A Quasi-Pyrrhonian Metaphilosophical Puzzle

Some of us are tempted by the metathesis (MT) that every substantive philosophical thesis is such that the arguments for it and the arguments against it are equally plausible and thus 'cancel out.' But the metathesis is itself a philosophical thesis. So if the metathesis is true, then every argument in support of it is cancelled out by an equally plausible argument against it.  But then (MT), if true, is such that we cannot have any good reason to accept it.

Is there a genuine problem here for a latter-day quasi-Pyrrhonian who subscribes to the metathesis?

Definitions

D1. An argument A1 for a thesis T cancels out an argument A2 for the negation of T just in case both arguments are equally plausible to the producers(s)/consumers(s) of the arguments, assuming that these individuals are 'competent practitioners.'

Plausibility is relative to an arguer and his audience, if any.  Thus plausibility is unlike soundness, which is absolute, like truth herself.  Note that there cannot be sound arguments both for a thesis and its negation. For if there is a sound argument for T, then T is true. And if there is a sound argument for ~T, then ~T is true. This is 'fallout' from the definition of 'sound,' see D2 below. But then (T & ~T) is true which violates the Law of Non-Contradiction.

Canceling out is symmetrical: If A1 cancels A2, then A2 cancels A1. It seems to follow that canceling out is also conditionally reflexive, which is to say that if A1 cancels A2, then A1 cancels itself. Right? 

A competent practitioner is not the same as an epistemic peer.  A number of individuals may be epistemic peers, but all incompetent. I won't try for a crisp definition of 'competent practitioner,' but if Tom is a competent practitioner in the philosophy of religion, say, then he is a a sincere truth seeker, not a quibbler or a sophist; he knows logic and the empirical disciplines that bear upon the arguments he is discussing; he is familiar with the relevant literature; and so on.

D2. An argument is sound just in case it is valid and all of its premises are true.

D3. An argument for a thesis is unopposed just in case there is no argument for its negation plausible to all competent practitioners.

D4. A proposition is rationally acceptable just in case it involves no logical contradiction, and coheres with the rest of what we know or justifiably believe.

Rational acceptability, like plausibility, and unlike truth, is a relative property: That water is an element was rationally acceptable to the ancient Greeks, but not to us.

The Puzzle as an Aporetic Tetrad 

1) Every substantive philosophical thesis is such that the arguments pro et contra cancel out. (MT)

2) MT is a philosophical thesis.

3) A philosophical thesis is rationally acceptable only if there is at least one good unopposed argument for it.

4) MT is rationally acceptable.

Solutions

The quartet of propositions is inconsistent. Any three limbs, taken in conjunction, entail the negation of the remaining one. Which should we reject? (2) is not plausibly rejectable: metaphilosophy is a branch of philosophy.

One could hold that the first three propositions are true, but the fourth is false. This implies that a proposition could be true but not rationally acceptable.  But if MT is true but not rationally acceptable, what reason could we have for believing it?

A better solution of the tetrad is by rejection of (1). This is the position of the optimist about philosophical knowledge. He holds that some theses are supported by unopposed arguments and that we know what these arguments are.

I accept (1) on the basis of strong inductive evidence which renders it rationally acceptable. Accepting as I do (1), (2), and (4), I must reject (3).  Well, why not?

Why can't I say the following? 

3*) A philosophical thesis is rationally acceptable just in case there are some good arguments for it accepted by some competent practitioners.

Why Accept the Metathesis?

MT expresses a very bold claim; I imagine most philosophers would just deny it. To deny it is to affirm that there is at least one philosophical thesis that can be conclusively demonstrated.  Can anyone give me an example? It has to be a substantive thesis, though, not, for example the thesis that it is contradictory to hold that it is absolutely true that all truths are relative.  Here are some examples of substantive philosophical theses:

• There are no nonexistent objects.
• There are uninstantiated properties.
• There are no modes of existence.
• The properties of particulars are tropes, not universals.
• God exists.
• The soul is immortal.
• The human will is libertarianly free.
• Each of us is numerically identical to his living body.
• I am not my living body; I merely have a living body.
• Anima forma corporis.
• Die Welt ist meine Vorstellung.
• Laws of nature are just empirical regularities.
• Truths need truth-makers.
• Only facts could serve as truth-makers.
• There are no facts.
• Relations reduce to their monadic foundations.
• There are no properties, only predicates.
• The predicate 'true' serves only as a device for disquotation.
• Race is a social construct.
• Social and economic inequalities are justified only if they benefit the worst-off.
• And so on.

