Epistemology and Logic

Stephen Boydstun's picture
Submitted by Stephen Boydstun on Sat, 2009-02-28 17:28

One concept of an arbitrary claim would be: Start with the grammatical form of some type of declarative sentence such as “Some ___ are ___ because of ___.” Select entries for the blanks at random, constrained only by correctness in their grammatical part of speech. For example: “Some mountains are mutants because of musicality.” There are ready reasons for saying such a claim is not sensible. Mountains are not living, so not mutants. Mountains are not vocal, so not musical. This arbitrary claim is doubly false (at least doubly, likely more). It is also not sensible, because one who knows the meanings of the terms knows this way of connecting them in an assertion yields a falsehood.

 

Let’s constrain the arbitrariness in selecting entries for the blanks just enough to avoid that kind of ready dissolution. “Some mountains are elevated because of magnetic properties of their minerals.” This assertion is dubious and somewhat ambiguous, but it is sensible, at least on its face. The ambiguities in the statement might be cleared up, the truth of the claim investigated. Meantime, there is no evidence for the truth of the claim.

 

The type of arbitrary claims that Leonard Peikoff treats in Objectivism: The Philosophy of Ayn Rand are claims that could be generated as in the preceding paragraph. They are claims devoid of evidence (163). But Peikoff’s (and Rand’s) target sort of arbitrary claims are a subclass of those. They are arbitrary claims loaded with shielding against rational assessment for truth. The particular claim I generated concerning the elevation of mountains does not imply or insinuate that its truth cannot be assessed by further observation and logical reasoning. Under Peikoff’s divisions, my arbitrary claim generated in a quasi-random way is not an arbitrary claim in his sense.

 

Should we say that it is possible that some mountains are elevated because of magnetic properties of their minerals? This is definitely an implausible cause of mountain elevation. We have well-founded accounts already of how mountains are formed. The forces figuring in those accounts are so much stronger than any local naturally occurring magnetic fields we have encountered on earth. The proposition is implausible. It is so implausible, I would not encourage its investigation.

 

Are we ignorant of whether some mountains are elevated because of magnetic properties of their minerals? No. We know that it is very probably false. Under Peikoff’s divisions, we can say that the negation of the claim is probably true. We do not say the claim is possibly true, for there is no evidence at all in favor of it (176–78).

 

Epistemologically speaking, a claim whose negation is probably true could itself be not possibly true. Logically speaking, it doesn’t work that way. If not-A is probably true, then not-A is possibly true and A is possibly true.

 

What is the difference between epistemology and logic, particularly the difference underlying their different principles in the preceding paragraph?


( categories: )

Epistemic Possibility

Stephen Boydstun's picture

Thanks, Aaron and Kasper and Lindsay.

~~~~~~~~~

It is typical for philosophers today to distinguish between not only logical and epistemological possibility, but between those two and conceptual possibility. The last is a valuable mode of reasoning where we consider what presupposes what. I would classify this sort of conceptual possibility as a type of logical possibility. So, to say “Mutation presupposes reproductive life, therefore no mountains are mutants” is to say mutant mountains are not logically possible.

~~~~~~~~~

In their Introduction to Conceivability and Possibility, Tamar Gendler and John Hawthorne distinguish various concepts of epistemic possibility that have been offered. Graded from most permissive to least, they are:

1.    P is epistemically possible for S just in case S does not know that not-P.

2.    P is epistemically possible for S just in case S could not reasonably be expected to ascertain not-P on the basis of what S knows.

3.    P is epistemically possible for S just in case S’s evidence does not warrant S’s believing not-P.

4.    P is epistemically possible for S just in case P is consistent (metaphysically compossible) with all that S knows. (p. 3)

I am reluctant to make epistemic possibility fundamentally relative to particular knowing persons. I am reluctant to accept the “possible for S” restriction in all those formulations. A more impersonal sense of epistemic possibility seems useful. It is agreed all around that logical possibility is not relative to particular persons; either no contradiction can be proven from P using standard rules of deduction or a contradiction can be so proven. In moving from logical possibility to epistemic possibility, I would not make so strong the relativity to a particular knowing subject.

I would speak of epistemic possibility relative to human knowledge, rather than relative to only the knowledge of the individual. Human knowledge is the ultimate field of play for epistemic possibility. When one takes on a proposition such as “Some mountains are elevated because of magnetic properties of their minerals,” one will begin reviewing what is known about the processes of mountain formation. That done, I propose a fifth rule, rather than any of the earlier four:

5.    P is epistemically possible just in case: P is consistent with all that is known about its topic (and all presuppositions of that knowledge), and there is some evidence for P.

