EINFÜHRUNG IN DIE THEORETISCHE PHILOSOPHIE:

SPRACHPHILOSOPHIE

Nathan Wildmannathan.wildman@uni-hamburg.de

FREGE’S ON SENSE AND

REFERENCEWhy postulating a third realm is necessary to

capture the meaning of singular terms

SOME PRELIMINARIESThree plausible principles

TRUTH: If expression E is true in language L, then E is meaningful in L.

MEANINGFULNESS: If expression E is meaningful in language L, then each constituent expression of E is meaningful in L.

COMPOSITIONALITY: The meaning of a complex expression depends on the meaning and arrangement of its constituent parts.

SOME PRELIMINARIESThis last point pushes us to the following:

Suppose that expression a and expression b have the same meaning. We can then construct complex expressions with them as parts and, provided the other parts are the same, these new complex expressions are the same as well.

COGNITIVE VALUE:If two expressions differ in cognitive value, they

must differ in meaning.

‘BUCEPHALUS IS A HORSE’

Bucephalus is a horse

What does this sentence mean?

‘BUCEPHALUS IS A HORSE’

Give the Prelims (esp. COMPOSITIONALITY) , the question on the previous slide breaks down into two new

questions:

What does ‘Bucephalus’ mean?What does ‘is a horse’ mean?

Bucephalus is a horse

Singular Term Predicate

‘BUCEPHALUS IS A HORSE’Singular term =df an expression that purports to stand for a single, distinct object

Four kinds: Ordinary proper names

– ‘Barkles, Prof. Schnieder’ Definite descriptions

– ‘The dog on the table, The Present King of France’ Singular indexical pronouns

– ‘I, Here, Now’ Demonstratives

– ‘This; This dog’

‘BUCEPHALUS IS A HORSE’

Terminological point:

When Frege (as translated by Black & Fitel) uses the expression ‘proper name’ in ‘On Sense and Reference’ he means ‘singular term’ in general, not just ‘ordinary proper name’

BUCEPHALUSAccording to the Naïve Theory,

a singular terms’ meaning is its reference

‘Bucephalus’ refers to/denotes the following object:

BUCEPHALUSWhat does ‘The favourite horse of Alexander’ refer

to?

BUCEPHALUSSo we have two terms that refer to the same thing,

and therefore mean the same thing:

Question: Is the Naïve Theory correct? Namely, do these terms mean the same

thing?

BUCEPHALUSIntuitive conclusion:

same truth conditions, extension, reference

Consequence: substitute co-referring terms salva veritate

‘Bucephalus is a horse’ ⇳‘The favourite horse of Alexander is a horse’

Isn’t the bottom sentence rather… obvious?

RELATED

‘Superman’ & ‘Clark Kent’ refer to the same object

Lois believes that Clark Kent is a reporter.

Lois does not believe that Superman is a reporter.

How to explain the difference between Lois’ beliefs, given that Superman is Clark Kent?!?

IDENTITY STATEMENTSWhat is an identity statement?

When we have two singular terms linked by an ‘is’

‘Bob Dylan is Robert Zimmerman’

Can be contrasted with a predicational statement, which has a singular term linked to a predicate

‘Bob Dylan is a musical genius’

IDENTITY STATEMENTS

We can translate identity statements into quasi-formal language as follows, to avoid confusing

ourselves about which ‘is’ is used:

Hesperus = PhosphorusBruce Wayne = Batman

Prof. Schnieder = Dr. Schnieder

IDENTITY STATEMENTS

By so translating, we treat ‘=’ as being a singular term for the identity or equality relation

You’re all familiar with this relation – you used it in school:

5 x 5 x 5 = 125x2 + 2x + 2= 4

FREGE ON IDENTITY

Frege’s opening question:

‘Equality gives rise to challenging questions which are not altogether easy to answer. Is it a relation? A

relation between objects, or between names or signs of objects?’

