I have lost about a half dozen. How about you? I am interested in your stories, but even more in your analysis.
Austin Ruse bemoans friendships lost. His piece ends:
Maybe my friend is right. Maybe we can’t be friends right now, maybe never. For me, though, that would be unspeakably sad. Message to my old pal: my door is always open.
Unspeakably sad? I see things differently. People who lost their minds over Trump, people too stupid to see past the man's obnoxious style and credit his ideas and numerous positive accomplishments; people who refused to see Biden for what he is, a fraud, a phony, a brazen liar, an empty suit rooted in no principle, morally corrupt, physically feeble, and non compos mentis; people who donned useless masks out of ovine fear, people who went along, to get along, with wokery and trans-delusionality and the celebration of thugs and criminals and every manner of loser -- such people were never worthy of my friendship in the first place. They were false friends from the start and I am glad circumstances made them show their true colors. Good riddance!
Some say Trump is the Great Divider. Nonsense. He is the Great Clarifier.
"If RFK [Jr.] goes third party, it would be doomsday for Democrats. It could bring Donald Trump back to the White House. And if that happens, Democrats [will] have only themselves to blame for their idiotic, authoritarian policies on everything from vaccine mandates to drag queen story hours to transgender athletes bullying girls."
What makes a pair of shoes a pair and not just two physical artifacts? Nominalist answer: nothing in reality. Our resident nominalist tells us that it is our use of 'a pair' that imports a unity, conventional and linguistic in nature, a unity that does not exist in reality apart from our conventional importation. We are being told that out there in the world there are no ones-in-many, let alone any ones-over-many. If that is right, then there are no sets. For a set is a one-over-many in this sense: it is one item distinct from its many members. (Let's not worry about the null set, which has no members and unit-sets or singletons which have exactly one member each. Here lies yet another rich source of aporiai, but one problem at a time.)
If there are no sets, then there are neither finite sets nor infinite sets. There are just pluralities, and all grouping, collecting, subsuming under common rubrics, unifying, etc. is done in language by language-users. What I will try to show is that if you think carefully about all of this you will have to make distinctions that are inconsistent with nominalism.
My aim is purely negative: to show that the nominalism of the resident nominalist is untenable. If you have read a good amount of what I have written you will recall that I am a solubility skeptic, which in this instance means that I am not endorsing any realist solution of the problem. I am not pushing an opposing theory.
I will start with some data that I find 'Moorean,' i.e., rationally indisputable and pre-theoretical. (Unfortunately, one man's datum is another man's theory.) The phrase 'a pair' has a sense that remains the same over time and space, a sense that is the same for all competent speakers of English whether here or abroad. The same holds for ein Paar in German, and similarly for all languages. The sense or meaning of an expression, whether word, phrase, sentence, etc. must be distinguished from the expression. An expression is something physical and thus sensible. The sensible is that which is able to be sensed via one of our senses. I hear the sound that conveys to me the meaning of 'cat,' say, or I see the marks on paper. Hearing and seeing are outer senses that somehow inform us or, more cautiously, purport to inform us of the existence and properties of physical or material things that exist whether or not we perceive them. But I don't hear or see the meaning conveyed to me by your utterance of a sentence such 'The cats are asleep.' The sentence, being a physical particular, is sensible; the meaning is intelligible. That's just Latin for understandable. I hear the words you speak, and if all goes well, I understand their meaning or sense, thereby understanding the proposition you intend to convey to me, namely, that the cats are asleep. Note that while one can trip over sleeping cats, one cannot trip over that the cats are asleep.
There are two distinctions implicit in the above that need to be set forth clearly. I argue that neither is compatible with nominalism
A. The distinction between the sense/meaning of a linguistic expression and the expression. Why must we make this distinction? (a) Because the same sense can be expressed at different times by the same person using the same expression. (b) Because the same sense can be expressed at the same and at different times by different people using the same expression. (c) Because the same sense can be expressed in different languages using different expressions by the same and different people at the same and at different times. For example the following sentences express, or rather can be used to express, the same sense (meaning, proposition):
The cat is black. Il gatto è nero. Die Katze ist schwarz. Kedi siyah. Kočka je černá.
So the sense of a word or phrase or sentence is a one-in-many in that each tokening of the word or phrase expresses numerically the same sense. A tokening, by definition, is the production of a token, in this case, a linguistic token. One way a speaker can produce such a token is by uttering the word or phrase in question. Another way is by writing the word or phrase down on a piece of paper. (There are numerous other ways as well.) This production of tokens therefore presupposes a further distinction:
B. The distinction between linguistic types and linguistic tokens. In the following array, how many words are there?
cat cat cat
Three or one? Is the same word depicted three times? Or are there three words? Either answer is as good as the other but they contradict each other. So we need to make a distinction: there are three tokens of the same type. We are forced by elementary exegesis of the data to make the type-token distinction. If you don't make it, then you will not be able to answer my simple question: three words or one?
You see (using the optical transducers in your head, and not by any visio intellectualis) the three tokens. And note that the tokens you now see are not the tokens I saw when I wrote this entry. Those were different tokens of the same type, tokens which, at the time of your reading are wholly past. Linguistic tokens are in time, and in space, which is not obviously the case for linguistic types. I said: not obviously the case, not: obviously not the case. You see the three tokens, but do you see the type of which they are the tokens? If you do, then you have powers I lack. And yet the tokens are tokens of a type. No type, no tokens. So types exist. How will our nominalist accommodate them? He cannot reduce types to sets of tokens since he eschews sets. No sets, no sets of linguistic tokens. Linguistic types are multiply instantiable. That makes them universals. But no nominalist accepts universals. Nominalists hold that everything is a particular. I grant that the rejection of sets and the rejection of universals are different rejections. But if one rejects sets because they are abstract objects, one ought also to reject universals for the same reason.
Now glance back at the first array. What we have there are five different sentence tokens from five different languages. Each is both token - and type-distinct from the other four.
To conclude, I present our nominalist with two challenges. The first is to give a nominalist account of linguistic types without either reducing them to sets or treating them as ones-in-many or ones-over-many. The second challenge is to explain the distinction between the sense or meaning of an expression, which is not physical/material and the expression which is.
Suppose he responds to the second challenge by embracing conceptualism according to which meanings are mental. Conceptualism is concept-nominalism, as D. M. Armstrong has maintained. My counterargument would be that the meaning/sense expressed by a tokening of 'The cats are asleep' is objectively either true or false, and thus either true or false for all of us, not just for the speaker. Sentential meanings are not private mental contents. Fregean Gedanken, for example, are not dependent for their existence or truth-value on languages or language-users.
A contender for the greatest, tightest band of the '60s, featuring Mike Bloomfield on guitar, my second guitar hero. I saw him play at the Monterey Pop Festival in '67. The Jewish kid from an affluent Chicago suburb exemplifies cultural appropriation at its finest. His riffs derive from B. B. King but he outplays the King of the Blues. Is that a racist thing to say? It can't be racist if it's true.
From Dylan's Down in the Groove album, Ugliest Girl in the World. From racism to sexism. But it can't be sexist if it's true. For any X, it can't be X-ist if it is true. Is it speciesist to say that man is the crown of creation, or to prefer human beings to robots? Humanity first!
Refreshingly realistic but also deeply troubling. I fear the author is right. Conservatives lost the culture war and so now:
Conservatives do not have a viable path to political power any other way. The issues of national survival are of primary importance. There is no point in fighting a culture war if we don’t have a country in which this war can take place. [. . .]
Trying to rehash these old battles in the present political moment, when institutional Christianity no longer has any meaningful political or cultural clout, is a waste of time—at least at the national level.
