Prof Edgington - Merton St
@10 on Wednesday, 03 May, 2000
German philosopher, mathematician 1848-1945
we owe him today�s modern standard logic
re: structure + workings of language
immediate impact on Russell and early Wittgenstein
and also the logical positivists (the Vienna circle), e.g. Hempel, Karnap
his primary goal: bring rigour to maths, developing water-tight notion of proof � logic before was too crude for the intricacies of maths, to distinguish valid/invalid forms of reasoning
Frege = a sort of Aristotelian logic: recognises certain patterns of syllogism
principle weakness: could tell us about the inferential powers of sentences containing more than one expression of generality
e.g. everybody loves at least somebody
but maths is replete with relations
many attempts to solve, but no general solution
there was no conception of a complete propositional logic
1. the sentence = the primary unit of language
= the unit by which we perform a speech act, �make a move in the language game�, get across a belief � sub-sentential components are simply means to that end
2. arguably, indicative sentences are the most basic kind
a proposition can be put forward with different force (statement, question, command etc.)
indicative - adj. 1 Gram. Designating the mood of a verb
of which the essential function is to state an objective fact (as opp. to
something wished, thought of, etc., by the speaker). lme.
a. j. ayer Every indicative sentence, whether it is literally meaningful or not,
shall be regarded as expressing a statement.
if we focus on indicative sentences, and the
rest will fall into place
3. meanings of words � systematic contributions to meanings of sentences
word = smallest semantically significant unit, out of which sentences are constructed
�word� does not necessarily correspond to the spaces in a sentence - endings to form plurals, comparatives, tenses
e.g. �walked� contains 2 semantically significant units
never ask for the meaning of
a word in isolation - Frege
no point in establishing word-world relations, or symbols standing for something, unless you go on to use them
to know the meaning of an
indicative sentence is to know under what conditions it is true � Frege
4. meaning of indicative sentences = truth condition
someone who understands knows how things have to be in order to be true
2 sentences can have the same truth conditions, but still have different tone/colouring
e.g. dog/cur, and/but
what is it to know the truth conditions of a sentence?
by showing that you know how to find out whether or not a sentence is true
= a verificationist theory of meaning
e.g. this painting was painted by Goya
well, I know about painting, Goya and about this painting, so I understand it
but if someone asks me if the sentence is true, I won�t have any idea � I will need to ask an art historian � so demanding that we know how to find out if it�s true seems like a more demanding criteria
raises the question: what is truth?
truth is useful for certain types of generality � but shouldn�t think of it as substantive at all (Horrock � trying to define meaning without reference to truth)
= deflationist
substantive = adj. 1 Having a
separate and independent existence; not dependent on or subsidiary to another,
independent, self-sufficient. lme.
Davidson
5. different semantic categories of words
words make different semantic contributions to sentences in which they occur
proper names - for singular terms, i.e. any expression whose purpose is to identify objects, incl I, you, that painting, the capital of France
many sentences are about objects. its truth conditions depend on which objects the sentence is about, so the job of this category is to identify on which objects the sentence depends
6. predicates
Frege: difference between name + predicate = more radical than previously thought
before: predicates were founded on t notion of a name, general names, as opp to particulars, names of properties
but how can 2 names make a sentence which says something T/F?
predicate = becomes a sentence when the gaps are filled with names
e.g. ______ walked
so predicates are like sentences, but incomplete
there are complex predicates, just as there are complex single terms
take a complex sentence, remove a name, and you have a predicate
Dummett � uses complex predicates for multiple generalities
� logic of expressions of generality
in the context of his
1. difference tween indicative/declarative?
2. what is the �mood� of a verb?