tag:blogger.com,1999:blog-6245381193993153721.post8231176424743514938..comments2019-08-18T06:08:17.469-07:00Comments on Social Democracy for the 21st Century: A Realist Alternative to the Modern Left: Epistemology in Modern Analytic Philosophy: A ReviewLKhttp://www.blogger.com/profile/06556863604205200159noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6245381193993153721.post-15908530809128279472013-09-27T02:14:56.009-07:002013-09-27T02:14:56.009-07:00Allow me to take a step back for a moment because ...Allow me to take a step back for a moment because I think I should have clarified a bit (or you can clarify a bit). <br /><br />If I understand you, you're claiming that a type (3) analytic statement is, say, a theorem from an argument with premises which are, themselves, analytic. Is this correct?<br /><br />So ultimately a type (3) analytic statement should purely follow from classical logic + definitions and nothing more. <br /><br />Part of what I think is that formal systems aren't purely logical (what's logic?) nor purely definitional. They postulate things. In geometry we postulate lines and circles (well, Euclid told us we can draw them, language which is quite distinct from Hilbert's more Platonic language). In set theory we postulate sets.<br /><br />I'm suggesting that I have no logical obligation to postulate these. In fact, I can postulate other statements which are contrary to these and make alternative perfectly consistent formal system. <br /><br />On what grounds ought we privilege one such system over the other? <br /><br />Without offering an answer to that, I will say that they aren't purely logical grounds. And as such I have to conclude such systems are not analytic. Perhaps they are "a priori" (if we take, say Phillip Pinkerton's suggestion that the statements follow from the definitions and rules of the game.). Samuel Gotihttps://www.blogger.com/profile/07700141552017540854noreply@blogger.comtag:blogger.com,1999:blog-6245381193993153721.post-57718770408501214682013-09-26T13:31:57.606-07:002013-09-26T13:31:57.606-07:00Godel's 2nd incompleteness implies you can'...Godel's 2nd incompleteness implies you can't prove the system is consistent. If you can prove the system is consistent then I'm not sure how you can claim it's analytic. [OK, technically you can prove it's consistent via transfinite induction but I believe that raises just as many questions as it answers.]<br /><br />But here's a question for you. What do you count as a definition? Because, I'm willing to call a lot of things definitions but I have hard time believing that certain axioms are definitions. <br /><br />For example, would you consider each <a href="http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html" rel="nofollow">axiom of ZF (Or ZFC)</a> to be a definition? IMO, most of them aren't <i>merely definition</i> but also <i>posit the existence</i> of said entities defined. For a non Platonic interpretation, it's as if it's constructing the existence of sets.<br /><br />So I would be willing to agree with the statement that "most of classical mathematics" can be derived from set theory but I'm not convinced that set theory is analytic. In some cases you can even deny some of the axioms and get a different consistent theory. (Axiom of choice is independent IIRC; I wouldn't be surprised if others were as well). <br /><br />And last point, since you brought up sense (3) here, can you give me a statement that is <i>true</i> and is <i>analytic</i> in sense (3)?<br /><br />I have reservations about the examples you used. For example, what does it mean to say that an object "is red"? To be clear, I'm asking how you would formalize a proof of that statement from a set of definitions. I'm not saying it can't be done I'm not sure that it can either. You're welcome to give another example of course. <br /><br />For example, I would claim it's not possible to derive what physics textbooks typically claim is Netwon's 2nd Law (F=ma) from what Newton actually said the 2nd Law to be (F=dp/dt) by mere definitions alone. You would need to assume something else (like Newton's first law) to derive the result and I'm not seeing how the additional assumption could be satisfied that would make it a definition. (If you're wondering what, when you apply the product rule, you get a term with dm/dt so you have to assume that it's 0 or assume something that would imply that it's 0.)Samuel Gotihttps://www.blogger.com/profile/07700141552017540854noreply@blogger.comtag:blogger.com,1999:blog-6245381193993153721.post-3057446874991341962013-09-25T12:33:25.019-07:002013-09-25T12:33:25.019-07:00"The issue is more confusing with things like...<i>"The issue is more confusing with things like mathematics. With the failure of logicism, where does mathematics fit?"</i><br /><br />But in what sense did logicism fail? <br /><br />According to Stephen P. Schwartz ( A Brief History of Analytic Philosophy: From Russell to Rawls. Wiley-Blackwell, Chichester, UK, 2012. p. 19), the consensus today is still that most of classical mathematics can be derived from pure logic and set theory. To that extent, it would appear to be analytic a priori in sense (3) above.<br /><br />When applied to the world, applied mathematics would appear to be synthetic a posteriori -- just like geometry we must distinguish pure mathematics from applied mathematics.Lord Keyneshttps://www.blogger.com/profile/06556863604205200159noreply@blogger.comtag:blogger.com,1999:blog-6245381193993153721.post-38356314324270885752013-09-25T12:01:43.855-07:002013-09-25T12:01:43.855-07:00I guess part of the concern is that a lot of these...I guess part of the concern is that a lot of these lines are blurred. Putnam seemed to characterize it as the difference between a "dichotomy" and a "distinction". Quine's critique of analytic/synthetic (along with Putnam's critique of fact/value) showed it wasn't a dichotomy but there still may be subtle differences. (I think Putnam said he got Quine to concede this.)<br /><br />The issue is more confusing with things like mathematics. With the failure of logicism, where does mathematics fit? It's not exactly analytic. <br /><br />It's certainly not in sense (1). <br /><br />Arguing for it in sense (2) would be difficult but perhaps possible. <br /><br />Regarding sense (3), I never know what to make of those statements. Regarding the examples, I share Mike Huben's sentiment from <a href="http://socialdemocracy21stcentury.blogspot.com/2013/09/an-observation-on-deduction.html" rel="nofollow">this post</a>. Do we mean "color" as a psychological phenomenon or as a metaphysical? If the former, then would it be extended? If the latter, then coming up with how to to even define color is pretty vague. I mean, if I shine a "red" light (what's a "red" light?) on a "white" object (what's a "white" object?) is it "white" or "red"?<br /><br />The other issue is that even mathematics (or at least parts of it) have been regarded as, at least, quasi-empirical inquiries. Even Godel suggested this with regard to the continuum hypothesis, a view Martin Davis has dubbed "Empirical Platonism". <br /><br />I almost get the impression we have a tool set, a proverbial hammer so to speak, but we're not working with nails. Perhaps we need different tools.Samuel Gotihttps://www.blogger.com/profile/07700141552017540854noreply@blogger.com