COVID-19 made the weakness of American Christianity painfully clear. Protestant and Catholic churches alike overwhelmingly declared themselves nonessential during the spring of 2020. That was, sadly, merely an acknowledgement of a longstanding reality.
Virtually no one today cares what the pope or any megachurch pastor, for that matter, has to say about political and cultural life. Their endorsements do not move the needle and their influence has had little to no bearing, even on their own flocks, when it comes to preserving the older standards of Christian morality and decency.
[. . .]
We live in a country where the president says it is antisemitic to ban trans surgery for minors. And yet you will strain yourself trying to hear any priest or pastor say a word in response. Millions of Americans are hurting, desperately confused about their very identity and sexual impulses, and the leaders of the churches have almost nothing to say. Nonessential workers indeed.
[. . .]
One wonders what purpose, at this point, the differentiation between denominations even serves. Pope Francis, just like John MacArthur, agrees with the leftist view of racism. And Tim Keller, just like Pope Francis, lauds mass immigration. On the most prominent liberal issues of our day there is total agreement among the leaders of the West’s supposedly different Christian denominations.
America has a moral majority, all right. It’s just liberal. The Left controls every institutional power center in America. Wall Street, the media, the universities, Hollywood, the military—you name it—everywhere the liberal consensus reigns supreme. There is not a single Fortune 500 company in America, not one, that would denounce transgender surgery for minors.
Those institutions shape the public consciousness in a way social conservatives simply cannot. Manufactured consent is real and all around us. A large portion of Americans simply accept whatever their televisions and cellphones tell them to believe no matter how perverted, wrong, or harmful. Even many of those who do not agree with it, at least bow to the moral consensus. Think of all those many millions who got vaccinated, not because they wanted to, but because their “job required it” or because they couldn’t “travel without it.”
The idea that large numbers of Americans are going to “wake up” and “push back” is simply a cope. That’s not how popular opinion works. The idea that Americans are going to see transgenderism as a bridge too far is, I think, much overhyped. I remember the gay marriage “debates,” such as they were. I remember Prop 8 passing in 2008 in California. I also remember how none of these setbacks for the Left ultimately had any bearing in the end. By 2015, gay marriage was the law of the land. Today it is untouchable liberal orthodoxy supported by a majority of Americans, including large numbers of “conservatives.”
Deploying more 10,000-word essays on teleology and the new natural law isn’t going to solve the social issue problem either. Millions of Americans didn’t start shoving dildos in orifices, guzzling sex change hormones, and consuming billions of hours of pornography a year because they read an article or heard an argument. These sexual and social perversions spring from a much deeper source, one that isn’t going to be solved by policy wrangling in D.C. think tanks.
The spiritual crisis that afflicts the West runs far deeper than most social conservatives want to admit. They don’t understand how bad things really are, which is why they stand around, mouths agape, as they try to figure out what a “furry” is or why U.S. military officers dress up in leather “pup play” fetish gear while they sodomize each other in uniform and then post photos to social media.
In light of our ongoing moral and spiritual crisis, I fully expect that the Bud Light/Dylan Mulvaney controversy is merely a blip that will soon pass. In the 1990s Ikea ran the world’s first commercial featuring a gay couple. In 2022, Ikea was valued at $17 billion. Go woke, go broke?
Sure.
The Matt Walsh’s of the world won’t want to hear this, but trying to fight the Left on gender with desiccated Socratic arguments (“What is a woman?”) is a losing battle. Owning liberals with facts and logic is mostly a waste of time.Political power doesn’t flow from scoring debate points in the “free marketplace of ideas.” It comes from the willingness to impose one’s beliefs on others and possessing the resources to do so.
All morality requires enforcement.
The Left implicitly understands that point. They are more than happy to crush their opponents. Just ask Donald Trump, John Eastman, Douglas Mackey, or any of the January 6 defendants. Strip away civilization and politics boils down to the distinction between friend and enemies. [You need a reference to Carl Schmitt here, son.] That’s why the White House hosted a trans day of visibility just two days after a transgender terrorist murdered six Christians in Tennessee.
At some point, every political regime must put its foot down. Some people think cannibalism is wrong, others think that it is right. If the former are to prevail politically they must be willing to use force against the latter. In the end, this is what morality requires. This is what morality is.
BV: The sound point here is that morality is just a lot of impotent prescriptions and proscriptions without an enforcement mechanism. But that is not to say that might makes right. If the enforcer is to enforce good and not evil, then the enforcer must either be God or, here below, godly men and governments.
Conservatives and Christians today simply lack the force of will to impose their social morality on the Left. That is why they lose cultural battles and the Left wins. Conservatives aren’t even willing to mock their enemies. If you want to make “respectable” social conservatives and Christians uncomfortable, call a prostitute a “whore” in their presence. Mock OnlyFans as a den of “sluts.” Express deep revulsion at sodomy. Watch them writhe in psychic pain.
Such firm moral condemnation, I am frequently told, is “judge-y” and “un-Christian.” “We” need to “watch our tone” as “we” seek to “draw others to the faith.” As their flock comes under attack from wolves, the shepherds condemn those who would fight back. There are many such cases.
The deep-rooted weakness of the American Christian Right is a serious problem. I wish it wasn’t this way. I wish my fellow Christians had more spirit. I wish our leaders would lead. That isn’t the reality we have, though, as much as I may wish otherwise.
Right now, conservatives in deep red areas can still fight cultural battles at the local and state levels. Even some purple states, at the local level, still provide a way to maneuver against the Left’s cultural hegemony. Everywhere else, and at the national level especially, conservatives must sideline the cultural battles in favor of the issues of national survival.
Trump showed that even in our degraded moral culture, a huge percentage of Americans still want the nation to survive. They don’t hate themselves despite all the propaganda to which they’ve been subjected. The old pre-World War II conservative consensus in favor of protectionism, non-intervention, and immigration restrictions is still enormously popular.
If we win on those fronts and secure a future for our country then, and only then, will we have a chance to fight once again for the family, for our faith, and for a return of moral decency.
That day, however, is still a long way off. We have work to do.
Why present evidence for something so obvious? Because there are a few 'liberals' whose thinking is not entirely emotion-driven and are therefore open to persuasion.
One day, well over 40 years ago, I was deeply tormented by a swarm of negative thoughts and feelings that had arisen because of a dispute with a certain person. Pacing around my apartment, I suddenly, without any forethought, raised my hands toward the ceiling and said, "Release me!" It was a wholly spontaneous cri de coeur, a prayer if you will, but not intended as such. I emphasize that it was wholly unpremeditated. As soon as I had said the words and made the gesture, a wonderful peace descended upon my mind, and the flood of negativity vanished. I became as calm as a Stoic sage.
I wrote recently that the only way out is through, but Malcolm Pollack's most recent offering is much better; it is indeed brilliant. It divides into three parts. There is first a litany of what ails us. The second part explains why the ills listed are upon us. The general answer is that
. . . an aggressive, secular pseudo-religion, which denies all transcendent order and natural categories, has seized control of the minds of scores of millions of Americans, and of the levers of political power and information dissemination. This ersatz religion holds as its highest principle the flattening of every natural distinction, and all social hierarchies, except of course the hierarchy that places itself in the position of commanding power over every institution, and over all of civil society.
This general answer is then fleshed out with a list of the specific truths that the secular pseudo-religion brands as heresy.
The third part of the essay raises the question of what we can do about the miasmic mess we are in. Pollack rejects as hopeless three ways out that quite naturally suggest themselves: voting, a return to federalism, and armed revolt.
