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Necessity and Conventions

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Necessity and Conventions

TecnoTut
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Posted 01/27/04 - 04:57 PM:	#1
How is it known that every number has a successor, that straight lines can intersect each other no more than once, that causes precede their effects, and that the electron either went through the slit or it did not? In cases like these it is not easy to find observable, empirical evidence and it is implausible to postulate special modes of intuitive access to the phenomena in question. Yet such statements are reliable in sciene and can hardly be dismissed as meaningless metaphysical excess. In response to this problem some positivists and empiricists (e.g. Poincare, Hilbert, Carnap, Reichenbach and Ayer) developed a strategy known as conventionalism. The idea was and still is that certain statements, including fundamentals principles of logic, mathematics and geometry, are asserted as a matter of conventional stipulation, being no more than definitions of some of their constituent terms – consequently they must be true because our commitment to them cannot be justified and the facts in virtue of which they are true are simply the facts of our having made those particular decisions about the use of words. This was popular during the 20’s, 30’s, and 40’s but has since fell into disfavor. The main reason is because it is unclear how our arbitrary and contingent conventions and decisions about the use of words result in the existence of necessary facts. More recent objections raised by Saul Kripke are that some necessary truths are not merely linguistic, but a posteriori.
He that dies pays all debts - Shakespeare's Stephano from The Tempest Truth is its own measure - Spinoza, Ethics IIp43s Those who deny [Aristotle's] first principle should be flogged or burned until they admit that it is not the same thing to be burned and not burned, or whipped and not whipped. - Ibn Sina (Avicenna)

Gassendi1
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Posted 01/28/04 - 08:03 AM:	#2
TecnoTut wrote: How is it known that every number has a successor, that straight lines can intersect each other no more than once, that causes precede their effects, and that the electron either went through the slit or it did not? In cases like these it is not easy to find observable, empirical evidence and it is implausible to postulate special modes of intuitive access to the phenomena in question. Yet such statements are reliable in sciene and can hardly be dismissed as meaningless metaphysical excess. In response to this problem some positivists and empiricists (e.g. Poincare, Hilbert, Carnap, Reichenbach and Ayer) developed a strategy known as conventionalism. The idea was and still is that certain statements, including fundamentals principles of logic, mathematics and geometry, are asserted as a matter of conventional stipulation, being no more than definitions of some of their constituent terms – consequently they must be true because our commitment to them cannot be justified and the facts in virtue of which they are true are simply the facts of our having made those particular decisions about the use of words. This was popular during the 20’s, 30’s, and 40’s but has since fell into disfavor. The main reason is because it is unclear how our arbitrary and contingent conventions and decisions about the use of words result in the existence of necessary facts. More recent objections raised by Saul Kripke are that some necessary truths are not merely linguistic, but a posteriori. ________________________________________ "The main reason is because it is unclear how our arbitrary and contingent conventions and decisions about the use of words result in the existence of necessary facts." There are no necessary facts, was the answer to that, wasn't it? That all things equal to the same thing are equal to each other, is a necessary truth which does not record a fact. Carnap and others would simply reply that you are mistaking a fact about language for a fact about the world. You should be in the formal mode rather than the material mode.

Analytic
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Posted 02/06/04 - 09:50 AM:	#3
TecnoTut wrote: How is it known that every number has a successor, that straight lines can intersect each other no more than once, that causes precede their effects, and that the electron either went through the slit or it did not? In cases like these it is not easy to find observable, empirical evidence and it is implausible to postulate special modes of intuitive access to the phenomena in question. Important questions. But why do you say it's not plausible to postulate some sort of intuition giving us these truths? TecnoTut wrote: More recent objections raised by Saul Kripke are that some necessary truths are not merely linguistic, but a posteriori. And before him, Gödel wrote quite interesting things in defense of mathematical Platonism. According to Gödel, we have some kind of sense organ that "sees" mathematical entities in their true reality. Well, that's just another way of putting that we have intuitions about them. (By the way, doesn't Chomsky say something very similar about grammatical rules - ie., that speakers have intuitions about them? And Chomsky seems to be interested primarily in that intuition, which he calls "competence".) So, why is intuition is out from the start?

Faustus
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Posted 02/06/04 - 10:03 AM:	#4
I'm reading a very interesting book right now which argues that the supposedly "eternal" rules of logic--and rationality in general--are entirely the product of evolution by natural selection. I have no idea how good the argument for this is, as I've just started, but it will be interersting to see how it plays out.

