Einführung in die Theoretische Philosophie: Sprachphilosophie

1. Einführung in die Theoretische Philosophie: Sprachphilosophie Nathan Wildman nathan.wildman@uni-hamburg.de

2. Frege’sOn Sense and Reference Why postulating a third realm is necessary to capture the meaning of singular terms

3. Some Preliminaries Three 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.

4. Some Preliminaries This 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.

5. ‘Bucephalus is a horse’ Bucephalus is a horse What does this sentence mean?

6. ‘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?

7. ‘Bucephalus is a horse’ Singular term =dfan expression that purports to stand for a single, distinct object Fourkinds: • 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’

8. ‘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’

9. Bucephalus According to the Naïve Theory, a singular terms’ meaning is its reference ‘Bucephalus’ refers to/denotes the following object:

10. Bucephalus What does ‘The favourite horse of Alexander’ refer to?

11. Bucephalus So 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 meanthe same thing?

12. Bucephalus Intuitive conclusion: • same truth conditions, extension, reference Consequence: substitute co-referring terms salvaveritate ‘Bucephalus is a horse’ ⇳ ‘The favourite horse of Alexanderis a horse’ Isn’t the bottom sentence rather… obvious?

13. 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?!?

14. Identity Statements What 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’

15. Identity Statements We can translate identity statements into quasi-formal language as follows, to avoid confusing ourselves about which ‘is’ is used: Hesperus = Phosphorus Bruce Wayne = Batman Prof. Schnieder = Dr.Schnieder

16. 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 = 125 x2 + 2x + 2= 4

17. 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?’

18. Frege on Identity When we express ‘Hesperus is Phosphorus’ using the ‘is’ of identity, ought we to write it as • Hesperus = Phosphorus • ‘Hesperus’ = ‘Phosphorus’

19. Identity as a Relation between Things When I say ‘Hesperus is Phosphorus’, I mean (1) Hesperus = Phosphorus Evening Morning =

20. Identity as a Relation between Things Frege 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=b is synthetic, a posteriori, of high cognitive value

21. Aside: A priori, A posteriori A 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

22. Aside: A priori, A posteriori a 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.

23. Aside: Analytic & Synthetic Analytic: 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.

24. Identity as a Relation between Things Further 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)

25. Identity as a Relation between Things Oedipuseventuallylearns (R) The motherofOedipus = thewifeofOedipus Reaction: • Oedipusputs out owneyes • Jocastacommitssuicide • Freud makestonsofmoney

26. Identity as a Relation between Things Jesus = Jesus The Son of God = The Son of God • Analytic, a priori, of negligible cognitive value Jesus = the Son of God • Synthetic, a posteriori, potentially of cognitive value

27. Identity as a Relation between Things Frege 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=b is synthetic, a posteriori, of high cognitive value

28. Identity as a Relation between Things Frege 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

29. 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.

30. Identity as a Relation between Things The argumentreconstructed (P1) Ifidentityis a relationbetweenobjects, ‘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.

31. Identity as a Relation between Names Let’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’

32. Identity as a Relation between Names Problem: (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?

33. Identity as a Relation between Names Frege 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

34. 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.

35. Dilemma about Identity A 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)

36. Identity as a Relation between Names The Frege ofOn Sense and Reference rejectsthisanswer: ‘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.’

37. 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.

38. 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?

39. 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’

40. Identity as a Relation between Names Imagine 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!

41. 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

42. Identity as a Relation between Names (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.

43. Dilemma aboutIdentity 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?

44. Diagnosingthe Problem The argument against identity relating objects (P1) Ifidentityis a relationbetweenobjects, ‘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.

45. Diagnosingthe Problem We know good reasons to believe premises (P2) and (P3) But why believe (P1) Ifidentityis a relationbetweenobjects, ‘a=a’ and ‘a=b’ must have the same meaning

46. Diagnosingthe Problem Answer: 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

47. Diagnosingthe Problem There 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!) =

48. Between Scylla & Charybdis Frege’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!

49. Between Scylla & Charybdis Frege: ‘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.’

50. Between Scylla & Charybdis C BC A AB B