Structured Propositions Like SofAs: objects, properties, relations Structural isomorphism w/ sentences New kind of “going together” Limits: articulated non-constituents “John is a tall ballet dancer” Limits: unarticulated constituents
Benefits Systematicity: if you can think aRb, you can think bRa Reverse compositionality Conflating contexts: ‘watch’ + PAST vs. ‘watch’ + PROG + PAST
Grainedness SPs strictly more fine grained than SofAs SPs determine sets of possible worlds, not vice versa (composition post-linguistic) No logical omniscience, deduction, aboutness problems Too much grain? A & B vs. B & A Names and natural kind terms, a = b vs. a = a
Problems Which set-theoretic objects? (order arbitrariness) Why do some set-theoretic objects have truth- conditions and others (regular ones) not? Is the “going together” really not set-theoretic? If not, then what is it?
Overly Linguistic-y? If propositions have a largely linguistic structure… do they get it from language? If so, are they really mind/ language dependent? If so, did the proposition that dinosaurs exist not exist until we did? And can animals think?
Interpreted Logical Forms Linguistic syntax LFs vs. surface structure (not particularly important) Interpreted LFs No new “going together”
Benefits Strictly greater grain the SPs (Hence same or worse grainedness problems, same or better benefits) Names and natural kind terms, a = b vs. a = a Meaningful sentences with empty names? Sensible why they have truth-conditions
Problems Compositionality? Speakers of different languages no longer expressing the same proposition, believing the same things Data: “I believed that even when I was a monolingual French speaker!” Attitudes, propositions dependent on language Pierre and “Londres est jolie”
Frege’s Legacy 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
Frege’s Ambition 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 Frege: such truths are analytic a priori. We know them via proofs which can be mechanically verified. This is called “logicism”
Frege’s Tragedy Right before the publication of the 2 nd volume of the Foundations of Arithmetic, Frege received Russell’s letter For the remaining 21 years of his life, Frege only published papers elaborating his philosophy of language
Naïve View Frege rejects the view that the meaning of a term is the object to which it refers ‘Naïve’ view because, lacking a theory, signs are signs of things, right? Motivated by Frege’s conception of logic, if we take what logic preserves to be meaning
Sense & Reference Frege instead opts for a two-level theory of meaning: sense & reference Different interpreters have given distinct glosses on Frege’s “sense” (a) Dummett: mode of presentation as a path to refernt, method for determining reference (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 (i) A proper name (‘George Foreman’, ‘Denmark’, ‘512’, etc.) (ii) A definite description (‘the square root of 2’, ‘the first female senator’, ‘the center of mass of the universe’, etc.) (iii) Presumably other definite NPs, like ‘he’, ‘it’, ‘that dog’ (iv) As we’ll see, sentences (v) 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: (a) That the meaning of a term is its referent (b) Anyone who knows the meanings of t and t’, where those meanings are identical, knows that t = t’
A Posteriori Identities That is, we don’t know a priori that ‘Today is Tuesday’ or ‘Garth Brooks is Chris Gaines’ even though the term reference is the same
The Problem The problem of cognitive significance is not about identity statements, however The sentences ‘He-Man enjoys battle’ and ‘Prince Adam enjoys battle’ differ in cognitive significance, even though neither is an identity statement. The problem is about co-referring terms that nevertheless have different meanings. Construct it by having 2 different ways of talking about the same thing
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
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 George W. Bush’ 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.
Not General And to top it all off, the metalinguistic account makes no headway on the general problem of cognitive significance We can’t say “Hesperus is bright” means “The referent of ‘Hesperus’ is bright”, because Phosphorus = the referent of ‘Hesperus.’
Leibniz’s Law Those objects are the same which may be switched for one another without changing the truth (salva veritate). 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 Frege noticed 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.
Three Options 1. Deny Leibniz’s Law and abandon our “semantic innocence” 2. Deny the counterexamples and claim that, e.g., (1) and (1’) cannot differ in truth-value 3. Claim that in the context of a propositional attitude verb, terms do not have their usual referents
Senses For Frege, senses are objective: two people who grasp the sense of ‘horse’ are grasping one and the same thing. The sense of a word is grasped by everyone who understands it Each object can be the referent determined by many (perhaps infinite) senses. That is, many different locutions (with different meanings) can all pick out the same thing. Some senses have no referent, e.g. ‘the least rapidly converging series’ or ‘Odysseus.’
