Thursday, November 03, 2011

Truthmakers and infinite regress

Vallicella has a post here about my post here. Of my argument he says “this is a terrible, a thoroughly and breath-takingly rotten, argument which is why no one in the literature (to the best of my knowledge) has ever made it.” Don’t hold back, Bill!

Actually my argument has a close affinity to Frege’s argument against the correspondence theory of truth, but never mind. Let’s restate it. Let’s suppose that any sentence of the form “S phi's” has a truthmaker. But that truthmaker cannot be S itself, for the reasons Vallicella adduces in an earlier post. If I understand his argument, it is that if phiis ‘sits’, it is contingent whether Socrates is sitting or not, so the truthmaker for ‘Socrates is sitting’ cannot be Socrates himself.

That is his argument. I merely extend it to the verb ‘exists’. Let phi be ‘exists’. Since it is contingent whether any object (apart from God) exists or not, it follows – if Bill’s argument is valid – that the truthmaker T of ‘S exists’ is different from S itself. And then we get an infinite regress, for ‘T exists’ must also have a truthmaker. By equal reasoning, the truthmaker U of that sentence must be different from T, and so on.

I am not saying that Bill’s argument is valid. I am saying that, if it is valid, then equally my argument is valid, unless he shows how the verb ‘exists’ differs in any way from verbs like ‘sits’. Which I don’t think he has done.

He might argue that ‘exists’ is not a predicate, whereas ‘sits’ is. I reply, it is a predicate. ‘- exists’ is satisfied by Obama, but not by the Tooth Fairy. Perhaps there are other arguments that would justify his conclusion. But the point is, he has to give one.

Another argument against truthmakers is that if ‘it will rain on Friday’ has a truthmaker, then it must be a presently existing truthmaker (for the sentence, if true, is true now). So, today being Thursday, the truthmaker for ‘it will rain on Friday’ exists now. By the same reasoning, it had a truthmaker yesterday, given that if ‘it will rain on Friday’ is true today, the same sentence must have been true yesterday. But we cannot change the past. Therefore, if truthmakers for future tense statements exist we cannot determine what happens in the future. But we can determine what happens in the future. Therefore there are no truthmakers for future tense statements, and if so, what reason is there to believe they exist at all?

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36 Comments:

Blogger Anthony said...

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12:37 pm  
Blogger David Brightly said...

>> Which I don't think he has done.

No, but there's an argument just under the surface. He says, I think, that a truthmaker for P(s) is an entity t such that 't exists' --> P(s). This rules out s as a truthmaker when P is 'sits' but not when P is 'exists'.

1:03 pm  
Blogger J said...

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3:15 pm  
Blogger J said...

Ah I thought this was about ..scholastic mysteries (ie, the truth-giver as in....what maketh an acorn into ..an oak).

Now its just back to the old truth-verification discussion.

In that sense I wd agree (reluctantly) with Mav P, that the Truth of an ordinary proposition (or statement) depends on...an observable state of affairs, extralinguistic "fact" , at least at one point (one doesn't need to keep checking the ...boiling point of H20..do we...maybe a Popperian might) --that is, except for analytical propositions (ie, logical/math. tautologies). ..nearly Tractarian-or something.

(Re the ontological argument, see Kant--I wd have to agree saying "X exists "(a quantifier, raht) is different than "X sits/eats. reads MeinKampf etc.' Re Tony_Ayn--even a broken clock is right two times a day)

3:18 pm  
Blogger Edward Ockham said...

David: "No, but there's an argument just under the surface. He says, I think, that a truthmaker for P(s) is an entity t such that 't exists' --> P(s). This rules out s as a truthmaker when P is 'sits' but not when P is 'exists'. "

If you look at his blog, where he is discussing with Peter Lupu, that's not the reason he is giving. I don't follow the reason he is giving.

4:26 pm  
Blogger Edward Ockham said...

This is a logic blog, and ad hominem such as calling someone a troll, is a logical fallacy. Can people avoid all forms of logical fallacy please, or I will block them.