Comments

[The Soaring Turkey]

How about “There are property-instances”? It seems to be a Moorean fact. (I set aside the question of whether property-instances are complex entities involving universals, or simple ones, for now.)

[BV]

That things have properties is a Moorean fact. That there are property-instances is a bit of theory.

[The Soaring Turkey]

That things have properties is a Moorean fact. That there are property-instances is a bit of theory.

Where property is taken in the broadest possible sense, so that “Things have properties” isn't a substantive thesis?

[Vlastimil]

Bill,

What's 'plausibility', on your reading?

[Vlastimil]

You might want to comment on this list of alleged achievements in analytic metaphysics:
m-phi.blogspot.cz/2012/07/list-of-achievements-of-analytic.html

[Vlastimil]

Also, I am not sure in what sense (1) coheres _inductively_ with the rest of what you justifiably-believe if what you justifiably-believe includes, inter alia, that arguments for and against _justifiability of induction_ cancel out. Without that coherence, (1) would not seem rationally acceptable. In other words, isn't it self-defeating to argue for some thesis inductively while being at the same time agnostic about the epistemic value of induction?

[BV]

Excellent comments/questions, Vlastimil. You are a considerable help to me, and you are a real philosopher. I also admire you for being able to philosophize so well in a foreign language. Thanks for the link. Here is part of what I found there:

1. Leibniz’s Principle of Identity of Indiscernibles.
2. Theory of continuous quantities, from Leibniz to Robinson.
3. Frege’s analysis of cardinality.
4. Abstraction and abstraction principles (Frege, Dedekind).
5. Invention of quantification theory; predication; what variables are (Frege).
6. Existence not a predicate, rather a quantifer (Frege).
7. Concepts as functions (Frege).
8. Theory of infinity (Bolzano, Cantor).

What is meant by 'achievement'? In one sense it is an achievement to formulate and defend a thesis such as the Identity of Indiscernibles. But IdIn is not an achievement if we are looking for an established result.

IdIn is arguably false. You have heard me refer more than once to Max Black and his iron spheres. You know how the refutation goes.

So without expending any intellectual effort, I just blew #1 clean out of the water. Not a good start for this list of 'achievements'!

#6 is an achievement? Is this guy joking? Have you read my book on existence?

#7: concepts are functions?? A brilliant idea, but not an achievement in the relevant sense. Surely you are aware of the paradox of the horse.

#8: The Bolzanian-Cantorian theory of the infinite is brilliant, but William Lane Craig et al. will have no trouble raising embarrassing questions.

The list in question is the work of a dogmatist. There is no place in philosophy of dogmatists.

[BV]

Typo Man strikes again!

There is no place in philosophy FOR dogmatists.

[The Soaring Turkey]

What do you mean by conclusively demonstrated? (“A thesis, T, is conclusively demonstrated if and only if not every argument pro et contra T cancels out”?)

[The Mysterious Ostrich]

Agree with Bill on horse paradox, and IdIn.

Quantification theory is not philosophy, likewise continuous quantity.

Even some of us nominalists believe that existence is a predicate.

The Cantorian theory of the infinite depends on the existence of sets, which we Ockhamists dispute.

[BV]

>>What do you mean by conclusively demonstrated?<<

I mean that the thesis has been proven to the satisfaction of all competent practitioners. Consider the thesis T that there are abstract objects, and that some of them are (mathematical) sets. Has this been proven to the satisfaction of all competent practitioners? No, because among the Ockhamists there are some CPs. So T has not been conclusively demonstrated.

It is not an established result in the sense in which there are established results in the hard sciences.

Suppose every argument for T can be opposed reasonably and plausibly by an argument against. Then I say that T has not been conclusively demonstrated or proven.

Of course, T might nonetheless be true. But the same goes for ~T.

