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

“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:

A & B A&B

Meaning of “Superman Flies”

Meaning of “Clark Kent Flies”

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)

Interpreted Logical Forms

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”

Superman,

flies,

Meaning of “Clark Kent Flies”

Clark Kent,

flies,

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 est rond.

Sense

Gottlob Frege

• 1848-1925• German mathematician• Principal contributor to modern

logic• Worked on the foundations of

mathematics• Anti-semite, not very nice

Gottlob Frege

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.

Overview of “On Sense and Reference”

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.

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

1. Superman can fly.2. The referent of ‘Superman’ can

fly.3. Clark Kent = the referent of

‘Superman.’4. Clark Kent can fly.

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.”

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 .