senses. sense frege’s goal frege: mathematical truths are analytic a priori. we know them via...

Senses

Sense

Frege’s Goal

Frege: mathematical truths are analytic a priori. We know them via proofs which can be mechanically verified. This is called “logicism.”

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

Frege rejects 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.

MindSense of “Dog” Dog

?

Dog

grasps determines

means

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”

Cognitive Significance

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, sentencesv. 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 referentb) 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.

Frege’s Puzzle

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

ThinkersSense of “Dog” Dog

? grasp determines

Senses

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.’

MindSense of “Dog”

Dog

?grasps determines

?

?Sense of “Michael’s favorite animal”

Sense of “Canine”

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

Associated Image

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.”

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 .

Sense to the Rescue: Cognitive Significance

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.

Sense to the Rescue: Frege’s Puzzle

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.