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RolfAndreassen12y00

[I]t would be very strange to say that I don't have beliefs with substantive content about, say, the the Fundamental Theorem of Algebra.

I am, nonetheless, willing to bite this bullet. You do not have beliefs about the FTA; you have opinions on the usefulness of the definitions which imply it. Moreover, your phrase "deductive evidence" is an oxymoron. Deduction is not evidence, it is tracing the consequences of definitions; definitions are not beliefs. All theorems are in some sense tautologies, that is, they are inherent in the axioms. So a "belief about" a theorem is actually a "belief about" the axioms, and this is precisely what I'd like to forbid.

asr12y00

You do not have beliefs about the FTA; you have opinions on the usefulness of the definitions which imply it.

This is false as a psychological description of my personal state of mind. I don't know the precise definitions that entail the FTA and I certainly don't know a proof. (In particular, I don't think I could give you a correct construction or definition for the real numbers.) I believe in the theorem because I've seen it asserted in trustworthy reference works. Somebody somewhere might have beliefs about the theorem that were tied to their beliefs... (read more)

3TheOtherDave12y

Do I similarly not believe that there isn't a piece of chocolate cake floating in the asteroid belt? Cuz it sure feels like I believe there isn't a piece of chocolate cake floating in the asteroid belt. And if I don't believe that proposition, what is the thing I'm doing to it that feels so much like belief, and why does it feel so much like belief?

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8 Attempting to rescue logical positivism

by RolfAndreassen

25th Apr 2013

1 min read

8

Very brief recap: The logical positivists said "All truths are experimentally testable". Their critics responded: "If that's true, how did you experimentally test it? And if it's not true, who cares?" Which is a fair criticism. Logical positivism pretty much collapsed as a philosophical position. But it seems to me that a very slight rephrasing might have saved it: "All _beliefs_ are experimentally testable". For if the critic makes the same adjustment, asking "Is that a belief, and if so -" you can interrupt him and say, "No, that's not a belief, that's a definition of what it means to say 'I believe X'."

A definition is not true or false, it is useful or not useful. Why is this definition useful? Because it allows us to distinguish between two classes of declarative statements; the ones that are actual beliefs, and the ones that have the grammatical form of beliefs but are empty of meaningful belief-content.

It seems to me, then, that both the positivists and their critics fell into the trap of confusing 'belief' and 'truth', and that carefully making this distinction might have saved positivism from considerable undeserved mockery.

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[-]Protagoras12y140

Logical Positivism didn't fall because people asked if the verification principle is verifiable; most LPists were clear that the verification principle was supposed to be analytic (it's somewhat murky what that means, but for present purposes it should suffice to note that in any version it amounts to something similar to what you suggest here). This version of history is even worse than the story that LPism failed because of the impossibility of drawing the analytic/synthetic distinction; at least that criticism was actually made, and believed by some, though it also fails to explain the disappearance of LPism as there still seem to be large numbers of philosophers who believe in analyticity or something like it. Why none of the believers in analyticity call themselves Logical Positivists any more is a complicated question, and while there are some substantial issues involved, some of it seems to involve something more like a change of fashions.

[-]Chris_Leong5y20

What do the philosopher call themselves then these days?

[-]RolfAndreassen12y10

Ok, then consider the rephrasing as a means of, firstly, repairing the analytic/synthetic distinction, and secondly, dressing it up in newly-fashionable terms for the twenty-first century. :)

[-][anonymous]12y40

At least here, you've just stated, not repaired or defended, a view implying the analytic/synthetic distinction.

In order to repair the analytic/synthetic distinction, we should first get in view what broke it. One of the most important papers criticizing LPism on this score was Quine's "Two Dogmas of Empiricism". So we'd need to read and respond to that. So here.

[-]Protagoras12y10

For anyone who wants more, one of the earliest responses to Quine, Grice and Strawson's "In Defense of a Dogma," is here. I'm also quite fond of Carnap's reply to Quine in Carnap's volume in the Library of Living Philosophers, but I don't think that's online anywhere.

[-]Richard_Kennaway12y120

"No, that's not a belief, that's a definition of what it means to say 'I believe X'."

That's not a definition, it's an act of linguistic warfare.