Obviously some forms of logical fallacy are hard to spot and to correct, but this one isn't.

4:28 pm  
Blogger J said...

Are you referring to me?I did not write "troll," at least here. But I did say....the .."Truth of an ordinary proposition (or statement)--say "OJ was guilty"-- depends on...an observable state of affairs, extralinguistic "fact" (and I might have added... evidence), at least at one point." Do you agree or disagree with that, Ed-Ock. (tho' there are propositions--tautologies, or identities of log.math.--that do not)

4:43 pm  
Blogger J said...

re Existence, you do know what existential and universal quantification are, right Ed-Ock? So ,in terms of predicate logic, ""X exists" does have a meaning quite different than an ordinary verb-predicate as .."sits/eats/plays the fiddle",etc. As in...some (at least one X) As per the old King of France klassic (and..examining reality--observation--we note no King of France (well, the ultra-skeptic might say..could there be a King of France in orbit around Antares, or other parts of the universe??? Unlikely. But not impossible perhaps). Ergo, any predications of "King of France" (he's bald etc) are false, since the statement is false . Bertie to the rescue! Doe the Mav P agree? I doubt it.

5:09 pm  
Blogger J said...

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5:14 pm  
Blogger Anthony said...

>> If you look at his blog, where he is discussing with Peter Lupu, that's not the reason he is giving.

It's one of the reasons he is giving. However, he is also saying other things. Among them, that existence is not a predicate (he says "'Tom is tired' is a predication whereas 'F exists' is not a predication but an existential sentence").

Then, finally, he says that the "TM principle applies only to contingent sentences." First of all, here he is going much further than just saying that truthmakers exist. He is saying (at least implying) that truthmakers exist for all contingent sentences, and that truthmakers do not exist for all non-contingent (which I assume he considers "necessary") sentences.

That would be interesting if it were true, as it would show that there is indeed a distinction between the contingent and the necessary.

6:23 pm  
Blogger Anthony said...

Are we allowed to call each other cyberpunks?

6:50 pm  
Blogger J said...

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6:52 pm  
Blogger J said...

""it would show that there is indeed a distinction between the contingent and the necessary.""

Ah yes, now Moe grabs his hammer and smashes in Leibniz's bust.

7:09 pm  
Blogger Anthony said...

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8:47 pm  
Blogger Anthony said...

This comment has been removed by the author.

9:02 pm  
Blogger Anthony said...

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9:28 pm  
Blogger Edward Ockham said...

>>So ,in terms of predicate logic, ""X exists" does have a meaning quite different than an ordinary verb-predicate as .."sits/eats/plays the fiddle",etc.

Yes I'm aware there are problems there.

10:51 pm  
Blogger J said...

As far as their treatment of "facts" (and the perception thereof) goes, Mav P's accounts are not much superior to Aynthony's--naive empiricism in both cases (at least in regard to BV's "truthmaker" schtick). In both cases, the perceived phenomena (or sense data as Russell called it) may or may not be fact, as in true/accurate (even when it is been put in language as a report, declaration of "fact" etc). It might be a hasty conclusion sort of thing--Smoke most likely means fire, but not always (its...a car with bad engine, burning oil etc..not a brush fire). Pretty obvious Phil 101 issue--ie, the perception of an event X, or apparent event may not be the event itself (false accusations are like this as well--ie, one "Billy V' appears on Amber Alert as a suspected sex offender, his face posted on news everywhere--but lo and behold! he has an airtight alibi--he was at Dennys, and the dishwasher vouches for him). History itself presents the same issue (...prove "Shakespeare" existed, and the "facts" of his life, ie wrote plays ,etc---yes highly likely..but again the claims are themselves contingent and there are alternative candidates for who wrote the plays-- DeVere, IIRC)

11:02 pm  
Blogger Anthony said...

