Einführung in die Theoretische Philosophie: Sprachphilosophie

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

Russell’s On Denoting & Descriptions Or, the lecture where we discuss a series of puzzles& problems that concerned theThird Earl Russell

Puzzles A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical sciences. I shall therefore state [several] puzzles which a theory [of] denoting ought to be able to solve; and I shall show later that my theory solves them. -Russell

The Plan • Re-state the Puzzles • Frege’s Answers to the Puzzles • Some Russellian objections to Frege • The Basics of Russell’s views Stated • Over-view of Russell’s solutions to the Puzzles

Stating the Puzzles • Frege’s Puzzle: How can two identity statements differ in cognitive value, if the terms involved refer to the same thing? • Predicational Puzzle: How can two predicational statements differ in cognitive value, if the singular terms involved refer to the same thing? • Substitution Puzzle: How can a = b but ‘S believes that a is F’ not mean the same as ‘S believes that b is F’?

Stating the Puzzles One of the first difficulties that confronts us, when we adopt the view that denoting phrases express a meaning and denote a denotation, concerns the cases in which the denotation appears to be absent. -Russell, OD

Stating the Puzzles • Empty Names Puzzle: how can ‘a is F’ be meaningful when ‘a’ stands for a non-existing or fictional entity? • Law of Excluded Middle: How can it be that, for any formula ϕ, (ϕ V ϕ)? • Negative Existentials Puzzle: How can ‘a does not exist’ be true?

Stating the Puzzles A quick aside: Note that (1) – (3) concern cognitive value. Meanwhile, (4) – (6) concern talk of non-existents. More importantly: The Naïve Theory is unable to solve any of them!

Frege’s Solutions • Frege’sPuzzle: How can two identity statements differ in cognitive value, if the terms involved refer to the same thing? • Frege’sAnswer:Because the terms have different senses! • Predicational Puzzle: How can two predicational statements differ in cognitive value, if the singular terms involved refer to the same thing? • Frege’sAnswer:Because the terms have different senses!

Frege’s Solutions (3) Substitution Puzzle: How can a = b but ‘S believes that a is F’ not mean the same as ‘S believes that b is F’? • Frege’s Answer:indirect discourse In indirect (oblique) discourse we speak of the sense, e.g., of the words of someone else. From this it becomes clear that also in indirect discourse words do not have their customary reference; they here name what customarily would be their sense. (Frege, OSR) • Indirect discourse: talk regarding the sense • Direct discourse: talk regarding the reference

Frege’s Solutions So, when we engage in indirect discourse, an expression does not refer to it’s referent, but rather to its sense • Lois believes that {Clark Kent is a reporter}. • Lois does not believe that {Superman is a reporter}. • George believes that {Scott wrote Waverly}. • George doesn’t believe that {Walter wrote Waverly}. • Rule of thumb: if a sentence occurs within a ‘that’-clause, it’s an instance of indirect discourse

Frege’s Solutions • Empty Names Puzzle: how can ‘a is F’ be meaningfulwhen ‘a’ stands for a fictional entity? • Frege’s Answer:Expresses a thought, but lacks a referent! • Charlieis a unicorn. {[Charlie] + [is a unicorn]} • Charlie is the star of a series of Youtube cartoons. • Charlie has evil friends.

Frege’s Solutions (5) Law of Excluded Middle: How can it be that, for any formula ϕ, (ϕ V ϕ)? • The Present King of France: is or isn’t he bald? By the law of excluded middle, either ‘A is B’ or ‘A is not B’ must be true. Hence either ‘The present King of France is bald’ or ‘The present King of France is not bald’ must be true. Yet if we enumerated the things that are bald, and then the things that are not bald, we should not find the present King of France in either list. Hegelians, who love a synthesis, will probably conclude that he wears a wig. (Russell)

Frege’s Solutions (a) ‘The Present King of France is bald’ Frege: (a) expresses a thought but lacks a referent • Referent of sentence is it’s truth-value Conclusion: (a) lacks a truth-value! (b) ‘The Present King of France is not bald’ Frege: (b) expresses a thought but lacks a referent • Referent of sentence is it’s truth-value Conclusion: (b) lacks a truth-value!

Frege’s Solutions • The problem: for anyformula ϕ, (ϕ V ϕ) Substitute either (a) or (b) in for ϕ – we get a violation! (5) Law of Excluded Middle: How can it be that, for any formula ϕ, (ϕ V ϕ)? • Frege’s Answer: It isn’t! We just have to accept that there are truth-value gaps.

Frege’s Solutions • Negative Existentials Puzzle: How can ‘a does not exist’ be true? • ‘The Present King of France doesn’t exist’ • ‘Charlie the Unicorn doesn’t exist’ • Frege’s Answer: ‘Affirmation of existence is in fact nothing but the denial of the number nought’ (Die Grundlagen der Arithmetik). I.e. - existence is ‘a property of a concept’. The predicate ‘exists’ is therefore understood to be attached to a first-level predicate, and hence is itself not a first-level predicate but a second-level one.