TecnoTut
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Posted 02/06/04 - 10:43 AM:	#5
analytic wrote: Important questions. But why do you say it's not plausible to postulate some sort of intuition giving us these truths? Because in many cases (although not all) we need empirical access. And in other cases, our intuitions simply are not strong enough. Analytic wrote: And before him, Gödel wrote quite interesting things in defense of mathematical Platonism. According to Gödel, we have some kind of sense organ that "sees" mathematical entities in their true reality. Godel did state that mathematical entities exist (but not in time and space). He believed in a priori necessities, but not a posteriori necessities. Kripke claimed that latter. Analytic wrote: (By the way, doesn't Chomsky say something very similar about grammatical rules - ie., that speakers have intuitions about them? And Chomsky seems to be interested primarily in that intuition, which he calls "competence".) Chomsky said grammatical rules are innate, but he never said anything of the sort that they are necessary propositions.
He that dies pays all debts - Shakespeare's Stephano from The Tempest Truth is its own measure - Spinoza, Ethics IIp43s Those who deny [Aristotle's] first principle should be flogged or burned until they admit that it is not the same thing to be burned and not burned, or whipped and not whipped. - Ibn Sina (Avicenna)

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Posted 02/06/04 - 11:14 AM:	#6
Faustus wrote: I'm reading a very interesting book right now which argues that the supposedly "eternal" rules of logic--and rationality in general--are entirely the product of evolution by natural selection. I have no idea how good the argument for this is, as I've just started, but it will be interersting to see how it plays out. Could you tell me who wrote it and what's its title? By the way, such books are galore nowdays. But I usually have the vague impression that finally they prove something different from what they originally wanted to prove. To give an evolutionary explanation of humans' logical capacities is great, but it's a completely different enterprise from deriving logic (or rationality) itself on evolutionary principles. The latter seems a bit circular, to say the least. It is as if a physicist tried to explain the properties of light on the evolutionary principles of how the human eye evolved. Anyway, it must be a good book.

Faustus
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Posted 02/06/04 - 11:21 AM:	#7
Analytic wrote: Could you tell me who wrote it and what's its title? Darned if I can remember. I started it just before I got hooked on the Dennett thread, so I've temporarily stopped reading it. When I get home from work I'll post the title and author for ya.

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Posted 02/06/04 - 11:45 AM:	#8
TecnoTut wrote: Because in many cases (although not all) we need empirical access. And in other cases, our intuitions simply are not strong enough. Which cases do you have in mind? Are you thinking about the way we learn (say) mathematical concepts? I grant that intuitions are often not strong enough. We are even liable to make mistakes. But this is the case with all external stimuli too (e.g. seeing, hearing...) Wouldn't this analogy make just a little bit more plausible that in both cases there is something external that is being grasped, in having a sensation in the former case, or an intuition in the latter? TecnoTut wrote: Godel did state that mathematical entities exist (but not in time and space). He believed in a priori necessities, but not a posteriori necessities. Kripke claimed that latter. Granted. For example, identity statements. And he is right about that, I think. Well, now that I'm trying to recall the details (in Naming and Necessity, I think but I might be wrong), he reduces statements of the form a=b through Leibniz principle and an (at least in my opion, a little too quick) application of a substitution to the a priori truth a=a. And although the former isn't usually known a priori, the latter is. Q.E.D. But isn't this a sleight of hand? After all, he only shows that statements of the form of a=b are nothing but statements of the form a=a in disguise, so it takes some (sometimes very great) effort for us to discover it. But this rather reminds me of the problem of logical omniscience, which concerns propositional attitudes and not metaphysics. TecnoTut wrote: Chomsky said grammatical rules are innate, but he never said anything of the sort that they are necessary propositions. Granted. Chomsky doesn't really like that sort of thing.

Death Monkey
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Posted 02/06/04 - 11:57 AM:	#9
TecnoTut, How is it known that every number has a successor, that straight lines can intersect each other no more than once, that causes precede their effects, and that the electron either went through the slit or it did not? These seem to me to be two different kinds of questions. For the first two, we know that those statements are true in certain mathematical systems, because they can be derived from the axioms of those systems. As for the last two, I would not claim that we know they are true at all. It is possible (as far as we know) that in some cases cause may not precede effect. And the claim that the electron either went through one slit or the other appears to be demonstrably false under certain conditions, or at the very least, a statement which does not accurately describe what is actually happening. DM
Pseudoscience makes Baby Jesus cry.

Faustus
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Posted 02/07/04 - 01:32 PM:	#10
The book I mentioned was The Evolution of Reason: Logic as a Branch of Biology by William S. Cooper. A very different Bill Cooper than the author of the Pale Horse book, of course!

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