If you were actually defining a word, you could replace the word by any made up string of letters, and the definition would have the same effect: an indication of what you will mean when you later use that word. "That's a definition of what it means to say 'I flamjink X'." does exactly the same work as "That's a definition of what it means to say 'I believe X'." Uttering the latter sentence tells nobody anything about what anyone else means when they use the word "believe". It merely informs them of a personal decision that you have taken about how you will henceforth use the word.

But that is not the intended function of "No, that's not a belief, that's a definition of what it means to say 'I believe X'". It's an attempt at expropriating the word, an attempt to decree not merely how other people must henceforth use the word, but to decree that that is what they always meant by it -- what the word itself "really means". If that's what it "really means", then that's what everyone previously using it must really have meant -- by definition!

Rephrasing your next paragraph:

A definition is not true or false, it is useful or not useful. Why is this definition useful? Because it allows us to distinguish between two classes of declarative statements; the ones that are actual flamjinks, and the ones that have the grammatical form of flamjinks but are empty of meaningful flamjink-content.

Doesn't sound so convincing. It may very well be helpful to distinguish beliefs that are testable from beliefs that are not, and to make up a name for the former class (although "testable" seems to serve well enough already). But none of that deprives the non-testable beliefs of meaningful belief-content.

[-]DanielLC12y50

I would like to expand civilization as far as possible. If I attempt to send life beyond the cosmological event horizon, there is no experiment that can verify whether or not it succeeds. It would be useful to have some way of expressing whether or not I think sending settlers beyond it is worth the risk. I would call this belief that they'd succeed.

[-][anonymous]12y50

So I agree with what Protagoras said about the causes of the fall of LP: there wasn't really anything like a firm refutation, though important versions of LP like Carnap's were beleaguered by criticisms like Quine's attack on the analytic/synthetic distinction "Two Dogmas of Empiricism". I think the reason why LP fell was just that it went about saying all sorts of questions were meaningless questions, questions about ethics, metaphysics, etc. And people just got sick of that. The questions persisted, and our desire to ask them and talk about them didn't die out for the claim that all our attempts to do so were mere poetry. The nails in the coffin were really just a series of influential and brilliant philosophers in the 70's, like John Rawls and David Lewis who simply ignored the LP view about meaningfulness, and wrote books about ethics and metaphysics that people were interested enough in to discuss, argue with, or build off of.

If I'm right, this bodes ill for a revival: whether or not LPists are right about meaningfulness, people just find the LPist's world too impoverished to live in.

[-]Creutzer12y00

I think it's very likely that this is indeed what happened.

David Lewis who simply ignored the LP view about meaningfulness, and wrote books about [...] metaphysics

As far as I know, though, Lewis is revered for his contributions to logic and linguistics, but the rest isn't taken very seriously. What the hell is modal realism even supposed to mean? It may be, though, I'm in the wrong circles and there are some that do.

[-]David_Gerard12y10

What the hell is modal realism even supposed to mean?

The claim that MWI is true and all those possible worlds really exist is pretty much modal realism, insofar as it's the claim that all possible worlds are as real as this one.

[-]CarlShulman12y50

MWI doesn't give worlds with different fundamental physical laws.

[-]ArisKatsaris12y50

The claim that MWI is true and all those possible worlds really exist is pretty much modal realism, insofar as it's the claim that all possible worlds are as real as this one.

Please let's not be confusing MWI with Tegmark IV here.

Modal realism talks about all logically possible worlds and so it's much closer to Tegmark's Ultimate Ensemble.

[-]David_Gerard12y20

This appears to be a similar confusion over the word "possible" to the one that lets some people think p-zombies are an idea worth considering.

[-][anonymous]12y30

Well, one of the possible (and by Lewis' lights, actual) worlds is the world in which MWI is false.

[-]asr12y30

I suspect the claim "All beliefs are experimentally testable" is either vacuous or false. Our evidence for most of mathematics is deductive, not empirical. But it would be very strange to say that I don't have beliefs with substantive content about, say, the the Fundamental Theorem of Algebra.

You might say that mathematical investigation is a kind of experiment -- but in that case one wonders what causes for a belief aren't experiment. Is any evidence whatsoever 'experiment'?

[-]RolfAndreassen12y00

[I]t would be very strange to say that I don't have beliefs with substantive content about, say, the the Fundamental Theorem of Algebra.

[-]TheOtherDave12y30

Do I similarly not believe that there isn't a piece of chocolate cake floating in the asteroid belt?

Cuz it sure feels like I believe there isn't a piece of chocolate cake floating in the asteroid belt.