The question is not whether or not perceptions are infallible. Optical illusions certainly occur (as well as auditory illusions, and other-sensory illusions). Occasionally one may perceive that object A is in front of object B, when in fact object B is in front of object A. For most people this is relatively infrequent, though. And it doesn't change the fact that instances of relations (e.g. that one item is in front of another item) can be perceived. It merely means that perceptions are not infallible.

But percepts are not the same as conclusions. If one perceives smoke, and concludes that there is fire, the latter is not a percept. As I said in my clarification, my thesis is that one can sometimes perceive some facts, not that all facts are perceived.

Perception is the base of knowledge. All knowledge is based on perception. But knowledge doesn't stop at perception. As humans we also have the ability to form concepts, and thereby to obtain knowledge beyond that which we can directly perceive.

11:34 pm  
Blogger J said...

It merely means that perceptions are not infallible.

and had you ever read a page of Hume you'd realize (or perhaps not)...knowledge via experience is not necessary, but contingent. Perhaps something happens ...all the time, AFAWCT so we call it "true" (ie...ie, the proposition that "the boiling point of water/H20 at sea level is 100 C" IS true--but in 10,000 years?? Who knows) but still not logically necessary (as mathematical truths are,or say a tautology). Consider the differences between..the "truths" of the periodic table, "economics" and ..weather forecasting (hardly regular ,or even predictable much of the time). Ergo, Probability usually an issue as well. Hume's not the final word (as Kant realized)...but an important word(especially to ...dogmatists of various types--even the atheist-materialist sort). But for the naive empiricists (you)...seeing is believing.

12:00 am  
Blogger Anthony said...

You juxtapose knowledge obtained via observation vs. "mathematical knowledge". But mathematical knowledge *is* obtained via observation in the exact same way as any other knowledge. Mathematical knowledge is not knowledge but for the observable concretes from which it is abstracted. The Pythagorean theorem has no meaning but for the physical validity of the postulates it is based on. Specifically, the parallel postulate, which not only "might not be" true in 10,000 years, but as was postulated by Einstein and proven by experiment, is only approximately true right here on earth today.

1:40 am  
Blogger Anthony said...

"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." - Albert Einstein, Sidelights On Relativity

1:50 am  
Blogger J said...

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7:31 am  
Blogger J said...

Pythagorean theorem has no meaning but for the physical validity of the postulates it is based on.

Ed-Ock.'s site (AFAICT) is about philosophical issues --not the Carl Sagan-ish pop-science--is it not, Ed-Ock?--such as those related to analyticity/a priori and universals (or not), yet even in terms of a sort of primitive-functionalism, you're mistaken. Gen.Rel. applies at vast distances, with strong gravitational fields. Newtonian mechanics (and euclidian space) still applies and works in earth's gravity. When designing/building a skyscraper the architects/engineers are using euclidian space (and axioms).
Like playing chess with someone who doesn't know how the pieces move. Horsie?

9:06 am  
Blogger Anthony said...

General relativity applies at all non-quantum distances, and it differs geometrically from Newtonian physics in all but inertial frames of reference. Newtonian physics "works" here on earth, which is not an inertial frame of reference, but only approximately. There are small errors.

This is very much a philosophical issue. I highly suggest you read "Geometry and Experience", which is the second lecture in "Sidelights on Relativity", by Albert Einstein. It is available free at gutenberg (http://www.gutenberg.org/cache/epub/7333/pg7333.html). And it is very much a lecture on epistemology, at least the first half of it. Einstein's theories of relativity are very much epistemological.

I want to follow with a quote, but there's just so much from that lecture to quote. It's only a few pages long. Maybe I'll make some out of context snippets to try to pique your interest.

"Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things."

"The older interpretation:—Every one knows what a straight line is, and what a point is. Whether [...] is not for the mathematician to decide. He leaves the question to the philosopher. [...] the axiom stated above is, like all other axioms, self-evident, that is, it is the expression of a part of this a priori knowledge."