Frege’s Solutions (i) ‘Lionel Messi exists’ According to Frege, this says that there is a concept (the referent of a predicate), namely the concept of being Lionel Messiwhich has an instance. (ii) ‘The concept of being Lionel Messi has an instance’

Frege’s Solutions (i) ‘The Present King of France doesn’t exist’ According to Frege, this says that there is a concept (the referent of a predicate), namely the concept of being The Present King of France which lacks any instances. (ii) ‘The concept of being the Present King of France has no instance’ • Frege’s Answer: Existence is a second level predicate

Frege’s Solutions • Frege’s Puzzle: How can two identity statements differ in cognitive value, if the terms involved refer to the same thing? • Frege’s Answer:Because the terms have different senses! • Predicational Puzzle: How can two predicational statements differ in cognitive value, if the singular terms involved refer to the same thing? • Frege’s Answer:Because the terms have different senses! • Substitution Puzzle: How can a = b but ‘S believes that a is F’ not mean the same as ‘S believes that b is F’? • Frege’s Answer: Theory of Indirect Discourse

Frege’s Solutions • Empty Names Puzzle: how can ‘a is F’ be meaningful when ‘a’ stands for a non-existing or fictional entity? • Frege’s Answer:Expresses a thought, but lacks a referent! • Law of Excluded Middle: How can it be that, for any formula ϕ, (ϕ V ϕ)? • Frege’s Answer: It isn’t! We just have to accept that there are truth-value gaps. • Negative Existentials Puzzle: How can ‘a does not exist’ be true? • Frege’s Answer: Existence is a second level predicate

Russell’s Objections To Frege Russell rejected Frege’s solution to (5) …consider ‘the King of France is bald.’ …This also ought to be about the denotation of the phrase ‘The King of France’. But this phrase, though it has a meaning… has certainly no denotation, at least in any obvious sense. Hence one would suppose that ‘the King of France is bald’ ought to be nonsense; but it is not nonsense, since it is plainly false. –Russell, OD

Russell’s Objections To Frege Or again consider such a proposition as … ‘If u is a unit class, the u is a u’. This proposition ought to be always true, since the conclusion is true whenever the hypothesis is true. But ‘the u’ is a denoting phrase, and it is the denotation, not the meaning that is said to be a u. Now if u is not a unit class, ‘the u’ seems to denote nothing; hence our proposition would seem to become nonsense as soon as u is not a unit class. Now it is plain that such propositions do not become nonsense merely because their hypotheses are false.

Russell’s Objections To Frege The king in The Tempest might say, ‘If Ferdinand is not drowned, Ferdinand is my only son.’ Now, ‘my only son’ is a denoting phrase, which, on the face of it, has a denotation when, and only when, I have exactly one son. But the above statement would nevertheless be have remained true if Ferdinand had been in fact drowned. Thus we must either provide a denotation in cases in which it is at first sight absent, or we must abandon the view that the denotation is what is concerned in propositions which contain denoting phrases. - Russell, OD

Russell’s Objections To Frege A different example: • ‘Russell once objected to Frege’s story about the meaning of proper names OR Chewbacca is a Wookie.’ • This disjunction is true! The argument re-constructed: • We use non-denoting phrases in logically constructed expressions. • These do not become nonsense when a term used therein doesn’t have a referent – they retain their truth values. • Frege would have us say they become nonsense. • Therefore Frege is wrong.

Russell’s Objections To Frege A cheap fix: deny that there are any empty terms – i.e. posit, for every apparently denoting term, a denoted object! This is the Meinongian solution. Of the possible theories which admit such constituents the simplest is that of Meinong. This theory regards any grammatically correct denoting phrase as standing for an object. Thus ‘the present King of France’, ‘the round square’, etc. are supposed to be genuine objects. It is admitted that such objects do not subsist, but nevertheless they are supposed to be objects. (Russell, OD)

Russell’s Objections To Frege Problem: this solution is going to quickly lead to problems with the law of non-contradiction. • Is the Present King of France bald? Is he not bald? • Does he exist? Does he not exist? Further Problem: This is a very, very strange ontology. • What is the possible fat man in the doorway like?

Russell’s Objections To Frege In such theories, it seems to me, there is a failure of that feeling for reality which ought to be preserved even in the most abstract studies. Logic, I should maintain, must no more admit a unicorn than zoology can; for logic is concerned with the real world just as truly as zoology, though with its more abstract and general features. … to maintain that Hamlet, for example, exists in his own world, namely, in the world of Shakespeare's imagination, just as truly as (say) Napoleon existed in the ordinary world, is to say something deliberately confusing, or else confused to a degree which is scarcely credible. There is only one world, the ‘real’ world: Shakespeare's imagination is part of it, and the thoughts that he had in writing Hamlet are real. So are the thoughts that we have in reading the play. But it is of the very essence of fiction that only the thoughts, feelings, etc., in Shakespeare and his readers are real, and that there is not, in addition to them, an objective Hamlet. When you have taken account of all the feelings roused by Napoleon in writers and readers of history, you have not touched the actual man; but in the case of Hamlet you have come to the end of him. . . . If no one thought about Hamlet, there would be nothing left of him; if no one had thought about Napoleon, he would have soon seen to it that some onedid. (Russell, Descriptions)

Russell’s Objections To Frege Another cheap fix: pick some purely conventional denotation for the supposedly empty terms. E.g. let all non-denoting singular terms denote  ‘But this procedure, though it may not lead to actual logical error, is plainly artificial, and does not give an exact analysis of the matter.’ (Russell, OD) • Santa Claus has no members. •  has no members.

