends:

   Forget that bitch
   And dally with me.
   Else I'll decimate
   Your library.

Innumeracy in the Check-Out Line

The Sarah Lee frozen pies were on sale, three for $10, at the local supermarket. I bought two, but they rang up as $4.99 each. I pointed out to the check-out girl that this was wrong, and she sent a 'gofer' to confirm my claim. Right I was. But now the lass was perplexed, having to input the correct amount by hand and brain. She had to ask me what 10 divided by 3 is. I was nice, not rude, and just gave her the answer sparing her any commentary.

(It's a crappy job, standing up eight hours per day, in a confined space, an appendage of a machine. I make a point of trying to relate to the attendants, male and female, as persons, at the back of my mind recalling a passage in Martin Buber's I-Thou in which he says such a relation is possible even in the heat of a commute between passenger and bus driver.)

But now I can be peevish. They learn how to put on condoms in these liberal-run schools but not how to add, subtract, multiply and divide? And how many times have I encountered pretty young things in bars and restaurants who are clueless when it comes to weights and measures?  At a P. F. Chang's the other day I asked whether the beer I wanted to order was 22 oz.  The girl said it was a pint, "whatever that is." This was near Arizona State and it is a good bet that she was a student there.  How can such people not know that there are two pints in a quart, that a pint is 16 fluid ounces, that four quarts make a gallon , . . . , that a light-year is a measure of distance not of time, . . . .

Can we blame this one on libruls too?  You betcha!  A librul is one who has never met a standard he didn't want to undermine.

You many enjoy John Allen Paulos, Innumeracy.  In case it isn't obvious, innumeracy is the mathematical counterpart of illiteracy.

Doron Zeilberger's Ultrafinitism

This is wild stuff; I cannot say whether it is mathematically respectable but the man does teach at Rutgers.  It is certainly not mainstream.  Excerpt:

It is utter nonsense to say that sqrt 2

 is irrational, because this presupposes that it exists, as a number or distance. The truth is that there is no such number or distance. What does exist is the symbol, which is just shorthand for an ideal object x that satisfies x² = 2.

Now what the hell does that mean? A rational number is one that can be expressed as a fraction a/b where both a and b are integers and b is not 0. An irrational number is one that cannot be expressed in this way.  By the celebrated theorem of Pythagoras, a right triangle with sides of 1 unit in length will have an hypotenuse with length = the square root of 2.  This is an irrational number.  But this irrational number measures a quite definite length both in the physical world and in the ideal world.  How can this number not exist?  It is inept to speak of a symbol as shorthand for an ideal object since, if x is shorthand for y, then both are linguistic items.  For example 'POTUS' is shorthand for 'president of the United States.'  But 'POTUS' is not shorthand for Obama.  'POTUS' refers to Obama.  Zeilberger appears to be falling into use/mention confusion.  If the symbol for the sqrt of 2 refers to an ideal object, then said object is a number that does exist.  And in that case Zeilberger is contradicting himself.

What's more, it seems that from Zeilberger's own example one can squeeze out an argument for actual infinity.  We note first that the decimal expansion of the the sqrt of 2 is nonterminating:  1.4142136 . . . .  We note second that the length of the hypotenuse is quite definite and determinate.  This seems to suggest that the decimal expansion must be actually infinite.  Otherwise, how could the length of the hypotenuse be definite?

As an ultrafinitist, however, Zeilberger denies both actual and potential infinity:

. . . the philosophy that I am advocating here is called

ultrafinitism. If I understand it correctly, the ultrafinitists deny the existence of any infinite, not [sic] even the potential infinity, but their motivation is `naturalistic', i.e. they believe in a `fade-out' phenomenon when you keep counting. [. . .]

So I deny even the existence of the Peano axiom that every integer has a successor.

As I said, this is wild stuff.  He may be competent as a mathematician; I am not competent to pronounce upon that question.  But he appears to be an inept philosopher of mathematics.  But this is not surprising.  It is not unusual for competent scientists and mathematicians to be incapable of talking coherently about what they are doing when they pursue their subjects.  Poking around his website, I find more ranting and raving than serious argument.

The ComBox is open if someone can clue us into the mysteries of ultrafinitism.  There is also some finitist Russian cat, a Soviet dissident to boot, name of Esenin-Volpin, who Michael Dummett refers to in his essay on Wang's Paradox, but Dummett provides no reference.  Is ultrafinitism the same as strict finitism?