Sense - PowerPoint Presentation

Slide1

SenseSlide2

structured propositionsSlide3

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 constituentsSlide4

Benefits

Systematicity: if you can think

aRb

, you can think

bRa

Reverse compositionality

Conflating contexts: ‘watch’ + PAST vs. ‘watch’ + PROG + PASTSlide5

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 = aSlide6

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?Slide7

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?Slide8

interpreted logical formsSlide9
Slide10

Interpreted Logical Forms

Linguistic syntax

LFs vs. surface structure (not particularly important)

Interpreted

LFs

No new “going together”Slide11

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-conditionsSlide12

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

”Slide13

senseSlide14

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

 Slide15

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

”Slide16

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 languageSlide17

Overview of “on sense and reference”Slide18

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 meaningSlide19

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

referentSlide20

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

”Slide21

Cognitive significanceSlide22

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

phrasesSlide23

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’Slide24

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 sameSlide25

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 thingSlide26

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 workSlide27

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

wordsSlide28

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’Slide29

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

.Slide30

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.’Slide31

Frege’s puzzleSlide32

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.Slide33

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.Slide34

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,

etcSlide35

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

.Slide36

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 referentsSlide37

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.’Slide38

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 asphaltSlide39

The Telescope Analogy

A

nyone

can see the optical image in the telescope—it’s objective—but it is not the object itself, but merely a presentation of itSlide40

Dummett and Evans again

The

path is there for

everyone

Two

people can both bear the same relation R to a third thingSlide41

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.Slide42

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.Slide43

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)Slide44

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 factsSlide45

Relation between S and Truth-Value

T

he

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.”Slide46

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.Slide47

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

.Slide48

Sense to the rescue: cognitive significanceSlide49

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.’Slide50

Mereology of Sense

Notice that this requires a substantive theory of the composition of senses, which Frege does not

provide.

T

he

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.

A

nalogy

: my right-half + my left-half = my upper-half + my

lower-half.Slide51

Sense to the rescue: frege’s

puzzleSlide52

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. Slide53

Violation of Compositionality?

Although Frege takes this to be in accord with the compositionality of reference, it clearly is not, as it violates locality.Slide54

Frege’s Solution to Frege’s Puzzle

I

n 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.Slide55

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.Slide56

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.