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What is the Purpose of Logic?
Posted: Fri Apr 24, 2015 2:57 pm
by Wyman
Logic can be viewed as a formalization of the arguments of ordinary language and/or a formalization of mathematical reasoning. Alfred Tarski believed that ordinary language could not be formalized because (at least in part) its concepts are too vague. Here is an excerpt from a book on the philosophy of logic on this topic (Haack):
One could think of a formal logical system as being devised in something like the following way. Some informal arguments are intuitively judged to be valid, others invalid. One then constructs a formal language in which the relevant structural features of those arguments can be schematically represented, and axioms/rules which allow the intuitively approved, and disallow the intuitively disapproved, arguments. This, of course, is at best a very sketchy 'rational reconstruction' and is not intended as detailed, serious history. Still, while I concede that formal logics have sometimes been devised simply out of mathematical curiosity, I think that something like the process I have described was at work when, for instance, Frege devised his Begriffsschrift. Of course, the standard logical languages are now so familiar that one is no longer very conscious of how and why they were first constructed. But the same process can be seen in recent attempts to devise new formalisms for hitherto neglected kinds of argument; see, for example, the procedure adopted by D.K. Lewis 1973 in devising his analysis of counterfactuals.
The question is, do you think formal logic is a description of (specifically) mathematical reasoning or a formalization of the accepted (intuitive) arguments of ordinary language - or do you have a different interpretation?
Food for thought: To see one instance of how badly formal logic represents ordinary language, take material implication (If p then q). In formal logic, this truth function is always true except where p is true and q is false. Thus, the following statements are true in symbolic logic:
If pigs fly (F), then New York is a tiny town (F)
If pigs fly (F), then New York is a Big City (T)
If New York is a big City (T), then 2 + 2 = 4 (T).
Re: What is the Purpose of Logic?
Posted: Fri Apr 24, 2015 9:43 pm
by Impenitent
I think formal logic tries to force general language into the boxes created by the language of mathematics
-Imp
Re: What is the Purpose of Logic?
Posted: Mon May 04, 2015 3:20 pm
by HexHammer
Please snap out of your religious logic orgasm!
Re: What is the Purpose of Logic?
Posted: Mon May 04, 2015 3:34 pm
by Wyman
HexHammer wrote:Please snap out of your religious logic orgasm!
If logic gave me an orgasm, then I really would never get any work done!
Re: What is the Purpose of Logic?
Posted: Mon May 04, 2015 3:58 pm
by duszek
Wyman wrote:
If pigs fly (F), then New York is a tiny town (F)
If pigs fly (F), then New York is a Big City (T)
If New York is a big City (T), then 2 + 2 = 4 (T).
There is no connection between statement 1 and statement 2 (in terms of meaning).
Can we create a better example to illustrate and to examine whether the mathematical forumla can work for language ? I will try to think of one myself.
One also needs to differentiate between "if and only if" and "if and the other way round" and "if but not (necessarily) vice versa".
Re: What is the Purpose of Logic?
Posted: Mon May 04, 2015 10:44 pm
by Impenitent
the logical positivists already have gone down that rabbit hole...
-Imp
Re: What is the Purpose of Logic?
Posted: Mon May 04, 2015 10:49 pm
by Melchior
What is the purpose of light?
Re: What is the Purpose of Logic?
Posted: Mon May 04, 2015 11:00 pm
by Wyman
Melchior wrote:What is the purpose of light?
It's physical so it has no purpose. Logic is studied and created by humans, which makes my question meaningful.
Re: What is the Purpose of Logic?
Posted: Tue May 05, 2015 12:38 am
by Melchior
Wyman wrote:Melchior wrote:What is the purpose of light?
It's physical so it has no purpose. Logic is studied and created by humans, which makes my question meaningful.
Nope. Try again.
Re: What is the Purpose of Logic?
Posted: Tue May 05, 2015 2:18 am
by Wyman
Have you been drinking today? You've been particularly obnoxious, attacking old vegetarians and whatnot. So why was logic invented?
Re: What is the Purpose of Logic?
Posted: Sun May 10, 2015 3:54 pm
by Dalek Prime
This is one of Melchior's less obnoxious moments, I thought....
Anyways, logic and formal language allow me a living as a programmer.
Re: What is the Purpose of Logic?
Posted: Mon May 11, 2015 1:30 am
by Arising_uk
Melchior wrote:What is the purpose of light?
Well, ignoring the teleology I'd say it was so that things could be seen.
Re: What is the Purpose of Logic?
Posted: Mon May 11, 2015 1:47 am
by Dalek Prime
Arising_uk wrote:Melchior wrote:What is the purpose of light?
Well, ignoring the teleology I'd say it was so that things could be seen.
By whom? Light existed long before living sight.
Re: What is the Purpose of Logic?
Posted: Mon May 11, 2015 2:17 pm
by Wyman
Dalek Prime wrote:This is one of Melchior's less obnoxious moments, I thought....
Anyways, logic and formal language allow me a living as a programmer.
Good, so there's one purpose. Did it, like light, exist before there were any humans to use it?
Re: What is the Purpose of Logic?
Posted: Mon May 11, 2015 10:26 pm
by Dalek Prime
Wyman wrote:Dalek Prime wrote:This is one of Melchior's less obnoxious moments, I thought....
Anyways, logic and formal language allow me a living as a programmer.
Good, so there's one purpose. Did it, like light, exist before there were any humans to use it?
I consider it a creation of the mind. It is directed by the mind, and conversely gives direction to it. Light is a physical phenomenon, and doesn't require the mind to exist. I say this because we've all seen the after effects of things being sun bleached, or light reaching us from a time before the mind existed, from space. Natural language was made necessary by the mind to communicate with other minds and, at least in written form, came about as a result of the agricultural revolution building larger, more stationary communities. And natural language predates formal language. That's my take on it, anyways.