And then comes the startling suggestion:
Perhaps, then, it is best in the long run not to slow this process by incremental and ineffective political resistance. It may be that such an approach, by making the decay more gradual, will also make it somehow more bearable, day by day, and might turn it from an acute and intolerable affliction to a slow and chronic decline — a creeping Brazilification, a great national frog-boiling. Perhaps we would be wiser simply to let the cleansing fire of fever run its course, and burn itself out. It will be painful, and surely debilitating for a while, but then it will be over. And then, at last, we can awaken, blink our eyes, and get back on our feet.
Another term for the Big Guy might be all it takes. Four more years!!
In sum, the only way out is through, and the best way through is pedal-to-the-metal, balls-to-the-wall, lets-go-Brandon! Let Biden finish the job, as he intends to do, and thereby finish us off. After an ignominious death, resurrection, a new Phoenix from the old ashes.
Might I suggest an historical parallel? Germany gone mad had to be destroyed before it could be rebuilt into sanity. It is perhaps a good thing that Hitler, drunk on his initial success, and consumed with hubris, overextended himself, thereby bringing to an end National Socialist totalitarianism. And so it may also be a good thing to allow the totalitarian-globalist-'woke'- race-delusional-culturally Marxist scum now in control of our once-great Republic to bring her to her knees where she will repent, suffer, and die to be reborn.
Nominalists say that the conception of an actual infinity of natural numbers depends on there being a set of all such numbers. But Ockhamists do not believe in sets. They say that the term ‘a pair of shoes’ is a collective noun which deceives by the singular expression ‘a pair’. Deceives, because it means no more than ‘two shoes’, and if there is only a pair of shoes, then there are only two things. But if a ‘pair’ of two things is a single thing, there are three things, the two things and the pair. Ergo etc.
I agree that there cannot be an actual infinity of natural numbers unless there is a (mathematical as opposed to commonsense) set of all such numbers. But of course this holds for all numbers, rational, irrational, transcendental, etc. Indeed, it holds for any category of item that is actually infinite. If there is an actual infinity of propositions, for example, then there must be a set of all propositions. I would point out however that there is nothing nominalistic about our friend's opening remark.
Nominalism kicks in with the claim that there are no sets. What there are are plural referring devices such as 'a pair of shoes' which fools us into thinking that in reality, i.e., extralinguistically, there are three things, a left shoe, a right shoe, and the pair, when there are only two things, the two shoes. The same goes for the following seemingly singular but really plural phrases: a gaggle of geese, a pride of lions, a parliament of owls, a coven of witches, etc.
This all makes good sense up to a point. When I put on my shoes, I put on one, then the other. It would be a lame joke were you to say to me, "You put on the left shoe and then the right one; when are you going to put on the pair?" To eat a bunch of grapes is to eat each grape in the bunch; after that task is accomplished there is nothing left to do. The bunch is not something 'over and above' the individual grapes that I still need to eat.
Consider now the Hatfields and the McCoys. These are two famous feuding Appalachian families, and therefore two pluralities. They cannot be (mathematical) sets on the nominalist view. But there is also the two-membered plurality of these pluralities to which we refer with the phrase 'the Hatfields and the McCoys' in a sentence like 'The Hatfields and the McCoys are families feuding with each other.'
If, however, a plurality of pluralities has exactly two members, as in the case of the Hatfields and the McCoys -- taking those two collections collectively -- then the latter cannot themselves be mere pluralities, but must be single items, albeit single items that have members. They must be both one and many. That is to say: In the sentence, 'The Hatfields and the McCoys are two famous feuding Appalachian families,' 'the Hatfields' and 'the McCoys' must each be taken to be referring to a single item, a family, and not to a plurality of persons. For if each is taken to refer to a plurality of items, then the plurality of pluralities could not have exactly two members but would many more than two members, as many members as there are Hatfields and MCoys all together. Compare the following two sentences:
1. The Hatfields and the McCoys number 100 in toto.
2. The Hatfields and the McCoys are two famous feuding Appalachian families.
In (1),'the Hatfields and the McCoys' can be interpreted as referring to a plurality of persons as opposed to a mathematical set of persons. But in (2), 'the Hatfields and the McCoys' cannot be taken to be referring to a plurality of persons; it must be taken to be referring to a plurality of two single items.
Or consider the following said to someone who mistakenly thinks that the Hatfields and the McCoys are one and the same family under two names:
3. The Hatfields and the McCoys are two, not one.
Clearly, in (3) 'the Hatfields and the McCoys' refers to a two-membered plurality of single items, each of which has many members, and not to a plurality of pluralities. And so we must introduce mathematical sets into our ontology.
My conclusion, contra the resident nominalist, is that we cannot scrape by on pluralities alone. (Man does not live by manifold alone! He needs unity!) We need mathematical sets or something like them: entities that are both one and many. A set, after all, is a one-in-many. It is not a mere many, and it is not a one 'over and above' a many. The nominalist error is to recoil from the latter absurdity and end up embracing the former. The truth is in the middle.
What I have given is an argument from ordinary language to mathematical sets. But there are also mathematical arguments for sets. Here is a very simple one. The decimal expansion of the fraction 1/3 is nonterminating: .33333333 . . . . But if I trisect a line, i.e., divide it into three equal lengths, I divide it into three quite definite actual lengths. This can be the case only if the the decimal expansion is a completed totality, an actual infinity, not a merely potential one. An even better example is that of the irrational number, the square root of 2 -- it is irrational because it cannot be expressed as a ratio of two numbers, the numerator and the denominator of a fraction as in the case of of the rational 1/3. If the hypotenuse of a right triangle is units of length, that is a quite definite and determinate length. How could it be if the decimal expansion however protracted did not point to a completed totality, an actual infinity?
REFERENCES
Max Black, "The Elusiveness of Sets," Review of Metaphysics, vol. XXIV, no. 4 (June 1971), 614-636.
Stephen Pollard, Philosophical Introduction to Set Theory, University of Notre Dame Press, 1990.
His main target was the corrupt relationship between large corporations and captured administrative bureaucracies. He has spent his career battling such corruption in the realm of environmental regulation and wants to use his knowledge and experience to expand that battle to the whole of the administrative state. In what might have been the biggest applause line of the night, he said as president he would never be muscled or manipulated by any bureaucrat or lobbyist.
[. . .]
To be sure, he has been on record in being among the climate-change alarmists in even recent history. Have his views on this topic shifted in light of the fake COVID science of the last three years and the lockdown experience? Perhaps so. Many people on the left have begun to rethink this topic and perhaps RFK is among them. He certainly seems to have zero interest in anything like a “great reset” and he is not a member of the World Economic Forum.
[. . .]
His next area was the most satisfying to me personally. He broke the public silence on the critical issue of COVID lockdowns. He chronicled the astonishing expense for which we gained nothing, and blasted companies like Amazon that censored contrary views while driving the competition out of business. He spoke with fire about the shutting down of small business and the violation of people’s property rights and religious liberties and illustrated a profound command of the facts, being how the lockdowns created an even worst public-health crisis.
[. . . ]
Finally, he called for a national conversation about this proxy war that is developing with Russia. The first excuse for U.S. involvement was purely humanitarian but it is mutating into yet another disaster along lines of the Iraq war. He demanded an immediate end to U.S. funding and a push for a diplomatic solution before it is too late. He further called for closing military bases around the world and bringing the troops home, plus a revival of U.S. economic strength. In the course of this discussion, he explained with great competence the threat to the U.S. dollar from the recent moves by BRICS to abandon trade in the dollar.
Were you draftable during the Vietnam era? What's your story?
UPDATE (4/23)
A correspondent and I both lament the non-inclusion of a certain period piece by Country Joe and the Fish. Said correspondent points out that the CJF tune is based on Louis Armstrong, Muskrat Ramble from 1926.
DIVERSITY demands that crash dummies be of all sizes, shapes, races, ethnicities, animal species including trans-species hybrids such as the Cat Man, and also 'genders' including trans-dummies, and let's not exclude living humans who 'identify' as crash dummies the better to facilitate their exit from life's freeway.