[BV]

>>so that “Things have properties” isn't a substantive thesis?<<

It isn't a philosophical thesis, but a pre-philosophical (proto-philosophical, pre-analytic, pre-theoretical) data sentence. It is a datum that things have properties. The cup is blue; the coffee is hot; the table is rectangular. Generalizing, things have properties.

'Things have properties' is not a philosophical thesis. The following are philosophical theses:

Properties are universals.
Properties are tropes.
Things have properties by instantiating them.
Things have properties by containing them (as on a bundle theory).
The things that have particulaers are bare particulars or thin particulars.
Things are really facts or states of affairs. (Bergmann, Armstrong)

And so on.

Each of the above is a substantive philosophical thesis.

A statement of a Moorean fact is not a philosophical thesis.

[BV]

>>The things that have particulaers are bare particulars or thin particulars.<< That should be: The things that have properties are bare particulars or thin particulars.

[BV]

Vlastimil: >>In other words, isn't it self-defeating to argue for some thesis inductively while being at the same time agnostic about the epistemic value of induction?<<

The thesis is: Every substantive philosophical thesis is such that the arguments pro et contra cancel out.

Let us assume that the arguments for and against the epistemic value of induction cancel out. Even so, it doesn't follow that induction lacks epistemic value, and I am not saying that it does.

Why can't I reasonably argue inductively while remaining agnostic about the epistemic value of induction?

[BV]

Let me repeat my challenge. Give me an example of a substantive philosophical thesis that has been conclusively proven to the satisfaction of all competent practitioners.

Example of a substantive philosophical thesis: Real time is exhausted by McTaggart's B-series.

[The Soaring Turkey]

How about “Predicate nominalism is false”? It's philosophical. (What else could a thesis about “predicate nominalism” be?) And it seems substantive. (It's the claim that an entire philosophical position is false.)

[Vlastimil]

Bill,

Thanks for the kind words.

Now, you have not said what you mean by 'plausibility' but I guess you mean something like _appearing overall to have a true conclusion_.

Next, I don't believe that here on earth there is, was, or ever will be _anything_ proven to the satisfaction of all roughly competent practitioners. Perhaps for any claim whatsoever there is or was somebody who doubted it explicitly or implicitly but was competent on your definition (a sincere truth seeker, not a quibbler or a sophist; he knows logic and the empirical disciplines that bear upon the arguments he is discussing; he is familiar with the relevant literature). So I can't meet your challenge.

Perhaps you will object that doubting certain claim (e.g. that squares are not round) rather shows that the doubter does not satisfy your definition of competence. The standard is higher, you might say, than I surmised from your statement of the definition (e.g. it is not enough to be familar with the literature in a superficial way, it is required to really understand the literature throughout). But thence this counterobjection: if the standard is higher, what not say that doubting some of the claims on your list (e.g. God exists) also shows incompetence, camouflaged by superficial or merely apparent competence?

Here's my final thought. It is not true that for any given claim on your list the arguments cancel out in the plausibility they have _for me_. Again, it may be true that for any claim there is, was, or will be somebody roughly competent who thinks, thought, or shall think that they _should_. But so what? Competence is degreed. I may have good reasons to believe that mine exceeds his, at least on a handful of themes. This idea seems implicit in the following quotation from Tim McGrew's contribution in the Four Views on Christianity and Philosophy (Zondervan 2016, 126): "Suppose I hold that P is true, and I discover that my respected colleague Dr. X disagrees. Should this discovery shake my confidence in P? In the usual sort of case, I think the answer is that it should not, or at least not much. For in the usual case I have my reasons for believing that P, and I have done my best to judge how the total evidence bears on it. If Dr. X disagrees, that fact itself gives me some reason to doubt that Dr. X is _fully_ informed or _fully_ rational with respect to this particular point. My judgement is defeasible, of course. Perhaps Dr. X will sway me with his complex, multilayered argument, or with the introduction of some new and relevant information of which I was previously unaware. And of course, if I have given the matter no previous consideration and am merely offering my casual opinion, then the case may be quite different. But when I am in possession of arguments and reasons, the mere fact that we have a disagreement generally casts more doubt on the suggestion that Dr. X is my [equally competent] peer than it does on P." (my emphasis)

Notably, defending MT, don't you think you are more competent than many other metaphilosophers, even though you'd still say they are, in a (rough) sense, competent anyway?