FREGE ON IDENTITY

When we express ‘Hesperus is Phosphorus’ using the ‘is’ of identity, ought we to write it as

(1) Hesperus = Phosphorus

(2) ‘Hesperus’ = ‘Phosphorus’

IDENTITY AS A RELATION BETWEEN THINGSWhen I say ‘Hesperus is Phosphorus’, I mean

(1) Hesperus = Phosphorus

Evening Morning

=

IDENTITY AS A RELATION BETWEEN THINGSFrege points out the following:

‘a=a and a=b are obviously statements of differing cognitive value; a=a holds a priori and, according to Kant, is to be labelled analytic, while statements of

the form a=b often contain very valuable extensions of our knowledge and cannot always be

established a priori.’ a=a

is analytic, a priori, of negligible cognitive

value

a=bis synthetic, a posteriori,of high cognitive value

ASIDE: A PRIORI, A POSTERIORIA priori: literally, ‘from before’. Knowledge that is a priori is knowledge that can be gained independent of experience.

You don‘t need to get out of your armchair to know or learn something a priori.

All bachelors are unmarried men It is either raining or not raining outside

ASIDE: A PRIORI, A POSTERIORIa posteriori: ‘from the later’. Knowledge whose gaining requires experience.

You do have to get out of the armchair and go check on the world to know or learn something a posteriori.

All bachelors are happier than married men. It is raining outside.

ASIDE: ANALYTIC & SYNTHETICAnalytic: an expression who’s truth is guaranteed by the meanings of its constituent expressions

All vixens are female foxes

Synthetic: an expression that isn’t analytic

All vixens are not coloured green.

IDENTITY AS A RELATION BETWEEN THINGSFurther examples of cognitive difference

Oedipus & Jocasta

(M): Jocasta = the mother of Oedipus(unknown to Oedipus)

(W): Jocasta = the wife of Oedipus(known to Oedipus)

(J) Jocasta = Jocasta(known to Oedipus)

IDENTITY AS A RELATION BETWEEN THINGSOedipus eventually learns

(R) The mother of Oedipus = the wife of Oedipus

Reaction: Oedipus puts out own eyes Jocasta commits suicide Freud makes tons of money

IDENTITY AS A RELATION BETWEEN THINGS

- Analytic, a priori, of negligible cognitive value

Jesus = the Son of God

- Synthetic, a posteriori, potentially of cognitive value

Jesus =

Jesus

The Son of God =

The Son of God

IDENTITY AS A RELATION BETWEEN THINGSFrege points out the following:

‘a=a and a=b are obviously statements of differing cognitive value; a=a holds a priori and, according to Kant, is to be labelled analytic, while statements of

the form a=b often contain very valuable extensions of our knowledge and cannot always be

established a priori.’ a=a

is analytic, a priori, of negligible cognitive

value

a=bis synthetic, a posteriori,of high cognitive value

IDENTITY AS A RELATION BETWEEN THINGSFrege objects:

‘Now if we were to regard identity as a relation between that which the names ‘a’ and ‘b’

designate, it would seem that a=b could not differ from a=a.’

According to the Naive theory, the meaning of ‘a’ just is the referent of the term; same for ‘b’.

‘a = a’ and ‘a = b’ must, if true, mean the same thing

IDENTITY AS A RELATION BETWEEN THINGS

But two expressions that mean the exact same thing can’t have different cognitive values

COGNITIVE VALUE:If two expressions differ in cognitive value, they

must differ in meaning.

IDENTITY AS A RELATION BETWEEN THINGSThe argument reconstructed

(P1) If identity is a relation between objects, ‘a=a’ and ‘a=b’ must have the same meaning.

(P2) If two expressions mean the same thing, the do not differ in cognitive value.

(P3) ‘a=a’ and ‘a=b’ differ in cognitive value.

(4) ‘a=a’ and ‘a=b’ do not mean the same thing.

∴ (C1): Identity is not a relation between objects.

IDENTITY AS A RELATION BETWEEN NAMESLet’s then take the other horn and assume that identity is a relation between names.

So ‘Hesperus is Phosphorus’ ought to be written as

(2) ‘Hesperus’ = ‘Phosphorus’

IDENTITY AS A RELATION BETWEEN NAMESProblem:

(2) ‘Hesperus’ = ‘Phosphorus’

Indiscernibility of Identicals:If x and y are identical, then they have all the same

properties.

How many letters do our two words have?

IDENTITY AS A RELATION BETWEEN NAMESFrege to the rescue:

‘What is intended to be said by a=b seems to be that the signs or names ‘a’ and ‘b’ designate the same thing, so that those signs themselves would

be under discussion; a relation between them would be asserted.’

So instead of

(2) ‘Hesperus’ = ‘Phosphorus’

we should really write something like

IDENTITY AS A RELATION BETWEEN NAMES(3) The terms ‘Hesperus’ and ‘Phosphorus’

designate the same thing.