If those conditions were met, it would be the case that P lies, with objective probability, to the true-side of coin-flip randomness; it would be objectively more likely true than false. For the particular P about mountains under consideration, (5) is not satisfied. I’ll characterize it as very unlikely true and not an objective possibility.

"Are we ignorant of whether

Aaron's picture

"Are we ignorant of whether some mountains are elevated because of magnetic properties of their minerals? No. We know that it is very probably false. Under Peikoff’s divisions, we can say that the negation of the claim is probably true. We do not say the claim is possibly true, for there is no evidence at all in favor of it (176–78).

Epistemologically speaking, a claim whose negation is probably true could itself be not possibly true. Logically speaking, it doesn’t work that way. If not-A is probably true, then not-A is possibly true and A is possibly true.

What is the difference between epistemology and logic, particularly the difference underlying their different principles in the preceding paragraph?"

I think it is just how 'possibly' can be ambiguous because of different connotations between strict logic and the epistemological case. In logic, A with 99.99999% change and not-A at 0.00001% are both strictly 'possible' - but referring to them both with solely that term loses key information of degree.

I recognize the use of such strict usage in logic, but it doesn't make sense to pull the term 'possible' (without context of likelihood) then out to the realm of macroscopic facts of the mountain example. In common usage we'd simply never use the word 'possible' to describe 'something not known 100% to be at odds with the laws of the universe - but so unlikely as to not be worth investigation', which is what I believe describes your mountain/magnetic property example.

I think I've had some of the same questions on the flip side concerning 'certainty' and 'fact' as in OPAR. How can something be certain if you haven't checked everywhere in the universe, if there's any other remote possibility, etc.? I have largely felt settled though after coming to recognize them as roughly implying 'known beyond reasonable doubt', not 'known beyond any conceivable doubt'. The question of 'certain' at <100% or 'possible' at near 0% are interesting though, and I'm intrigued with this (I haven't read your follow ups yet on this thread, just the starting post).

Aaron

Cashing Out

Stephen Boydstun's picture

Let it be proposed that some odd counting numbers n are such that [(n·n) – 1] is not evenly divisible by 4 (scroll to page 46). Is this a logical possibility? If we say Yes, what do we mean? We mean there is no manifest falsity (such as a self-contradiction) in the stated conjecture. In ordinary parlance, that is what we mean by logical possibility. It is a very weak sense of logical possibility. If we conclude that the probability of the conjecture’s truth is not zero, based simply on this weak requirement, then we are dealing only in subjective probability.

An additional sense in which such a conjecture is said to be logically possible is that the proposition is either true or false. Those are the logical possibilities for it.

Yes, but looking at the methods of mathematics more particularly, I see a distinct and stronger candidate notion of logical possibility: where it has been demonstrated that the conjecture cannot be shown to be false by reduction to contradiction. (On this and other proof methods, see Cupillari.) I do not recall having ever seen such a demonstration, except, of course, as an implication of a proof of the conjecture (for the present conjecture, either coming up with at least one such odd counting number or proving the existence of such numbers without locating any of them) or of a proof that the conjecture, though sensible, can be neither proven nor disproven. (On the latter sort of situation, see Chaitin.) Were this notion of logical possibility sound for mathematics, it would be appropriate to designate it epistemological possibility for mathematics, to set it beyond mere coherence and logical bivalence.

Now if we have a proof of the conjecture, then we can say it is a logical possibility not only as a subjective estimate of non-zero probability, but as an objective probability equal to unity. That would only be saying that the actual is really possible. My candidate concept of epistemological possibility in mathematics is idle for the case: lack of proof, then proof. For the case of a conjecture that definitely proves to be neither provable nor not provable, the idea of logical possibility in either a subjective or an objective sense seems inappropriate because there is no prospect of an actuality for the matter. So I don’t see a place for distinctively epistemological possibility in mathematics.

Turn to logical possibility in natural science. There we do not prove simply by deductive and mathematical demonstrations. For counterexamples to a conjecture about nature, we do not look mostly inward. Our proofs are bonded through examination of nature. For natural science, a notion of epistemological possibility elaborated over logical possibility seems fitting.

A conjecture such as my quasi-random zero-evidence one about mountains is a logical possibility in the weak sense that evidence for it might be found that bears on the objective probability of its correctness and in the weak sense that it is either true or false. Prior to any evidence for or against the conjecture, talk of logical possibility pertains only to subjective probability and bivalence. A coin-flip, of course, has nothing to do with the truth of the matter; it is not cognitive. There is a concept of logical possibility, in a stronger and objective sense, meaningful once some evidence has been adduced, and this concept is not idle provided the evidence does not completely dispose the conjecture.