[Vlastimil]

Bill,

You're asking: "Why can't I reasonably argue inductively while remaining agnostic about the epistemic value of induction?"

Well, because your own reason is undecided about that value. Arguing inductively seems reasonable only if one lacks undefeated defeaters for induction itself. If one has them, arguing inductively seems incoherent, even insincere.

[The Happy Ostrich]

>>How about “Predicate nominalism is false”?

Predicate Nominalism: ‘there is nothing like scarletness’. What on earth does that mean?

What about the thesis that such statements are simply incoherent? And that the ‘arguments’ pro and contra cancel out simply because of the incoherence, or because there is no way of making them coherent except by analysing them into statements that are trivially true or false.

I would probably reject (2) above.

[The Mysterious Ostrich]

I change my mind, I reject (1). It is not clear what 'cancel out' means.

[BV]

Vlastimil,

By 'competent practitioner' I do not mean an ideally competent practitioner (ICP).

There are plausible arguments for God and plausible arguments against. Do you agree? Plausible to whom? To competent practitioners in the phil. of religion.

We agree that either God exists or God does not exist. And we agree that if God exists, then there cannot be a sound argument for the nonexistence of God. (We agree on the df. of 'sound.') But a competent practitioner who is also intellectually honest (this is one of the moral qualifications for being a competent practitioner) ought to admit that it is not known which of the plausible arguments are sound arguments. (Perhaps it is here where you begin to disagree.)

But if there were an ICP in the phil. of rel. then he would know which of the plausible arguments are sound and which are not. But I am not concerned with the ideally competent, but with us 'here below' in this 'fallen world.'

It seems to me that intellectual honesty demands of us that we admit that none of the extant arguments for and against the existence of God are conclusive.

Do you agree?

[BV]

Perhaps I should add that I am not talking about arguments in themselves in some Platonic sense as an array of abstract objects (Fregean propositions) that subsist apart from any mind. I am talking about arguments as they are involved in our life of inquiry, as they play an epistemic role in said life, as a means to knowledge or justified belief.

[BV]

>>Now, you have not said what you mean by 'plausibility' but I guess you mean something like _appearing overall to have a true conclusion_.<<

Plausibility is not truth, despite the fact that much that is plausible is true, and much that is true is plausible. The plausible may turn out to be false.

Plausibility is not possibility, despite that fact that much that is possible is plausible, and much that is plausible is possible. The plausible may turn out to be impossible.

Plausibility is not objective probability.

Plausibilty is relative, not absolute: if an argument is plausible, then it is plausible to someone, and perhaps everyone.

Plausibility is similar to epistemic possibility. If Jones is dead and buried in a cemetery, then he can't be in his office. It's impossible. But for all I know, he is in his office. So it is epistemically possible for me that Jones is in his office inasmuch as his being in his office is consistent with what I know or justifiably believe.

A proposition is plausible to me if it seems to me to be true given the rest of what I know or reasonably believe.

An argument is plausible to me if it seems to me to be sound given the (limited) rest of what I know or justifiably believe.

Can you poke holes in these explanations of 'plausible'?

[The Happy Ostrich]

Ah I see

"3) A philosophical thesis is rationally acceptable only if there is at least one good unopposed argument for it."

I.e. the arguments do not 'cancel out'. Cancelling out means there are no good unopposed arguments for the thesis. Correct?

[Vlastimil]

Bill,

Yes, your account of plausibility is fine.

No, I don't think I've encountered conclusive/compelling arguments for theism, or its negation.

I'm still not quite getting how you can insist that your inductive argument for MT is plausible -- and so not canceled out by any counterarguments? -- if you find arguments on behalf of induction canceled out. For arguments which cancel out (for you) arguments for induction should cancel out (for you) also all inductive arguments en masse, including the one for MT. Crudely put, given that induction is canceled out for you, your inductive argument for MT should be also canceled out for you, and so it should not be plausible for you.

