Download
1 / 66
660 likes | 800 Vues
Senses. Problems for Structured Propositions. Fineness of Grain. Problem for propositions = sets of possible worlds: the set of worlds where “2 + 2 = 4” is true is the same as the set of worlds where “ e i π + 1 = 0” is true. Fineness of Grain.
E N D
Fineness of Grain Problem for propositions = sets of possible worlds: the set of worlds where “2 + 2 = 4” is true is the same as the set of worlds where “eiπ + 1 = 0” is true
Fineness of Grain But many people believe that “2 + 2 = 4” is true without believing that “eiπ + 1 = 0” is true. The structured propositions theorist has no such problem: she can say there are two propositions. On proposition, for example, contains the number 2, the other does not.
Grain Too Fine? However, the structured propositions theorist will also be forced to admit that these are different propositions: B A B A & &
Why Are They Truth-Evaluable? According to the structured propositions theorist, propositions are abstract structures with objects and properties occupying certain places in those structures. Most abstract structures are not true or false. Why are these ones?
Language-Like Structure Structured propositions obviously have a structure. Where do they get it from? Why do they have the structure they do? The isomorphism with language suggests the structure comes from language.
Young Propositions But if structured propositions get their structure from language, then they could not exist before language. Thus the proposition that dinosaurs exist did not itself exist until dinosaurs were extinct!
Animal Thought Also, if the structure of propositions comes from language, and propositions are the objects of thought, doesn’t that mean non-linguistic animals cannot think? (Cf. LOT)
Fineness of Grain Returning to the Superman/ Clark Kent problem, perhaps we can increase the fineness of grain of structured propositions by not replacing the words with their meanings, but instead adding the meanings to the words.
Interpreted Logical Form Michael, likes, Paisley,
Meaning of “Superman Flies” flies, Superman,
Meaning of “Clark Kent Flies” flies, Clark Kent,
Language-Bound Beliefs The unfortunate thing about ILFs is that now it seems that French people don’t believe the world is round! Le monde estrond.
GottlobFrege • 1848-1925 • German mathematician • Principal contributor to modern logic • Worked on the foundations of mathematics • Anti-semite, not very nice
GottlobFrege Lived in relative obscurity—the mathematicians of his time could not comprehend the scope and value of his groundbreaking work Luckily, he was known to Russell and Wittgenstein
Mathematical Truths Frege’s life-long goal: reduce arithmetic to logic. Kant: the truths of arithmetic are synthetic a priori, and we know them through our faculty of intuition, they are preconditions of experience.
Mathematical Truths Frege: such truths are analytic a priori. We know them via proofs which can be mechanically verified. This is called “logicism.” (Frege still thought geometry was synthetic a priori.)
Russell’s Paradox Right before the publication of the 2nd volume of the Foundations of Arithmetic, Frege received a letter from Bertrand Russell. For the remaining 21 years of his life, Frege only published papers elaborating his philosophy of language.
Naïve View Fregerejects the view that the meaning of a term is the object to which it refers (its denotation). ‘Naïve’ view because, lacking a theory, signs are signs of things, right? The naïve view is motivated by Frege’s conception of logic, if we take what logic preserves to be meaning.
Two-Level Theory of Meaning Frege instead opts for a two-level theory of meaning: sense & reference.
means Dog determines grasps ? Sense of “Dog” Dog Mind
Dummett on Sense Different interpreters have given distinct glosses on Frege’s “sense.” (a) Dummett: mode of presentation as a path to referent, method for determining reference.