Associated Images In particular, they are not the “ideas” we associate with words. When I hear “horse”, I may think of a horse of a specific color, but “horse” doesn’t mean “brown horse.” Image depends on context, while sense is directly associated with the word itself (a) He rode his gallant horse (b) The horse stumbled on the wet asphalt
The Telescope Analogy Anyone can see the optical image in the telescope—it’s objective—but it is not the object itself, but merely a presentation of it
Dummett and Evans again The path is there for everyone Two people can both bear the same relation R to a third thing
Senses Frege says that a sign expresses its sense; and this sense designates its referent. To understand an expression is to grasp its sense; one need not know its referent.
Compositionality of Reference The reference of a complex expression is determined by the reference of its parts. This principle is motivated by logic itself: logic preserves truth; truth is unchanged by mode of presentation. The method of determination for Frege is function application.
Referent of a Sentence It can’t be a proposition: this violates compositionality of reference: if term A designates object O and B also designates O, it is not generally true that the proposition (“thought”) P(A) = the proposition P(B)
Referent of a Sentence Leibniz’s Law entails that the truth-value is unchanged when we allow arbitrary substitution of identicals. It’s a further claim of Frege’s that the truth-value is the only thing that remains unchanged. This implies that all truths have the same referent, The True. Perhaps this is supposed to be the totality of all facts
Relation between S and Truth-Value The relation between a sentence and its truth- value is not one of subject to predicate. First, although we say things like “The thought that it’s raining is true,” this means neither more nor less than “It’s raining.”
Judging ≠ Predicating Truth Second, to judge something true is not to predicate truth of it, Example: If the thought that flounders snore is true, then flounders snore. Example: Either the thought that snow is green is true or the thought that snow is white is.
Compositionality of Sense The sense of a complex expression is determined by the sense of its parts. This principle is motivated by a theory of language understanding: how we can understand a potential infinitude of novel utterances, given our finite means. Crucially, Frege gives no method of composition for senses.
Cognitive Significance To understand a word is to grasp its sense. One can grasp the sense of ‘Hesperus’ without knowing its referent. And in general, if we do not know the referents of the parts, we will not know the referent of the whole, that is, the truth value of ‘Hesperus = Phosphorus.’
Mereology of Sense Notice that this requires a substantive theory of the composition of senses, which Frege does not provide. The theory must say the complex ‘Hesperus is Phosphorus’ differs in sense from ‘P = P’, though this doesn’t fall out merely from its dependence on the sense of the parts. Analogy: my right-half + my left-half = my upper- half + my lower-half.
Motivation: Quotation “Benjamin Franklin” has 16 letters. Benjamin Franklin = the inventor of bifocals. “The inventor of bifocals” has 16 letters. Here we have an apparent violation of Leibniz’s Law. But the solution is obvious: ‘Benjamin Franklin’ does not have the same referent when it occurs inside quote marks as it does when it occurs outside of them.
Violation of Compositionality? Although Frege takes this to be in accord with the compositionality of reference, it clearly is not, as it violates locality.
Frege’s Solution to Frege’s Puzzle In propositional attitude ascriptions, words don’t have their customary referents. Frege claims that in these cases, the terms have their customary senses as their referents; these are then their indirect referents. This explains why you can’t substitute co- referring terms in attitude contexts.
More Motivations This isn’t entirely abstract speculation: Frege rightly points out that in propositional attitude contexts, what we care about is the thought, not whether it’s true (the customary referent). Furthermore, the fact that we can substitute two expressions with the same customary sense in these contexts salva veritate seems to suggest that the customary sense is the indirect referent.
The Infinite Heirarchy How is Frege going to treat embedded attitude ascriptions: “John believes that Lois believes that Superman can fly.” “that Superman can fly” will have as its referent its customary sense, which is itself a sense.