Newsgroups: sci.lang,talk.philosophy.misc
From: leemike@eecg.toronto.edu (Michael Lee)
Subject: Re: Logic
Organization: CSRI, University of Toronto
Date: 14 Dec 92 17:25:58 GMT

The propositions in themselves may not have any empirical content, 
however the rules employed, or the grammar, to constuct and transform
sytactically correct propositions may allude to certain underlying 
structures in the brain, i.e., by taking a metalogical point of view
about a system of logic, intrinsic thinking processes may be opened
to investigation.

>Then, what job does logic actually do ?  Logic is a subject which
>investigates logical concepts.  

The question that may then be asked, since you've given a statement
defining logic, is `what is a logical concept?'.  Actually, you haven't
given a definition of logic, you've merely placed the burden of 
defining from `logic' onto `logical concepts'.

>By the term "investigate", I mean
>"analysis".  Loosely speaking, logical concepts includes logical
>conectives (e.g. "and", "or", "if...then...", "not", "neither...or...",
>"unless", ...etc.) 

Are these statements (defining the symbols `&' for conjunction,
`V' for disjunction, `~' for negation, `->' for implication, etc.), 
`&', `A -> VB', `V~->', logical proposition?  They all include logical
connectives.  Stictly speaking a distinction can be made between the
two terms, `logical proposition' and `logical concept'; the former
refers to a syntactically correct predicate within a system of logic
, e.g., A -> B, the latter can refer to either metalogical ideas about 
logic or the transformation rules within logic, e.g., modus ponens is a 
logical concept.

>and also some of the concepts which frequently appear
>and is key to determine the truth value of our statements (such as "for
>all", "there is some", "there is at least twelve", "there is not", "it is
>possible", "it is not possible",...), some basic concepts (such as
>"true/false", "valid/invalid argument"...).  What a logicist does is to
>clarify all these concepts and find out the relation between them.  

In other words, the sole task of a logician is to clarify concepts
and find relations amongst theses concepts.  Hence logic is the
subject of clarifying the symbols of logical connectives and
quantifiers and finding the relation amongst these symbols.
However a logician is not necessarily confined to formalising
a logical system; a logician may query about metalogical concepts 
such as `can a deductive system be completely formalised in order 
to construct an absolute proof?' as Hilbert conceived the matter, 
`is arithmetic consistent?', `can all of mathematics be formalised', 
etc.  These queries were asked by mathematicians/logicians of the
19th and 20th century, such as Godel (being the most popular), and
a slew of others. 

>As an
>example, a truth table for "and" is a clean way to define the concept
>"and" in term of the concept "truth value".
>
>How can logic help us in thinking, if logic is really something like this
>?  Clear thinking requires clear concepts.  Logic helps us in this way ! 
>In fact, saying that logic gives us rule of thinking sometimes may be
>misleading (especially when we want to understand the nature of the
>subject; note that I only say that it is misleading, not say that it is
>wrong).

I guess the question that can be asked is `does these rules reflect
something which may be intrinsic to our thinking processes or do we
impose these rules on our thinking processes?', either way I would
think that these rules have a great deal to say on the stuctures of the
mind.  This would, however, contradict your earlier statement, if I
may paraphrase, indicating that logic is irrelevant to these structures.

>
>What is my point ?  My point is that logic, in this sense, is linguistic
>(of couse, the term "linguistic" is not quite well-defined).

I was asking the same question in reference to yourself of course.

I'm not quite so sure that logic is confined within linguistics or is
linguistic in nature.  Simply because logic requires language in order
to operate does not imply, even though they are strongly connected, that 
logic is bound to language.  One can certainly interpret logic from the
viewpoint of platonic realism, in which logic or pure mathematics is, par
excellence, the discoverer of objects accessible only to our intellect.  
In this scenario logic works beyond the confines of language. 

regards,
  Michael Lee
Newsgroups: sci.lang