"The more modern interpretation:—Geometry treats of entities which are denoted by the words straight line, point, etc. These entities do not take for granted any knowledge or intuition whatever, but they presuppose only the validity of the axioms, such as the one stated above [...] as void of all content of intuition or experience." "Schlick in his book on epistemology has therefore characterised axioms very aptly as 'implicit definitions.'"

"But a presentation of its principles thus clarified makes it also evident that mathematics as such cannot predicate anything about perceptual objects or real objects."

"Yet on the other hand it is certain that mathematics generally, and particularly geometry, owes its existence to the need which was felt of learning something about the relations of real things to one another." "To be able to make such assertions, geometry must be stripped of its merely logical-formal character by the co-ordination of real objects of experience with the empty conceptual frame-work of axiomatic geometry. To accomplish this, we need only add the proposition:—Solid bodies are related, with respect to their possible dispositions, as are bodies in Euclidean geometry of three dimensions. Then the propositions of Euclid contain affirmations as to the relations of practically-rigid bodies."

"Geometry thus completed is evidently a natural science; we may in fact regard it as the most ancient branch of physics. Its affirmations rest essentially on induction from experience, but not on logical inferences only."

"I attach special importance to the view of geometry which I have just set forth, because without it I should have been unable to formulate the theory of relativity."

"If we deny the relation between the body of axiomatic Euclidean geometry and the practically-rigid body of reality, we readily arrive at the following view, which was entertained by that acute and profound thinker, H. Poincare"

"Geometry (G) predicates nothing about the relations of real things, but only geometry together with the purport (P) of physical laws can do so."

"Envisaged in this way, axiomatic geometry and the part of natural law which has been given a conventional status appear as epistemologically equivalent."

"First of all, an observation of epistemological nature. A geometrical-physical theory as such is incapable of being directly pictured, being merely a system of concepts."

11:33 am  
Blogger Anthony said...

The errors are very very small. So yes, when designing/building a skyscraper the architects/engineers are using euclidian space (and axioms). But when designing/building a global positioning satellite system which has to maintain accuracy to the nanosecond over a span of decades, the architects/engineers are using non-euclidean space. These engineers know that the Pythagorean theorem, while a great approximation of reality for so many typical cases, is based on a flawed premise (the parallel postulate) and thus does not work for the detailed calculations they must make. Or, at least, these engineers apply the principles based on that knowledge, which was, I believe, first grasped by Albert Einstein.

Again, read the Einstein lecture on Gutenberg. I don't think it'll be completely over your head.

(And I don't say I agree with it in its totality. However, I think Einstein was on exactly the right track in his attempt to bring Mathematics back to reality, and in his insight that Geometry is, or at least ought to be, rooted in concepts formed by induction on observation, and not on non-inductive axiomatic fiat.)

11:52 am  
Blogger Anthony said...

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12:47 pm  
Blogger J said...

You don't need to spam away--just link to it.Or not
The attempt at an empirical grounding of Euclid mostly failed--most analytical types agreed, and other methods were used via first order logic and set theory(tho' like Newton mechanics, Euclidian axioms still work on earth, ie bridgebuilding (perhaps NASA-Co might have a few issues--either way you don't understand the functional points whatsoever)

Gen. and Spec. Rel. do pose philosophical issues--and even Einstein refers to Kant and even Hume quite often (and poor Schlick, analytical phil., whom AE quotes). But you don't understand what those issues are. (for that matter Spec.Rel. is not accepted in all quarters, and Einswine himself did not accept the Big Bang). So like start with that--or say your first syllogism--since this is about philosophy--not gee-willy pop-science factoids.

1:13 pm  
Blogger Anthony said...

Yes, Newtonian Mechanics work in certain contexts. And yes, Euclidean geometry works in certain contexts. That is my point. The periodic table works in certain contexts. Economics works in certain contexts. Weather forecasting works in certain contexts.

When the concepts are formed properly, and reason is used upon those concepts, they all work...in context.

(I have no idea what you are referring to by spam. Is it that I provided a URL? Am I not allowed to provide URLs?)