Finally, no, I don't mean ideal competence either. I disbelieve I will ever meet an ideally competent practitioner here on earth. (No, not even the mirror.) Now, on one reading of your df of competence, two people may be competent yet not really equally competent. E.g., both are quite sincere persons yet not equally, both are quite logical persons yet not equally, both are persons quite familiar with the relevant literature yet not equally. On another reading, this is not possible. Two competent people must be equally sincere, logical, familiar with the literature etc. Time for a meaty example from the philosophy of religion: the McGrews' probabilistic argument for Jesus' resurrection (philpapers.org/rec/MCGTAF). The argument and the McGrews' replies to objections -- i.e. replies included in the linked paper, or replies offered on the Web or in correspondence -- have always seemed much more plausible than the raised objections themselves. All the objections that I've seen have been fallacious or historically uninformed. I guess it's precisely here where you and I would disagree. Anyway, in case I am right, even if all the debaters were competent on the first reading of your df some might not be competent on the second one. And here's my challenge: can't you really think of just one substantial philosophical argument which has had in your eyes the same dialectial stamina that the McGrews' argument has had in mine?

[The Soaring Turkey]

This statement is awkward in the first place:

‘there is nothing like scarletness’

“There is nothing resembling scarlet.”
“There is nothing resembling scarlet, and scarlet doesn't exist.”
“There is nothing resembling instances of scarlet.”
“There are no instances of the colour scarlet, and nothing resembling them.”

But competent practitioners in the relevant subfield have more or less standard meanings for terms like “scarletness”.

Is there more to your point that I'm missing?

[BV]

V. says >>I'm still not quite getting how you can insist that your inductive argument for MT is plausible -- and so not canceled out by any counterarguments? -- if you find arguments on behalf of induction canceled out. For arguments which cancel out (for you) arguments for induction should cancel out (for you) also all inductive arguments en masse, including the one for MT. Crudely put, given that induction is canceled out for you, your inductive argument for MT should be also canceled out for you, and so it should not be plausible for you.<<

Suppose I reformulate MT as follows:

The problems of philosophy are insoluble: not soluble by us in this life to the satisfaction of all competent practitioners.

My argument for this is inductive: no phil. problem has ever been solved to the satisfaction, etc. This includes the problem of justifying induction. But I don't need to solve the latter problem to employ induction. Induction can be a reasonable procedure even if no has ever explained how it could be reasonable.

Can you rebut this?

Second, can you give me an example of a substantive phil. problem that has been solved to the satisfaction of all competent practitioners even if we confine ourselves to those in the actual world?

[The Happy Ostrich]

>>This statement is awkward in the first place
I took it verbatim from the SEP, which is meant to characterise ‘predicate nominalism’. It is unintelligible to me. ‘Scarlet doesn't exist’ is another.

>> Is there more to your point that I'm missing?
My point is that if there is a dispute between two parties, it is necessary to formulate the proposition in dispute, and that proposition has to be intelligible.

[Vlastimil]

Bill,

Can induction be a reasonable procedure even if no has ever explained how it could be reasonable? It can if reasonability is externalist. Or if induction is intuitive, undefeated intuitive procedures are reasonable and induction is an undefeated intuitive procedure. But do _you_ think that reasonability is externalist? Or that induction is undefeated?

Secondly, can I give you an example of a substantive phil. problem that has been solved to the satisfaction of all competent practitioners even if we confine ourselves to those in the actual world? Give me a readily applicable criterion of competence -- such that it will enable me to tell who's competent on your df of competence and who isn't -- and I will give you my answer.

[The Soaring Turkey]

Ostrich writes: I took it verbatim from the SEP, which is meant to characterise ‘predicate nominalism’. It is unintelligible to me. ‘Scarlet doesn't exist’ is another.

Suppose there is a room full of ontologists discussing the problem of universals. You would say that a significant number of them are engaging in a sort of grammatically correct babble at least part of the time?

I'm nowhere near as familiar with philosophy of logic and language literature as you are, but the sheer number of competent practitioners who don't find the sentence unintelligible gives me pause.

Perhaps I am just a funny bird.

[The Happy Ostrich]

>>the sheer number of competent practitioners who don't find the sentence unintelligible gives me pause

That is an interesting problem. I mention it here.