This is the Metalinguistic thesis about identity. Frege previously accepted such a view.

In short: Names usually stand for objects. But when flanking

a ‘=’ sign, the names pull double-duty, standing both for their content and for themselves.

DILEMMA ABOUT IDENTITYA previous time-slice of Frege:

‘Equality of content differs from conditionality and negation by relating to names, not to contents. Elsewhere, signs are mere proxies for their content, and thus any phrase they occur in just expresses a relation between their various contents; but names at once appear in propria persona so soon as they are joined by the symbol for equality of content; for this signifies the circumstance of two names’ having the same content. Thus, along with the introduction of a symbol for equality of content, all symbols are necessarily given a double meaning — the same symbols stand now for their own content, now for themselves. . . . The need for a symbol for equality thus rests on the following fact: the same content can be fully determined in different ways; and that, in a particular case, the same content is actually given by two ways of determining it, is the content of a judgement . . . It is clear from this that different names for the same content are not always a trivial matter of formulation; if they go along with different ways of determining the content, they are relevant to the essential nature of the case.’ (Frege, Bs, §8)

IDENTITY AS A RELATION BETWEEN NAMESThe Frege of On Sense and Reference

rejects this answer:

‘But this relation [identity] would hold between the names or signs only in so far as they named or

designated something. It would be mediated by the connection of each of the two signs with the same designated thing. But this is arbitrary. Nobody can

be forbidden to use any arbitrarily producible event or object as a sign for something. In that case the

sentence a = b would no longer refer to the subject matter, but only to our mode of designation; we

would express no proper knowledge by its means.’

IDENTITY AS A RELATION BETWEEN NAMES‘But this relation [identity] would hold between the

names or signs only in so far as they named or designated something. It would be mediated by the connection of each of the two signs with the same

designated thing.’

(2) ‘Hesperus’ = ‘Phosphorus’

(3) The terms ‘Hesperus’ and ‘Phosphorus’ designate the same thing.

IDENTITY AS A RELATION BETWEEN NAMES‘But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a

sign for something.’

There is no necessary connection between a name and the object named.

Is there something that makes it necessary that ‘Nathan’ refers to me?

Could you have been called something else?

IDENTITY AS A RELATION BETWEEN NAMES‘In that case the sentence a = b would no longer refer to the subject matter, but only to our mode of designation; we would express no proper knowledge by its means.’

If identity statements just tell us that two terms co-refer, they tell us nothing about the world.

But that’s not how identity statements work – I do say something about the world with claims like ‘Hesperus is Phosphorus’

IDENTITY AS A RELATION BETWEEN NAMESImagine that Lex Luther learns that

(CS) Clark Kent = Superman

If identity was just a relation between names, he must understand this as telling him that ‘Clark Kent’ and ‘Superman’ can be used to refer to the same object

This isn’t news – Luther wanted to know who Superman is, not whether he could call him by the same name as some mild-mannered reporter for the Daily Planet!

IDENTITY AS A RELATION BETWEEN NAMES(P1) If identity is a relation between names, then what we learn from identity statements is that two

terms designate the same thing

(P2) If what term we use to designate an object is arbitrary, then learning that two terms

designate the same thing does not give us proper knowledge

(P3) What term we use to designate an object is arbitrary

(4) Learning that two terms designate the same thing does not give us proper knowledge

(5) If identity is a relation between names, then identity statements do not give us proper knowledge

(P6) Identity statements do give us proper knowledge about the world

∴ (C2) Identity is not a relation between names.

IDENTITY AS A RELATION BETWEEN NAMES

DILEMMA ABOUT IDENTITY

Frege’s Puzzle About Identity:

Identity cannot be a relation between objects, nor can it be a relation between names of objects.

We are stuck either way.

What should we do?

DIAGNOSING THE PROBLEMThe argument against identity relating objects

(P1) If identity is a relation between objects, ‘a=a’ and ‘a=b’ must have the same meaning.

(P2) If two expressions mean the same thing, the do not differ in cognitive value.

(P3) ‘a=a’ and ‘a=b’ differ in cognitive value.

(4) ‘a=a’ and ‘a=b’ do not mean the same thing.

∴ (C1): Identity is not a relation between objects.

