"Book burning"

[civman2000]

Originally posted by Agathon
Logicism is the thesis that mathematics can be reduced to logic (i.e. at root they are the same thing). The attempt is generally regarded to have failed. IIRC (and this is moving far far away from my area of philosophical competence, so take it with a pinch of salt) you need to supplement it with set theory and maybe some other stuff too.

Er...how is set theory distinct from logic? Math CAN be reduced to the study of what can be proven through rigorous, logical arguments, from some collection of axioms (ie set theory). Can philosophy use logic without any axioms? Assuming the answer must be no, how are whatever axioms you would use in philosophy any less "empirical" than set theory?

I have nothing against philosophy. It's just not true that it's more rigorous or logical than math.

[Nostromo]

If philosophy were rigorous it could create its own symbolic logic.

In case you haven't heard, philosophers like Aristotle and the stoics invented logic. Of course, mathematicians like Frege and Russell (who was also a philosopher btw) took the matter into their own hands and created mathematical logic in the 20th century. One of most important philosophical movements of the 20th century, namely analytic philosophy, was based in part on that new logic: they saw that new logic as a method to do rigorous philosophy. A number of philosophers have invented logical systems based on that work in mathematical logic, stuff like deontic logic (for ethics), fuzzy logic, inductive logic, many-valued logic...

But these philosophers were overly optimistic: to deal with philosophical problems, logic is necessary, but not sufficient. Your still stuck with natural languages and their limitations. In other word, if mathematics and physics are more rigorous, its not because they're more logical, but because they're more mathematized.

[Nostromo]

Where'd you get that? I'm trolling AND I'm saying what I think is true AND I'm enlisting the support of others to own Aggie.

Gotcha! Well, well, well the fishies are bitting today!

[Nostromo]

Can philosophy use logic without any axioms?

Axiomatisation is one, popular, way to formalize logic. But there is also Gentzen's natural deduction method, which doesn't involve axioms, but only rules of inference.

[Nostromo]

More about logicism:

http://www.rbjones.com/rbjpub/philos/maths/faq001.htm

[Agathon]

I don't know, Ramo is quite open and articulate. Others are either trolling or, like Kuci, they're seeking the approval of the other scientists on 'poly: he's saying what he thinks they want to hear.

I don't know about Ramo, but the others are just being daft. Which is par for the course really -- they have little idea of what is done in current philosophy.

Do you do modern Analytic? I used to do epistemology and philosophy of language, but I gave it up for Ancient.

[Nostromo]

Do you do modern Analytic? I used to do epistemology and philosophy of language, but I gave it up for Ancient.

I am a philosopher of science, more or less in the analytic tradition. More or less since some of the people I studied, like Kuhn, Lakatos and Laudan, are not analytic philosophers. Yet I also studied Carnap, Popper and Hempel. Now I'm more interested in rationality or, to be more precise, irrationality. So I have moved on to philosophy of psychology and philosophy of mind. Given my topic, I also read a lot of psychology

[snoopy369]

Although i'm well aware that you OTers enjoy ... tangents, I'm going to make a (gasp) relevant argument to the original topic (/gasp)

Agathon, I have to argue with your original statement from a moral relativist point of view. Although you would defend, say, suppression of pedophilic pornography, and obviously have the general support of the society, you would also be required by your argument to defend the suppression of, say, marxist literature in many nations in the 1700s, christian literature in rome in AD 100, jewish literature in spain in AD 1500 (and most of the world at various points) ... and in 100 years, who knows what will happen? And what about different parts of the world, where very different things are acceptable morally (not necessarily just "more" or "less", either, but ... different nonconcentric areas of belief)? Who gets to pick whether, say, graphic pornography in general is 'burned' (as many people in, for example, the southern U.S., would argue), or just pedophilic pornography, or masochistic pornography, or, or... ??

Unless there's an actual immediate danger (as previously argued), I have a hard time agreeing with the banning of information, at all, and that means my line is the same as that of Oliver Wendell Holmes, Jr. (and Tom Clancy ) ... "clear and present danger". (Hence my strong distaste for the FCC and other federal censors. First amendment my @$* ... )

I'll also object to the categorization of the original argument as "empirical" rather than specific. Of COURSE he's using empirical arguments; it's a bloody moral argument, not a logical one. It's not something that can really be 'argued' effectively either, as a result, but, tant mieux - so much the better. We can all have a little fun and then continue believing what we deep down believe, and if someone comes to a realization that they deep down believe what i say, or what you say - so much the better

[Kuciwalker]

Originally posted by nostromo
In case you haven't heard, philosophers like Aristotle and the stoics invented logic.

Actually, no, they invented a particular logic. There are many logics (propositional, for instance). And it clearly isn't enough to fully describe the world. AFAIK there isn't a formal logic that exists that's powerful enough to fully describe the world (at least efficiently; the CS people may actually have figured out one that powerful). That's why we use language, which is not a formal logic.

[civman2000]

Originally posted by nostromo


Axiomatisation is one, popular, way to formalize logic. But there is also Gentzen's natural deduction method, which doesn't involve axioms, but only rules of inference.

Judging from what wikipedia says, I don't see any difference at all between "natural deduction" and standard mathematical logic; it seems to mainly be a difference of notation. You still cannot deduce anything in it without any assumptions (except tautologies, which hardly count as actually deducing something, and can also be deduced in set theory without using any of the axioms anyways), which is essentially the same as having axioms.

[BeBMan]

Originally posted by snoopy369
, marxist literature in many nations in the 1700s,

[Nostromo]

Actually, no, they invented a particular logic. There are many logics (propositional, for instance). And it clearly isn't enough to fully describe the world.

I know there are many logics: there are some examples in my post. I meant that Aristotle and the Stoics invented the discipline called logic.

AFAIK there isn't a formal logic that exists that's powerful enough to fully describe the world (at least efficiently; the CS people may actually have figured out one that powerful). That's why we use language, which is not a formal logic.

I know CS people use logic, but have they made contributions to logic? I haven't heard of any. At least, nothing comes to mind right now.

[GePap]

Math is playing with number, which are a human invention anyways. I am sure you can get very rigorous with the rules, and find all sorts of interesting things as the game is played. That does not mean that this game is superior to any other game, just different.

[Brent]

Ah, so numbers and measurement are meaningless, are they??

[Nostromo]

Judging from what wikipedia says, I don't see any difference at all between "natural deduction" and standard mathematical logic; it seems to mainly be a difference of notation. You still cannot deduce anything in it without any assumptions (except tautologies, which hardly count as actually deducing something, and can also be deduced in set theory without using any of the axioms anyways), which is essentially the same as having axioms.

Except that in axiomatic systems, just any assumption clearly won't do as an axiom. Of course, you have to start somewhere. But in natural deduction, these starting points are considered more like hypothesis than axioms, and they can be eliminated afterwards (with elimination rules), something you can't do in an axiomatic system.