EQUITY will then be served: an equal outcome will be achieved by all dummies including the dumb-assed Dems who 'identify' as inanimate dummies when they are 'merely' transgressive leftards.
INCLUSION rules out, or excludes, all conservatives from serving as crash dummies, and rules in all fat, ugly, 'vertically challenged,' and 'differently abled' persons especially such politicians as Lori Lightfoot and John Fetterman.
House Republicans voted Thursday to ban transgender female athletes from taking part in girls’ and women’s sports by amending Title IX protections to only apply to biologically female athletes.
Homebuyers with good credit scores will soon encounter a costly surprise: a new federal rule forcing them to pay higher mortgage rates and fees to subsidize people with riskier credit ratings who are also in the market to buy houses.
You see, self-control, self-reliance, deferral of gratification, financial responsibility and the like are 'white' virtues, and therefore 'racist.' 'Racists' whether white or black need to be punished with higher mortgage rates. 'Equity' demands it. In fact, credit ratings as such are 'racist' and 'white supremacist' and need to go the way of the SAT.
Consider the natural numbers (0, 1, 2, 3, . . . n, n +1, . . . ). If these numbers form a set, call it N, then N will of course be actually infinite. This because a set in the sense of set theory is a single, definite object, a one-over-many, distinct from each of its members and from all of them. N must be actually infinite because there is no greatest natural number, and because N contains all the natural numbers.
It is worth noting that 'actually infinite set' is a pleonastic expression. It suffices to say 'infinite set.' This is because the phrase 'potentially infinite set' is nonsense. It is nonsense (conceptually incoherent) because a set is a definite object whose definiteness derives from its having exactly the members it has. A set cannot gain or lose members, and a set cannot have a membership other than the membership it actually has. Add a member to a set and the result is a numerically different set. In the case of the natural numbers, if they form a set, then that set will be an actually infinite set with a definite transfinite cardinality. Georg Cantor refers to that cardinality as aleph-zero or aleph-nought.
I grant, however, that it is not obvious that the natural numbers form a set. Suppose they don't. Then the natural number series, though infinite, will be merely potentially infinite. What 'potentially infinite' means here is that one can go on adding endlessly without ever reaching an upper bound of the series. No matter how large the number counted up to, one can add 1 to reach a still higher number. The numbers are thus created by the counting, not labeled by the counting. The numbers are not 'out there' in Plato's topos ouranios waiting to be counted; they are created by the counting. In that sense, their infinity is merely potential. But if the naturals are an actual infinity, then they are not created but labeled.
Moving now from arithmetic to geometry, consider a line segment in a plane. One can bisect it, i.e., divide or cut it into two smaller segments of equal length. Thus the segment AB whose end points are A and B splits into the congruent sub-segments AC and CB, where C is the point of bisection. The operation of bisection is indefinitely ('infinitely') iterable in principle. The term 'in principle' needs a bit of commentary.
Suppose I am slicing a salami using a state-of-the-art meat slicer. I cannot go on slicing thinner and thinner indefinitely. The operation of bisecting a salami is not indefinitely iterable in principle. The operation is iterable only up to a point, and this for the reason that a slice must have a certain minimal thickness T such that if the slice were thinner than T it would no longer be a slice. But if we consider the space the salami occupies -- assuming that space is something like a container that can be occupied -- then a longitudinal (non-transversal) line segment running from one end of the salami to the other is bisectable indefinitely in principle.
For each bisecting of a line segment, there is a point of bisection. The question can now be put as follows: Are these points of bisection only potentially infinite, or are they actually infinite?
A Puzzle
I want to say that from the mere fact that the operation of bisecting a line segment is indefinitely ('infinitely') iterable in principle, it does notfollow that the line segment is composed of an actual infinity of points. That is, it is logically consistent to maintain all three of the following: (i) one can always make another cut; (ii) the number of actual cuts will always be finite; and that therefore (iii) the number of points in a line will always be finite, and therefore 'infinite' only in the sense that there is no finite cardinal n such that n is the upper bound of the number of cuts.
At this 'point,' however, I fall into perplexity which, according to Plato, is the characteristic state of the philosopher. If one can always make another cut, then the number of possible cuts cannot be finite. For if the number of possible cuts is finite, then it can longer be said that the line segment has a potentially infinite number of points of bisection. It seems that a potential infinity of actual cuts logically requires an actual infinity of possible cuts.
But then actual infinity, kicked out the front door, returns through the back door.
I have just posed a problem for those who are friends of the potentially infinite but foes of the actual infinite. How might they respond?
The urge to retreat is tempting, but the only way out is through. To float above the fray in the manner of a Rod Dreher is not the way; the only way out is through.
Minervic flights and the consolations of philosophy cannot be enjoyed when the barbarians are at the gates of one's stoa.
Now you know why I mix the abstruse and theoretical with the political and practical.
Conservatives, especially those of them given to contemplative pursuits, need to make their peace with activism in order to secure and defend the spaces of their quietism. And this with blood and iron if need be.
The owl of Minerva is a tough old bird, but no phoenix capable of rising from its ashes.
When the world and its hopelessness are too much with us, one can and must beat a retreat into the private life and the pleasures and pursuits thereof: body culture, mind culture, hobbies, family life, the various escapes (which are not necessarily escapes from reality) into chess, fiction, prayer, meditation, history, pure mathematics and science, one's own biography and the pleasant particulars of one's past, music, gardening, homemaking . . . . But all this by way of recuperation for the battle.
I pity the poor activist for whom the real is exhausted by the political. But I detest these totalitarians as well since they seek to elide the boundary between the private and the public.
So we need to battle the bastards in the very sphere they think exhausts the real. But it is and must be a part-time fight, lest we become like them. Most of life for us conservatives must be given over to the enjoyment and appreciation, in private, of the apolitical: nature, for example, and nature's God.
One of the old ones goes like this. "Ah had me a coupla Buds, but ahm none the wiser." I suggest as part of the punch back against the Anheuser-Busch Dylan Mulvaney wokery, the following:
I had me a couple of Buds and my schlong's no longer a riser.
But I am sure you can do better than that; combox open.
The logically prior question, of course, is why anyone of taste and discernment would drink the swill served up by Anheuser-Busch when you can drink some such fine German brew as St. Pauli Girl the poster 'boy' of which is a buxom wench (in sense 1) who is not only unambiguously female but also stacked and packed to the nines and hence in violation of all canons of wokery known to man.
If your head is screwed on Right, you will enjoy DeSantis' take on this brew-haha (I'm punning on brouhaha, as I'm sure you've noticed.)
Time to man up and bone up on your political ponerology the better to punch back against the 'woke' kakistocracy and all its works. Not much is at stake, of course, except the survival of civilization.
Here is another problem that needs to be carefully phrased.
I want to say that the pitch of a musical note is continuous through time. I mean, at any point in continuous time, i.e. time as specified by the real numbers, the pitch of the note (e.g. middle C) is the same.
However, the “physical” property that grounds the pitch is not continuous, but rather a cycle of different events.
That strikes me as a problem for the kind of physicalism according to which qualities “as we perceive them” are identical with the properties that ground them. For pitch is temporally continuous, the oscillation that grounds it is not temporally continuous, ergo etc.
It is a problem indeed, Ed, although I have questions about your formulation of it.
The problem is known in the trade as the Grain Problem. Whether it surfaces before Sir Arthur Eddington, I don't know, but he raises it, or at least anticipates it with his question about the 'two tables.' A lot of work was done on the Grain Problem by the great American philosopher Wilfrid Sellars, son of the rather less distinguished Roy Wood Sellars, but nonetheless a quantity to be reckoned with in his day.