Evans on Sense Different interpreters have given distinct glosses on Frege’s “sense.” (b) Evans: mode of presentation like a mode of dancing, way of relating to the referent
Sense & Reference Clearly, Frege thinks that sense determines reference “Reference” is known variously as ‘nominatum’, ‘denotation’, ‘bedeutung’, and even ‘meaning’ The two-level view is motivated by its solution to two puzzles: the puzzle of cognitive significance and “Frege’s Puzzle”
Names, for Frege • A proper name (‘George Foreman’, ‘Denmark’, ‘512’, etc.) • A definite description (‘the square root of 2’, ‘the first female senator’, ‘the center of mass of the universe’, etc.) • Presumably other definite NPs, like ‘he’, ‘it’, ‘that dog’ • As we’ll see, sentences • But not: verbs, common nouns, or quantifier phrases
Identity Statements It’s plausible to think that identity statements have as their meaning a relation that hold between a thing and itself (and nothing else) But this runs into a problem when we assume: • That the meaning of a term is its referent • Anyone who knows the meanings of t and t’, where those meanings are identical, knows that t = t’
A Posteriori Identities • Superman is Clark Kent • Today is Tuesday • Garth Brooks is Chris Gaines • William Sydney Porter is O. Henry • Cilantro is coriander • Groundhogs are woodchucks • Orcutt is the greatest Russian spy • That guy is the chief executive of Hong Kong
The Problem The problem of cognitive significance is not about identity statements, however The problem is about co-referring terms that nevertheless have different meanings. It arises whenever there are two different ways of talking about the same thing.
Not about Identity Sentences The sentences: • Superman can fly. • Clark Kent can fly. Differ in cognitive significance, even though they are not identity sentences.
The Metalinguistic Solution Perhaps ‘A = B’ really just means “the referent of ‘A’ is the same as the referent of ‘B’” That is, ‘=’ doesn’t express identity of referent but coreference of sign. Makes identity statements informative. Indeed, Frege held this view in his earlier work
A Posteriori Identities • ‘Superman’ refers to the same thing as ‘Clark Kent’ • ‘Today’ refers to the same thing as ‘Tuesday’ • ‘Garth Brooks’ refers to the same thing as ‘Chris Gaines’ • ‘William Sydney Porter’ refers to the same thing as ‘O. Henry’ • ‘Cilantro’ refers to the same thing as ‘coriander’ • ‘Groundhogs’ refers to the same thing as ‘woodchucks’ • ‘Orcutt’ refers to the same thing as ‘the greatest Russian spy’ • ‘That guy’ co-refers with ‘the chief executive of Hong Kong’
Word vs. World Frege didn’t even think it got the informativity of identity statements right, though We learn something about the world when we are told ‘the center of mass of the universe is the tip of the nose of Barack Obama’ On the proposed theory, however, we only learn about words.
Wrong Predictions Further, the manner of designation makes the difference, not merely differential signs For example ‘V = 5’ does not differ in cognitive significance from ‘5 = 5’
Doesn’t Work for Variables Finally, this account doesn’t explain the use of the identity symbol between variables (as in Leibniz’s Law): LL: For all objects x and y, if x = y, then Fx if and only if Fy.
Doesn’t Work for Variables Finally, this account doesn’t explain the use of the identity symbol between variables (as in Leibniz’s Law): LL: For all objects x and y, if ‘x’ refers to the same thing as ‘y’, then Fx if and only if Fy.
Not about Identity Sentences And to top it all off, the metalinguistic account makes no headway on the general problem of cognitive significance.
Not about Identity Sentences • Superman can fly. • The referent of ‘Superman’ can fly. • Clark Kent = the referent of ‘Superman.’ • Clark Kent can fly.
Leibniz’s Law Those objects are the same which may be switched for one another without changing the truth (salvaveritate). For any two names ‘A’ and ‘B’, the object ‘A’ designates is the object ‘B’ designates if and only from any sentence S(A) containing A, we can infer S(B) and vice versa.
Instances John met Benjamin Franklin. Benjamin Franklin = the inventor of bifocals. Therefore, John met the inventor of bifocals. Plato taught Aristotle. Aristotle = the teacher of Alexander the Great. Therefore, Plato taught the teacher of Alexander the Great.
Counterexamples Fregenoticed a certain class of words that can wreak havoc with Leibniz’s Law, the propositional attitude verbs: believe, know, discover, understand, recognize, say, doubt, etc
1. John believes Benjamin Franklin liked Belgian waffles. 2. Mary discovered that Benjamin Franklin liked potato salad. 3. Sam doubts that Benjamin Franklin liked deep dish pizza. 1’. John believes that the inventor of bifocals liked Belgian waffles. 2’. Mary discovered that the first postmaster general liked potato salad. 3’. Sam doubts that the author of Poor Richard’s Almanac liked deep dish pizza.