Yes, Einstein refers to Kant and to Hume and to other philosophers, in some cases positively, and in some cases negatively. And sometimes he was right, and sometimes he was wrong, and through his life he vacillated back and forth on certain key philosophical issues. But that is not my point. He has, I believe, always and consistently rejected Kant's doctrine of the a priori (at least implicitly, and later explicitly), but even that is not my point. My point is that the genius in Einstein's theory of relativity (especially the general theory) stemmed from the realization that so called "mathematical truths" do not hold a special untouchable place in gaining knowledge about reality. Whether Einstein knew it or not is not my point (though at least at some point in his life he did).

2:24 pm  
Blogger J said...

Gen.&Spec/Rel. depended upon mathematical truths, obviously--Minkowski's spacetime and the Lorentz transformation--and the coordinate system was still Cartesian. (And..Ayn Rand's axiom of "Existence exists!" was not involved). I never claimed Euclid was the final word on all mathematics or physics--that wasn't the point on the Pythagorean theorem, which eludes you (or say Frege's point in his essay "The Thought", which was about analytical-a priori truth itself--one might say formalism--, as opposed to knowledge derived from sense impressions) .

( Ed Ock perhaps you note Mav. Bill misreading Frege's on "the Thought" essay. Frege was a great logician IMO not quite a great epistemologist. But the essential point--quite platonic-- is that..knowledge via sense impression/experience does not provide a solid footing for knowledge, and truth whatever it is, resides in our "inner world"--not exactly no "truth bearer" or a regress. A somewhat typical formalist view. Frege doesn't refute the "correspondence theory" or via Quine ..observation statements, or even verification per se--he points out the obvious--empirical knowledge is contingent (ie non-necessity of empirical claims/propositions). One wonders if Frege (or Maverick for that matter) had ever read say Hume's Enquiry CHU (not that he would have cared for it)

4:19 pm  
Blogger Anthony said...

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6:05 pm  
Blogger Anthony said...

I thought you had juxtaposed "mathematical truths", such as the Pythagorean theorem, which you said were "logically necessary", against scientific truths, such as Newton's laws of motion, which you said were "contingent".

My point was, and is, that to the extent that these truths represent reality, and not fantasy, there is no distinction. (Actually I suppose that even to the extent they represent their own little fantasy worlds, there is no distinction.)

6:06 pm  
Blogger J said...

My point was, and is, that to the extent that these truths represent reality, and not fantasy, there is no distinction.

There you go again, Aynthony, mumbling about an issue you don't understand--ie, the analytical synthetic distinction. Euclidian geometry is not merely a representation of what you take to be "reality", is it--nor is algebra, trig, calc. (any integrals hanging on elm trees up there in Schmutzberg? Nein). Any perfect circles, triangles, or integers in nature?No. Maybe try Herr Doktor Frege's essay "The Thought" and offer a rebuttal--going to be a bit more challenging than yr fave Star Trek rerun. Or..Euclid. The issue is far more difficult than you realize.

12:52 am  
Blogger Anthony said...

Euclidian geometry, algebra, trig, and calc all deal with abstractions of reality. Abstractions don't hang on elm trees. But they aren't fantasies either.

1:03 am  
Blogger J said...

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3:18 am  
Blogger J said...

Actully Ed-Ock, shouldn't we question , one, whether Frege meant infinite regress, and two, whether Frege was correct? He said truth collapses, and in short we might infer that he's saying...empiricism (or is it..induction) fails--snow is white sometimes, tomorrow not. Maybe it has soot in it ("snow is white" is not a great example either-- what about probability, etc) But thats not a regress, more like...endless verification (ie sociologists often do that--do the same study every few years, since data changes etc) it's hardly a lengthy refutation--jus the unreliability of sense impressions, contingency, etc., and the superiority of his rational, formalist views. Provincial IMHO (like the writing of the..putative Fregean Billy Maverick)

4:04 am  

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