DIAGNOSING THE PROBLEM

We know good reasons to believe premises (P2) and (P3)

But why believe

(P1) If identity is a relation between objects, ‘a=a’ and ‘a=b’ must have the same meaning

DIAGNOSING THE PROBLEMAnswer:

the Naïve Theory !

The meaning of a singular term is the referent

The meaning of ‘Buceplaus’ is Bucephalus – the horse himself

The same with ‘The favourite Horse of Alexander’ – this means the horse himself

DIAGNOSING THE PROBLEMThere is therefore no way to explain the difference

in cognitive value between

(HH) Hesperus is Hesperus

(HP) Hesperus is Phosphorus

because asking about the meanings of ‘Hesperus’ and ‘Phosphorus’ immediately pushes us to their reference (which happens to be the same thing!)

=

BETWEEN SCYLLA & CHARYBDISFrege’s thought:

The second horn is insurmountable, but maybe not the first. If there was some third element, beyond

the name and the name’s referent, which explained difference in cognitive significance, then we would

have a solution to the puzzle!

BETWEEN SCYLLA & CHARYBDISFrege:

‘A difference can arise only if the difference between the signs corresponds to a difference in the mode of presentation of that which is designated. Let a, b, c be the lines connecting the vertices of a triangle with the midpoints of the opposite sides. The point of intersection of a and b is then the same as the point of intersection of b and c. So we have different designations for the same point, and these names … likewise indicate the mode of presentation; and hence the statement contains actual knowledge.’

BETWEEN SCYLLA & CHARYBDIS

A

B

C

BC

AB

BETWEEN SCYLLA AND CHARYBDISWe need some third element that captures the

mode of presentation of a object via a singular term

Will be distinct from the referent Will not just be the word itself Must be graspable by us

A BAD IDEA

Use ideas!

I.e. mental thing that occurs in your head when you use ‘The favourite horse of Alexander’ to refer to

Bucephalus

Proposal: different names are related to different ideas, and it is these different ideas that explains

the difference in cognitive value between ‘a=a’ and ‘a=b’

A BAD IDEAProblem:

‘Si duo idem facuint, non est idem. If two persons picture the same thing, each still has his own idea.

It is indeed sometimes possible to establish differences in the ideas, or even in the sensations, of different men; but an exact comparison is not

possible, because we cannot have both ideas together in the same consciousness.’

[If two do the same, it is not the same]

A BAD IDEAIdeas are essentially subjective – no matter how hard I try, I can’t have the same idea as you (or vice versa)

This is bad, because it seems pretty clear that we can both mean the same thing by what we say– ‘a common store of thoughts, a common science’ would be impossible

More generally, nobody could saying anything meaningful to anybody else

If meaning is objective and ideas are subjective, then ideas could not explain meaning

FREGE’S SENSIBLE SOLUTIONFrege’s suggestion:

‘It is natural, now, to think of there being connected with a sign (name, combination of words, letter), besides that to which the sign refers, which may be called the reference of the sign, also what I should like to call the sense of the sign, wherein the mode of presentation is contained. In our example, accordingly, the reference of the expressions ‘the point of intersection of a and b’ and ‘the point of intersection of b and c’ would be the same, but not their senses. The reference of ‘Hesperus’ would be the same as that of ‘Phosphorus’, but not the sense’

Reference

FREGE’S STORY FOR SINGULAR TERMS

Singular Term

DETERMINES

DENOTES/REFERS TO

EXPRESSES

Sense of Singular Term

FREGE’S STORY FOR SINGULAR TERMS

‘Bucephalus’

DETERMINES

DENOTESEXPRESSES

Sense of ‘Bucephalus’

FREGE’S STORY FOR SINGULAR TERMS ‘The Favourite Horse of Alexander’

DETERMINES

DENOTESEXPRESSES

Sense of the F.H.A.

FREGE’S STORY FOR SINGULAR TERMS‘The Favourite Horse of Alexander’ ‘Bucephalus’

EXPRESSES

EXPRESSES

DETERMINES DETERMINESSense

of the

F.H.A.

Sense of Buce.

SUMMING UP FREGE ON SINGULAR TERMS

‘Frege’s idea was that to understand an expression, one must not merely think of the reference that it is

the reference, but that one must, in so thinking, think of the reference in a particular way. The way

in which one must think of the reference of an expression in order to understand it is that

expression’s sense.’

(Evans 1981: 294)