Here is Sellars fils in his seminal essay, "Philosophy and the Scientific Image of Man," reprinted in his Science, Perception, and Reality (Routledge, 1963). The portion I am about to quote is from pp. 35-37. I take the text from Chrucky's online version.
It is worth noting that we have here a recurrence of the essential features of Eddington's 'two tables' problem -- the two tables being, in our terminology, the table of the manifest image and the table of the scientific image. There the problem was to 'fit together' the manifest table with the scientific table. Here the problem is to fit together the manifest sensation with its neurophysiological counterpart. And, interestingly enough, the problem in both cases is essentially the same: how to reconcile the ultimate homogeneity of the manifest image with the ultimate non-homogeneity of the system of scientific objects.
BV: Whether we are discussing colors with Sellars or sounds with Buckner, it is the same problem, that of reconciling the homogeneity of the manifest or phenomenal sensory quality with the non-homogeneity of the underlying scientific explanatory posits. For Sellars, of course, these posits are not mere posits but ultimately real, as you will see if you read below the fold.
Buckner's formulation above leaves something to be desired, however. He cites the continuous perception over time of the same note, middle C, let us say. But then in the very next sentence he reverts to a rarefied mathematical concept of continuity, thereby mixing phenomenological description with a mathematico-scientific construct. He thereby conflates phenomenal continuity with mathematical continuity. When I hear middle C sounding from an organ, say, over a non-zero interval of time, five seconds say, do I hear a series of points of time -- a series of temporally extension-less moments -- the cardinality of which is 2-to-the-aleph-nought? No. (The cardinality of the set of real numbers (cardinality of the continuum) is)
And then Ed goes on to say that "the 'physical' property that grounds the pitch is not continuous, but rather a cycle of different events." But that is not right either. Middle C depicted on an oscilloscope shows up as a sine wave:
Obviously the sine wave is continuous. What Ed wants to say, of course, is that the heard sound, the phenomenal sound, does not fluctuate as does the physical reality does, the physical reality that "grounds the pitch." Ed is equivocating on 'continuous.'
But I know what he is getting at, and it is a genuine problem. I am merely complaining about his formulation of it. Now back to Sellars, whose solution to the problem is not clear to me.
I mean remove documents from your glove compartment or other easily accessible areas in your vehicle wherein it would be unwise to carry them given the spike in crime of all sorts caused by such Democrat policies as defunding the police and eliminating cash bail. I count four levels of foolishness in decreasing levels of inadvisability:
1) Carrying your driver's license in the glove box.
2) Carrying the title to the vehicle in the glove box.
3) Carrying the vehicle registration in the glove box.
4) Carrying insurance cards in the glove box.
Since smash and grab is quick and easy and on the rise, the wise do not leave personal information easy of access in their vehicles. (You might want to look into installing a serious console or under-seat lock box.) One scenario goes like this: the thug learns your address and swipes your garage door opener. Now they have easy access to your garage and its contents, and if you are foolish enough to leave the door to your domicile unlocked, access to your house and its contents including wife and children.
Christ has harsh words for those who misuse the power of speech at Matthew 12:36: "But I say unto you, that every idle word that men shall speak, they shall give account thereof in the day of judgment." But what about every idle word that bloggers blog and Substackers stack? Must not the discipline of the tongue extend to the pen?
No, you useful idiots, white supremacy is not the greatest threat we face: it is no threat at all since it doesn't exist. A real threat we face, and a very serious one, is posed by an EMP directed against our unprotected grid. HT to JSO for the following two videos.
The whole article is hair-raising, but this jumped out at me:
About the same time that tensions were rising over Nancy Pelosi’s visit to Taiwan, reposts of a 2020 article by Major General Ed Thomas, the Commander of the Air Force’s Recruiting Service, began to pop up in the media. The headline? “Eighty-six percent of Air Force pilots are white men. Here’s why this needs to change.” Too many white men? Is that what our generals worry about? Like many other military top-brass, Major General Thomas seems to think that diversity wins wars. That’s why he put “improving diversity” on “the top of my to-do-list.”
What if, in the meritocracy the armed services are supposed to be, not enough nonwhites cut the mustard? Promote them anyway?
BV: This goes to the heart of the matter, namely the assault on merit in favor of 'diversity,' 'equity,' and 'inclusion' which in practice amount to governmentally enforced proportional representation, equality of outcome, and exclusion of 'racists' and 'white supremacists.' The destructive DEI agenda is predicated upon reality denial, in particular, the denial of the reality that we are not equal either as individuals or as groups in those empirically measurable respects that bear upon qualification for jobs and positions. The DEI agenda is dangerous and destructive because it allows the physically feeble and disabled, the mentally incompetent, the morally defective, and the factually ignorant and untrained to occupy high positions in government and industry. But 'allow' is too weak a word in this context; 'promote' is more to the point.
One reason this is dangerous is that our geopolitical adversaries do not subscribe to the destructive DEI ideology. While we self-enstupidate, they salivate.
How explain the popularity of DEI among the useful idiots? I suggest that it is due, at least in part, to the 'feel-good' nature of the DEI 'reforms.' They are found very appealing in this, the Age of Feeling.
How explain the popularity of DEI among the drivers of the demented doctrine? In the case of Major General Ed Thomas and his ilk it is probably sheer careerism. They go along not just to get along but to advance themselves career-wise, and the nation and the world be damned. It strains credulity to think that they actually believe the rubbish.
The new global-capitalist woke leftism (GCWL) is very different from the old socialist-humanist leftism (SHL, which I take to include both the Old Left and the New Left). I want to understand the similarities and the differences.
GCWL versus SHL
1) Both are secular and anti-religion. Since 1789 the Left has been virulently anti-clerical and anti-religious. Nota bene: an ersatz religion is not a religion! So stop calling leftism a religion, Dennis Prager.
2) Both target the middle class.
3) Both are internationalist and anti-nationalist.
4) The main difference seems to be that SHL is humanist while GCWL tends toward the erasure of humanity and humanism via anti-natalism, paganism, nature-idolatrous environmentalism, misanthropy, Orwellian subversion of language, and leukophobic ethno-masochism and much else besides.
So that's a start. Inadequate, no doubt.
James Soriano responded this morning:
I liked your January 26 post on the Globalist-Capitalist Woke Leftism, as well as the comments.
Here are a couple of points on the dissimilarities of the “Woke” compared to the “Old” and “New.”
(1)Both the Old Left and the New Left were hostile to capitalism, whereas the Woke Left finds it a useful tool.Today corporations big and small have become “woke” and are friendly to the Woke agenda.Any corporation insufficiently sympathetic to the Woke agenda is bullied until it wakes up.
(2)The Old Left got a Russian assist.After WWI, Russia secretly supported Communist parties and allied organizations in Europe and elsewhere.These subversive activities continued after WWII and into the New Left period.By contrast, the Woke Left gets an American assist.It is not secretive in any way.It’s in the open.
(3)The Old Left and the New Left thought of“revolution” as something that originates in society and then goes on to take over the state.But “woke” attitudes have already penetrated into the state.To a “woke” leftist, a revolution can also be something that moves from the state back into society for the purpose of stomping out pockets of resistance.
——
On this last point, we can make a distinction between a revolution BEFORE power and a revolution AFTER power.
Revolutions taking place before the revolutionaries consolidate power: Americans in 1776, Mao in China, Castro in Cuba, and Khomeini in Iran.
Revolutions taking place after the revolutionaries consolidate power:
— 1917.A small group of Bolsheviks take over the seat of government in St. Petersburg.The Russian Revolution took place after that event; there was no Bolshevik uprising prior to it.