And if I don't believe that proposition, what is the thing I'm doing to it that feels so much like belief, and why does it feel so much like belief?

[-][anonymous]12y00

I think that would count as a straightforward belief on Rolf's view, because you can test it empirically. We have to qualify that by saying you 'can in principle', since testing for that (especially a chocolate cake) would be impractical, but that's no problem for the meaningfulness criterion.

[-]TheOtherDave12y40

Which of course invites the question of whether I believe I can test it empirically.

Alternatively, one could ask whether I believe that a piece of chocolate cake didn't spontaneously materialize in the asteroid belt at 2:15pm EST on April 11 2012 and float there for fifteen minutes before dematerializing... unless we want to say that the fact that I could have tested it last year counts as "can test it in principle." Which I suppose is no sillier than anything else.

Regardless, I'm more interested in the second question. On Rolf's view, why do (e.g.) my opinions on the usefulness of the definitions which imply the Fundamental Theorem of Algebra feel so much like beliefs about the Fundamental Theorem of Algebra?

[-]RolfAndreassen12y50

Because the intuitions on which those opinions are based, actually are beliefs: They arise from your experience with subdividing things. The fifth axiom of Euclid's geometry may be a more helpful example here; it is the one which states that given a line and a point not on it, exactly one line may be drawn through the point which never meets the first one. By denying this axiom we get Riemannian or hyperbolic geometry. Now, of the three versions of the axiom, which one does it feel like you believe? I rather strongly suspect it is the Euclidean one; there's a reason it took two thousand years to formalise the other kinds of geometry. Yet they all describe the behaviour of actual straight lines in different circumstances.

[-]TheOtherDave12y30

(nods) That's an excellent answer. Thank you.

[-]Kindly12y10

On Rolf's view, why do (e.g.) my opinions on the usefulness of the definitions which imply the Fundamental Theorem of Algebra feel so much like beliefs about the Fundamental Theorem of Algebra?

Because maintaining all these levels of indirection is hard.

[-]asr12y00

You do not have beliefs about the FTA; you have opinions on the usefulness of the definitions which imply it.

Here's a related example with a larger bullet for you to chew on. Suppose I have a (small) computer program that takes arbitrary-sized inputs. I might believe that will work correctly on all possible inputs. Is that a belief or not? It can be made as rigorously provably correct as the FTA.

When I say "the program is correct", I am not saying "it is useful to construe the C language and the program code in such a way that...". I'm making an assertion about how the program would behave under all possible inputs.

Beliefs about computer programs might feel more empirical than beliefs about theorems, but they are logically equivalent, so either both or neither are beliefs, it seems.

[-]RolfAndreassen12y00

Please observe that one of the possible inputs to your computer is "A cosmic ray flips a bit and turns JMP into NOP, causing data to be executed as though it were code". In other words, your proof of correctness relies on assumptions about what happens in the physical computer. Those assumptions are testable beliefs, just like the intuitions that go into geometry or the FTA.

[-]Shmi12y-10

I suspect the claim "All beliefs are experimentally testable" is either vacuous or false.

Clearly it's false. Plenty of human beliefs are non-testable, some even self-contradictory. LP did not claim anything of the sort.

[-]Shmi12y00

The logical positivists said "All truths are experimentally testable"

Wasn't it more like "A statement is defined as meaningful if it's verifiable, and true if it's verified"?

[-]RolfAndreassen12y10

If you like; I don't see how that changes the argument. How do you verify "A statement is defined as meaningful if it's verifiable, and true if it's verified"? And if it's not verifiable, it's meaningless by its own assertion. But replace 'statement' with 'belief' and you get the same avoidance of the reflectivity problem, because you then have a statement about beliefs, not a statement about statements or a belief about beliefs.

[-]Shmi12y10

How do you verify "A statement is defined as meaningful if it's verifiable, and true if it's verified"?

You don't verify definitions, just like you said. Gotta start somewhere.

[-]MugaSofer12y-20

A definition isn't a statement, it's part of your vocabulary for discussing statements. Would it help if we replaced "statement" with "hypothesis" or "claim"?

[-][anonymous]12y-20

Turn it on its head by asking what (truth / belief / claim) may not be (tested / questioned / challenged). If the answer is none, including this question itself, then you've got your answer. If you can identify something that is not subject to inquiry, that is known true and known in every detail with no further knowledge possible, I'd like to see it.

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