Call epistemologically possible a conjecture, about nature, of which it can be said to which side of coin-flip randomness its objective probability lies. For such a conjecture, there is evidence. Conjectures sensible on the surface, but not meeting the criterion just stated are to be classed not objectively possible in this stronger, epistemological sense. For them there is as yet no contact with objective probabilities. (On the two types of probabilities, see Jetton.)

I want to reverse something I wrote in the initial post. I said that even though, upon reflection, we know that the negation of my conjecture about mountains is very probably true, hence possibly true, we should not say it is possibly false, from the standpoint of epistemology. That is incorrect. Once we are giving reasons for thinking my conjecture probably false, in an objective sense of probability, it is sensible to say, epistemologically, my conjecture is possibly true (in a vanishingly small way).

Tying a loose end, I say there is no counterpart in the investigation of nature to that mathematical case for which the idea of logical possibility—whether cashed in only subjective or also in objective probability—is inappropriate. There are no proofs that anything about nature is unprovable one way or another. Seeming cases to the contrary are signs we need to reform some concepts.

Two Clicks

Stephen Boydstun's picture

Here are some remarks from Leonard Peikoff on Possible, in exposition of Rand’s view.

 

"Where's the Bridge? Epistemology and Epistemic Logic"

Vincent F. Hendericks and John Symons

Philosophical Studies (2006)

Getting Started

Stephen Boydstun's picture

The usual broad definition of epistemology is that it is the theory of knowledge (FF 63). It is taken to include formulation and defense of the proper definition of knowledge and how knowledge is attained. This includes diagnosing pseudo-knowledge and deflating skepticism. From Protagoras to Rand, philosophy has included theory of what knowledge amounts to. Epistemology is older than its name.

Rand defined knowledge as “a mental grasp of a fact(Drunk of reality, reached either by perceptual observation or by a process of reason based on perceptual observation” (ITOE 45). The mental grasp spoken of here is a conceptual grasp. The product of the grasp is a truth (AS 1017; ITOE 63; a, b). Knowledge is restricted to certain sorts of truths, namely, those reached by perceptual observation or by a process of reason based on perception observation. In Rand’s writings and in Peikoff’s OPAR, the character of perceptual observation (c) and the said processes of reason receive further specification.

Among the processes of reason is deductive logic. Reason identifies and integrates perceptual information (AS 1016), and the method of reason is logic (FF 62), which Rand defined in general form as “the art of non-contradictory identification” (AS 1016). Logic pertains to reality, on Rand’s view and mine. “Logic has a single law, the Law of Identity, and its various corollaries” (PWNI 15). The law of identity, in Rand’s full sense, applies richly to reality (d, e, f, g).

Because there are no contradictions in reality (AS 1016), the principle of non-contradiction (PNC) can help one uncover falsehoods among ones beliefs. PNC can be used to improve the truthfulness of ones set of beliefs. Under the assumption that those beliefs are true, PNC and the rules of deductive inference tell one which of their implications cannot be false. PNC and rules of deduction can inform experimental inquiry. PNC and rules of deduction, together with the principles of mathematical induction, can lead to mathematical discoveries.

There are additional canons, epistemological ones beyond those of logic (and mathematics), for maintaining, improving, and expanding one’s knowledge. There are canons for rational belief beyond “disbelieve falsehoods” and conformance with principles of deduction. There are propositions that should be disbelieved even though they are sensible on the surface and logically possible. I submit that what is asserted by such propositions is to be judged not possible from the wider standpoint of epistemology.* Such is my candidate quasi-arbitrary, zero-evidence proposition: “Some mountains are elevated because of magnetic properties of their minerals.” 

This is a start.

 

*Notice that there are mathematical propositions that seem logically possible, yet can be proven to be false using mathematical induction.

Ha!

Lindsay Perigo's picture

The fact that they are used as such doesn't make them so, as the disastrous consequences should indicate.

Tuesday's fine. SOLO-PM me, or call or text me on my mobile.

See you Tuesday?

Kasper's picture

I would beg to differ.
Whims are constantly used as tools of cognition. They are inappropriate and improper but are used.
Reason uses logic as a tool of cognition - the only demonstrably proper tool.

Kasper

Lindsay Perigo's picture

"Whims" are not tools of cognition.

But while I'm in Auckland, do come up and see my whims sometime. Evil

(Oh, Christ, I hope no Americans read this. Eye )

Stephen

Kasper's picture

I am far too inexperienced for this one.

But

Isn't epistemology the title for the process which investigates how humans acquire knowledge?

Logic on the other hand is one of many methods of cognition. Other methods would be whims for example.

So the difference would be one investigates 'what' it is and the other is the 'how' it works

Comment viewing options

Select your preferred way to display the comments and click "Save settings" to activate your changes.