— 1932. The National Socialist German Workers' Party came to power by democratic means.The Nazi transformation of Germany took place after that event; there was no Nazi uprising prior to it. [It was 1933 -- BV]
— Historian Martin Kramer makes this revolution-before-and-after distinction regarding “moderate” Islamists.Many people in the Arab World fear that “moderates” like the Muslim Brotherhood would use democratic means to take over the state.They would then go on to Islamize society after they take power.Wokesters are like that, too.
JSO sends us to Will You Remember Me? by the Pine Box Boys. The dessicated soul of the secularist is incapable of understanding religion. He thinks he will eradicate it. But religion, like philosophy, always buries its undertakers.
Over the last 24 hours I have been obsessing over Kant's spherical triangles. He claims that they are incongruent counterparts. Now I understand how a hand and its mirror image are incongruent counterparts. (A right hand's mirror image is a left hand.) But it is not clear to me how Kant's spherical triangles are incongruent counterparts. Supplement the above diagram with a second lower triangle that shares its base (an arc of the equator) with that of the upper triangle and whose sides are two arcs whose vertex is the south pole.
David Brightly's comment is the best I received in the earlier thread. (He works in Info Tech and I believe he has an advanced degree in mathematics.) He writes,
Not clear to me either, Bill. Why does Kant resort to spherical triangles? [To show the existence of incongruent counterparts.] Consider first two right triangles in the plane with vertices (0,0), (3,0), (0,4) in triangle A and (0,0), (3,0), (0,-4) in B. In plane geometry A and B are considered congruent, not by translation or rotation in the plane but rotation out of the plane ('flipping') with their shared edge as axis. Now think of these triangles on the sphere with edges of length 3 along the equator and those of length 4 on a meridian. The lower triangle cannot be flipped into congruence with the upper---it curves 'the wrong way'. Congruence on the sphere is more restrictive than congruence in the plane. But they are mirror images of one another in the equatorial plane. Likewise, Kant's isosceles triangles cannot be flipped into registration. Has he just overlooked that they can be slid on the sphere into alignment?
As Brightly quite rightly points out, "The lower triangle cannot be flipped into congruence with the upper --- it curves 'the wrong way'." That was clear to me all along. My thought was that if you rotate the lower triangle through 180 degrees so that its southern vertex points north, it would fit right over the upper triangle. I think that is what David means when he writes, "they can be slid on the sphere into alignment."
In other words, the lower triangle needn't be rotated off the surface of the sphere with the axis of rotation being the common base, it suffices to slide the triangles into alignment and thus into congruence along the surface of the sphere.
Therefore: Kant's spherical triangles are not incongruent counterparts or enantiomorphs.
Now David, have I understood you? I am not a mathematician and I might be making a mistake.
Consensus is no guarantee of truth. If all or most of the experts in some subject area agree that p, it does not follow that p is true. But that is not to say, or imply, that consensus has no bearing on truth. A consensus of unbiased and uncoerced experts in a field is a reliable guide to truth in that field, assuming that the consensus is real and not the fabrication of, say, climate hoaxers.
Kitsch is art's comfort food: familiar, reliable in its satisfactions, readily available, not particularly nourishing, but also not challenging to its consumers, remunerative for its producers.
'Institutional capture' by anti-civilizational wokesters is fait accompli and we are collapsing on all fronts. Imagine being a English professor facing the daunting task, not of Higher Education, but of Higher Remediation.
Buckner demands an argument from incongruent counterparts to the ideality of space. But before we get to that, I am having trouble understanding how the 'spherical triangles' Kant mentions in the Prolegomena to Any Future Metaphysics, sec. 13, are incongruent counterparts. Perhaps my powers of visualization are weak. Maybe someone can help me.
I understand how a hand and its mirror image are incongruent counterparts. If I hold up my right hand before a mirror what I see is a left hand. As Kant says, "I cannot put such a hand as is seen in the glass in the place of its original; for if this is a right hand, that in the glass is a left one . . . ." (p. 13) That is clear to me.
Now visualize a sphere and two non-plane 'spherical triangles' the common base of which is an arc of the sphere's equator. The remaining two sides of the one triangle meet at the north pole; the remaining two sides of the other at the south pole. The two triangles are exact counterparts, equal in all such internal respects as lengths of sides, angles, etc. They are supposed to be incongruent in that "the one cannot be put in place of the other (that is, upon the opposite hemisphere)." (ibid.) That is not clear to me.
Imagine the southern triangle detached from the sphere and rotated through 180 degrees so that the south vertex is pointing north and the base is directly south. Now imagine the southern triangle place on top of the northern triangle. To my geometrical intuition they are congruent!
So, as I see it, hands and gloves are chiral but Kant's spherical triangles are not.
In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. An object that is not chiral is said to be achiral.
A chiral object and its mirror image are said to be enantiomorphs. The word chirality is derived from the Greek χείρ (cheir), the hand, the most familiar chiral object; the word enantiomorph stems from the Greek ἐναντίος (enantios) 'opposite' + μορφή (morphe) 'form'.
In an e-mail, a correspondent poses a problem that I will put in my own way.
BV is alone in a room facing a standard, functioning mirror and he is looking at a man, the man in the mirror. Call that man MM. So in this situation, BV is looking at MM. The question is this. Is BV numerically the same as MM? Or is BV numerically different from MM?
Surely it would be absurd to claim that there are two men in the room, the one facing the mirror and the one in (or behind) the mirror. The sensible thing to say is that MM is a mere image of a man, not a man. And of course it is the image of BV, not of any other man. Accordingly, when BV looks into the mirror, he sees himself via a mirror image. Now most people will stop right here and go on to something else. But philosophers are a strange breed of cat. They sense something below the mundane surface and want to bring it into the light.
Suppose BV points in the direction of the mirror and exclaims, "That's me! Look how beat-to-hell I've become!" But if MM is a mere image of a man, and not a man, then BV is not pointing at himself, the man BV, but at a mere image. This suggests, contrary to the point made in the immediately preceding paragraph, that there is a man in the mirror and that he is identical to BV! In the situation described, we seem to have good reason to affirm both of the following propositions despite their collective inconsistency:
1) BV is pointing at an image, not a man. (Because there is only one man in the room.)
2) BV is pointing at a man. (Because BV is pointing at himself, and BV is a man.)
This has got to be a pseudo-problem, right? Well then, dissolve it!
A Variant Puzzle
Perhaps the following variant of the puzzle is clearer. BV holds up his right hand and looks at it in the mirror. With the index finger of his left hand BV points to the hand in the mirror and says, "That is a beautiful hand!" With that same index finger he then points to the hand he is holding up and says the same thing. Pointing as he is in two different directions, BV is pointing at two different things, each of which is a hand. But then BV has two left hands and one right hand, for a total of three hands -- which is absurd. Why two left hands? Because the hand in the mirror is a left hand being the incongruent counterpart of the right hand BV is holding up.
Incongruent counterparts are discussed by Kant in no less than four places, twice in his pre-Critical writings and twice after 1781. More on this later.
Polarization in a physical body has to have a limit lest the polarized body break apart. (Imagine the distance between Earth's North and South poles -- 8595.35 miles -- increasing indefinitely.) It is no different with the body politic. We will eventually break apart or be broken apart by an external force (how about the ChiComs in cahoots with the Russkis?) if our political polarization continues. United we stand, divided we fall; come on now people, let's get on the ball. We won't of course.
Time was, when I read Mona Charen and George F. Will with quite a bit of approval. But then Trump came along and both lost their minds. Here is Will over at The Washington [Com]Post. Take a gander at the comments to gauge the level of present political polarization.
Dear old Mona's latest outburst anent Trump is such that I cannot bring myself to sully my site by linking to it.
Do you want to hear some sane and characteristically brilliant commentary by a lion of the law? Here is Alan Dershowitz on the Trump indictment. (HT: Vito Caiati)
Elliot C. asked me about tropes. What follows is a re-post from 30 March 2016, slightly emended, which stands up well under current scrutiny. Perhaps Elliot will find the time to tell me whether he finds it clear and convincing and whether it answers his questions.
................................
A reader has been much exercised of late by trope theory and other questions in ontology. He has been sharing his enthusiasm with me. He espies
. . . an apparent antinomy at the heart of trope theory. On the one hand, tropes are logically prior to objects. But on the other hand, objects (or, more precisely, the trope-bundles constituting objects) are logically prior to tropes, because without objects tropes have nowhere to be – without objects (or the trope-bundles constituting objects) tropes cannot be. Moreover, as has I hope been shown, a trope cannot be in (or constitute) any object or trope-bundle other than that in which it already is.
How might a trope theorist plausibly respond to this? Can she? [My use of the feminine third-person singular pronoun does not signal my nonexistent political correctness, but is an anticipatory reference to Anna-Sofia Maurin whom I will discuss below. 'Anna-Sofia'! What a beautiful name, so aptronymic. Nomen est omen.)
What are tropes?
It is a 'Moorean fact,' a pre-analytic datum, that things have properties. This is a pre-philosophical observation. In making it we are not yet doing philosophy. If things have properties, then there are properties. This is a related pre-philosophical observation. We begin to do philosophy when we ask: given that there are properties, what exactly are they? What is their nature? How are we to understand them? This is not the question, what properties are there, but the question, what are properties? The philosophical question, then, is not whether there are properties, nor is it the question what properties there are, but the question what properties are.
On trope theory, properties are assayed not as universals but as particulars: the redness of a tomato is as particular, as unrepeatable, as the tomato. Thus a tomato is red, not in virtue of exemplifying a universal, but by having a redness trope as one of its constituents (on the standard bundle version of trope theory) or by being a substratum in which a redness trope inheres (on a nonstandard theory championed by C. B. Martin which I will not further discuss). A trope is a simple entity in that there is no distinction between it and the property it ‘has.’ 'Has' and cognates are words of ordinary English: they do not commit us to ontological theories of what the having consists in. So don't confuse 'a has F-ness' with 'a instantiates F-ness.' Instantiation is a term of art, a terminus technicus in ontology. Or at least that is what it is in my book. More on instantiation in a moment.
Thus a redness trope is red, but it is not red by instantiating redness, or by having redness as a constituent, but by being (a bit of) redness. So a trope is what it has. It has redness by being identical to (a bit of) redness.
It is therefore inaccurate to speak of tropes as property instances. A trope is not a property instance on one clear understanding of the latter. First-order instantiation is a dyadic asymmetrical relation: if a instantiates F-ness, then it is not the case that F-ness instantiates a. (Higher order instantiation is not asymmetrical but nonsymmetrical. Exercise for the reader: prove it!) Suppose the instantiation relation connects the individual Socrates here below to the universal wisdom in the realm of platonica. Then a further item comes into consideration, namely, the wisdom of Socrates. This is a property instance. It is a particular, an unrepeatable, since it is the wisdom of Socrates and of no one else. This distinguishes it from the universal, wisdom, which is repeated in each wise individual. On the other side, the wisdom of Socrates is distinct from Socrates since there is more to Socrates that his being wise. There is his being snub-nosed, etc. Now why do I maintain that a trope is not a property instance? Two arguments.
Tropes are simple, not complex. (See Maurin, here.) They are not further analyzable. Property instances, however, are complex, not simple. 'The F-ness of a' -- 'the wisdom of Socrates,' e.g. -- picks out a complex item that is analyzable into F-ness, a, and the referent of 'of.' Therefore, tropes are not property instances.
A second, related, argument. Tropes are in no way proposition-like. Property instances are proposition-like as can be gathered from the phrases we use to refer to them. Ergo, tropes are not property instances.
One can see from this that tropes on standard trope theory, as ably presented by Maurin in her Stanford Encyclopedia of Philosophy entry, are very strange items, so strange indeed that one can wonder whether they are coherently conceivable at all by minds of our discursive constitution. Here is one problem.
How could anything be both predicable and impredicable?
Properties are predicable items. So if tropes are properties, then tropes are predicable items. If the redness of my tomato, call it 'Tom,' is a trope, then this trope is predicable of Tom. Suppose I assertively utter a token of 'Tom is red.' On one way of parsing this we have a subject term 'Tom' and a predicate term '___ is red.' Thus the parsing: Tom/is red. But then the trope would appear to have a proposition-like structure, the structure of what Russell calls a propositional function. Clearly, '___ is red' does not pick out a proposition, but it does pick out something proposition-like and thus something complex. But now we have trouble since tropes are supposed to be simple. Expressed as an aporetic triad or antilogism:
a. Tropes are simple. b. Tropes are predicable. c. Predicable items are complex.
The limbs of the antilogism are each of them rationally supportable, but they cannot all be true. Individually plausible, collectively inconsistent. The conjunction of any two limbs entails the negation of the remaining one. Thus the conjunction of (b) and (c) entails ~(a).
We might try to get around this difficulty by parsing 'Tom is red' differently, as: Tom/is/red. On this scheme, 'Tom' and 'red' are both names. 'Tom' names a concrete particular whereas 'red' names an abstract particular. ('Abstract' is here being used in the classical, not the Quinean, sense.) As Maurin relates, D. C. Williams, who introduced the term 'trope' in its present usage back in the '50s, thinks of the designators of tropes as akin to names and demonstratives, not as definite descriptions. But then it becomes difficult to see how tropes could be predicable entities.
A tomato is not a predicable entity. One cannot predicate a tomato of anything. The same goes for the parts of a tomato; the seeds, e.g., are not predicable of anything. Now if a tomato is a bundle of tropes, then it is a whole of ontological parts, these latter being tropes. If we think of the tomato as a (full-fledged) substance, then the tropes constituting it are "junior substances." (See D. M. Armstrong, 1989, 115) But now the problem is: how can one and the same item -- a trope -- be both a substance and a property, both an object and a concept (in Fregean jargon), both impredicable and predicable? Expressed as an aporetic dyad or antinomy:
d. Tropes are predicable items. e. Tropes are not predicable items.
Maurin seems to think that the limbs of the dyad can both be true: ". . . tropes are by their nature such that they can be adequately categorized both as a kind of property and as a kind of substance." If the limbs can both be true, then they are not contradictory despite appearances.
How can we defuse the apparent contradiction in the d-e dyad? Consider again Tom and the redness trope R. To say that R is predicable of Tom is to say that Tom is a trope bundle having R as an ontological (proper) part. To say that R is impredicable or a substance is to say that R is capable of independent existence. Recall that Armstrong plausibly defines a substance as anything logically capable of independent existence.
It looks as if we have just rid ourselves of the contradiction. The sense in which tropes are predicable is not the sense in which they are impredicable. They are predicable as constituents of trope bundles; they are impredicable in themselves. Equivalently, tropes are properties when they are compresent with sufficiently many other tropes to form trope bundles (concrete particulars); but they are substances in themselves apart from trope bundles as the 'building blocks' out of which such bundles are (logically or rather ontologically) constructed.
Which came first: the whole or the parts?
But wait! This solution appears to have all the advantages of jumping from the frying pan into the fire. For now we bang up against the above Antinomy, or something like it, to wit:
f. Tropes as substances, as ontological building blocks, are logically prior to concrete particulars. g. Tropes as properties, as predicable items, are not logically prior to concrete particulars.
This looks like an aporia in the strict and narrow sense: an insoluble problem. The limbs cannot both be true. And yet each is an entailment of standard (bundle) trope theory. If tropes are the "alphabet of being" in a phrase from Williams, then they are logically prior to what they spell out. But if tropes are unrepeatable properties, properties as particulars, then a trope cannot exist except as a proper ontological part of a trope bundle, the very one of which it is a part. For if a trope were not tied to the very bundle of which it is a part, it would be a universal, perhaps only an immanent universal, but a universal all the same.
Furthermore, what makes a trope abstract in the classical (as opposed to Quinean) sense of the term is that it is abstracted from a concretum. But then the concretum comes first, ontologically speaking, and (g) is true.
Interim conclusion: Trope theory, pace Anna-Sofia Maurin, is incoherent. But of course we have only scratched the surface.
Pictured below, left-to-right: Anna-Sofia Maurin, your humble correspondent, Arianna Betti, Jan Willem Wieland. Geneva, Switzerland, December 2008. It was a cold night.
The following incomplete draft has been languishing on my hard drive, on a memory stick, and in 'the cloud' since late November 202o. So I will post it now to see what comments Elliot C. (and anyone else) has to offer. In other threads he has shown a burning interest in this question.
.............................
1) I see a tree, a palo verde. Conditions are normal both inside and outside of me, the perceiver. My eyesight is 20/20, the lighting is good, etc. I see that the tree is green, blooming, swaying slightly in the breeze, and so on. I know (directly, i.e., in the temporal present, without reliance on memory or testimony or inference) that the tree has these and other properties, and I know this by sense perception, in this instance by seeing them, and indeed by seeing them without the aid of such instruments as binoculars or closed-circuit television. I know that the tree is green by seeing that the tree is green. But I cannot see that the tree is green without seeing green at the tree. So I know (directly) that the tree is green by seeing green at the tree. It follows that the property green is sense-perceivable. It is a sensible or observable property.
2) I presumably also know that the tree exists by seeing it. That is, my seeing the tree suffices for my knowing that it exists. And the birds in the branches? Likewise: I know that they exist by seeing them. But while I cannot know (directly) that the tree is green without seeing green at the tree, I can presumably know that the tree exists without seeing existence at the tree. For whatever existence is, it is not a sensible or observable property.I see the green of the tree, but not the existence of the tree. Green is observable; existence is not. If I do know that the tree exists by seeing it, how do I know this given that existence is not a sensible or empirically observable property or feature of the thing that exists?
3) And so we have a puzzle that arises naturally just by reflecting on some obvious data. The problem is expressible as an inconsistent pentad. The following propositions are individually plausible, and yet they are collectively inconsistent. Something's got to give. To solve the problem, we either reject or reformulate one or more of the propositions, or we argue that, despite appearances, the propositions are consistent.
a) I know that the tree exists.
b) I know that the tree exists by seeing that it exists.
c) An individual exists by instantiating the property of existence.
d) If I see that a thing has a property, then I see the property at the thing.
e) One cannot see or otherwise sense-perceive the property of existence.
The five propositions are (collectively) inconsistent. Any four of them, taken together, entails the negation of the remaining one. For example, the conjunction of the first four entails the negation of (e). So the only way to solve the problem is by rejecting/revising one or more of the limbs. But which one? Given the high plausibility of (a), (b), and (e), the natural candidates for rejection are (c) and (d).
Response 1: The existence of an individual is not a property it instantiates, but the individual itself.
Given that the pentad is inconsistent, one response to it is by rejecting (c) by rejecting a presupposition on which (c) rests, namely, that existence is a property of individuals. Suppose it is maintained instead that the existence of an individual is just that individual. Thus the existence of the tree is just the tree; it is not a property of the tree. If so, then there is no real, non-verbal, difference between the tree and its existence. A tree and an existent/existing tree are one and the same. To see the tree would be to see its existence. Equivalently, to see the tree would be to see an existing tree. If this is right, then the solution to the puzzle is straightforward: I know that the tree is green by seeing green at the tree, and I know that the tree exists simply by seeing the tree. Seeing a sense-perceptible thing suffices for knowing that it exists.
Rebuttal of Response 1
To see what is wrong with this response, consider a different example. I am looking at the Sun. While I am looking at it, it ceases to exist. Since it takes about eight minutes for the light of the Sun to reach the Earth, the following could happen: the object-directedness of the perceptual act undergoes no modification despite the fact that the object, the Sun, has ceased to exist. I continue for a few minutes to see something -- no seeing without seeing something -- but the something I see no longer exists. This shows that one cannot infer the real or extra-mental existence of the accusative of an act from the accusative's givenness. By the accusative of a mental act I mean that which appears to the mind in the act. In my first example, the accusative is the tree precisely as seen. The back side of the tree is not seen by me, and so it is not part of the accusative. And the same goes for the ant on the front side of the tree which I cannot see because of my distance from the tree. Of course, the tree in reality either has an ant on its front side or it does not. The tree in reality cannot be indeterminate in this regard, or in any regard. But the accusative, as such, is indeterminate in this regard. This is the fate of intentional objects generally qua intentional objects: they are incomplete. This incompleteness reflects the finitude of our minds.
In the second example the accusative is the Sun precisely as seen by me here and now. Therefore, if by 'existence' we mean existence in reality or existence in itself or extra-mental existence -- these being equivalent terms -- then I cannot know that a perceptible thing exists simply by seeing it. For it could be that the accusative does not exist at the time it appears. I see the Sun at a time when there is no Sun to be seen. Appearing and being (existing) fall asunder.
One can arrive at the same conclusion via the Cartesian dream argument. I see things in dreams that don't exist or that no longer exist. My use of 'see' here is obviously a phenomenological use. On this use, 'see' is not a verb of success: 'S sees x' does not entail 'S exists.' Phenomenologically, one can see and otherwise sense-perceive what does not exist. I had an extremely vivid lucid dream once in which I saw, heard, and touched a beloved cat that I knew was dead. I SAW the cat (in the phenomenological sense of 'see') despite its nonexistence in reality. I didn't remember the cat or imagine it: I saw it. I had a visual experience as of a cat even though my eyes were closed.
Or suppose a mad neuroscientist so stimulates a brain in a vat that the brain gives rise to a visual perception as of a tree just like the one in my opening example. (The brain is eyeless and is not connected to any optical transducers.) The accusative of the act is given but it does not exist in reality. You could say that in a case like this the accusative enjoys esse intentionale but not esse reale.
The upshot is that one cannot know that a perceptible item such as tree exists by seeing it. So response 1 fails.
Response 2: One can know that a visually-perceptible thing exists without seeing that the thing instantiates the putative property of existence and without seeing a thing that is identical to its existence. The existence of an individual does not belong to the individual.
On this response, a presupposition of all five limbs of the pentad is called into question, namely, the notion that existence belongs to existing things as it would belong to them if it were either a property of them, or identical to them, or hidden within them, or in some other way 'at' them or 'in' them. One way to deny this presupposition is by holding that the existence of a tree, say, is really a property of something else. One might say that the existence of trees is a property of the world-whole, the property of containing trees. To say that trees exist would then be to say that the world contains trees. Existence would then be a mondial attribute: it would be a property of the world. The existence of Fs is then just the world's having the property of containing Fs. The existence of Socrates is just the world's containing Socrates.
Rebuttal of Response 2
The theory is explanatorily circular and worthless for that reason. The world cannot contain Socrates unless Socrates exists. Before (logically speaking) the world can contain Socrates, Socrates must exist. To explain the existence of Socrates by saying that the world has him as a member is to presuppose the very thing that needs explaining, namely, the existence of Socrates. The circular is of embarrassingly short diameter.
units of length, that is a quite definite and determinate length. How could it be if the decimal expansion however protracted did not point to a completed totality, an actual infinity?
) 
Recent Comments