The Heart of Russell’s Objections Russell’s view: Language is a system for representing things and arrangements of things in the world. • Elements of language stand for things and properties, and complex expressions stand for complexes of things and properties. • Russell calls the kind of thing that a sentence, the most important linguistically complex expression, stands for (or expresses, or means) a proposition.

The Heart of Russell’s Objections • Constituents of propositions are the things the propositions are about: ‘I met Bertie’ expresses a proposition whose constituents are me, Bertie, and the relational property meeting. • A proposition (and any sentence that expresses it) is true iff the way things are arranged in the world ‘corresponds’ to the way the things are arranged in the proposition

The Heart of Russell’s Objections According to Russell: • The meaning of a sentence and the object of a thought is a proposition 2. Propositions are composed of objects and properties • A genuine proper name contributes the object it stands for to the proposition expressed by the sentence containing it. • Predicates contribute the properties /relations they stand for to the propositions expressed by sentences containingthem. • If ‘a’ is a name for a and ‘F( )’ is a one-place predicate that stands for the monadic property F, then ‘Fa’ expresses a proposition composed of a and F.

The Heart of Russell’s Objections Contrast with Frege: Truth is not a component part of a thought, just as Mont Blanc with its snowfields is not itself a component part of the thought that Mont Blanc is more than 4,000 meters high (Letter to Russell, 13 Nov. 1904) Thoughts, which are the meanings of sentences, are complexes of senses, not of things!

The Heart of Russell’s Objections ‘I believe that in spite of all its snowfields Mont Blanc itself is a component part of what is actually asserted in the proposition ‘Mont Blanc is more than 4000 metres high’. We do not assert the thought, for this is a private psychological matter: we assert the object of the thought, and this is, to my mind, is a certain complex (an objective proposition, one might say) in which Mont Blanc is itself a component part. If we do not admit this, then we get the conclusion that we know nothing at all about Mont Blanc. This is why for me the meaning of a proposition is not the true, but a certain complex which (in the given case) is true. In the case of a simple proper name like ‘Socrates’, I cannot distinguish between sense and meaning; I see only the idea, which is psychological, and the object. Or better: I do not admit the sense at all, but only the idea and the meaning.’ (Russell, Letter to Frege, 12 Dec. 1904)

The Heart of Russell’s Objections Russellian propositions: a proposition is a complex consisting of the very objects which are the values of the words which express the proposition Russellian propositions are object dependent: if no object, then no thought. Underlying idea: an ‘Object Theory of Reference’, according to which the meaning of a name is the object it stands for: ‘the name is merely a means of pointing to the thing, and does not occur in what you are asserting’. (Russell, Lectures on Logical Atomism)

Russell’s Positive Proposal So Russell doesn’t like Frege’s story about non-denoting terms, and he doesn’t like senses. What is he going to do? He can’t fall back to the Naïve theory. How is he going to solve the puzzles?

Russell’s Positive Proposal Think about the proposition which ascribes to you the property of being human <YOUis human> Imagine we remove you from the proposition. What’s left is the property of being human, and an empty ‘slot’. This might be expressed as either: < xishuman> <___is human>

Russell’s Positive Proposal These are propositional functions: functions which, when you add an object to them, give you back a proposition (which can then be either true or false). One way to get from a propositional function to a proposition is to fill the empty slot with an object – i.e. replace ‘x’ with a name: <Nathan is human>

Russell’s Positive Proposal But there is another way: rather than completing the propositional function with an object, we can say something about the propositional function itself. • We can say that the propositional function is always true, i.e., true no matter what object you fill the empty slot with: <For all x, xis human>

Russell’s Positive Proposal • We can also say that the propositional function is sometimes true, i.e., truewhen at least one object slotted into the proposition makes it true <Forsome x, xishuman> • Similarly for propositional functions which are nevertrue, i.e. false regardless of which object is slotted in: <Forno x, xis human>

Russell’s Positive Proposal Problem: we know how to say that a propositional function is satisfied by at least one, by every, and by no objects, but how can we use these devices to say that it is satisfied by exactly one? It remains to interpret phrases containing the. These are by far the most interesting and difficult of denoting phrases. Take as an instance ‘the father of Charles II was executed’. This asserts that there was an x who was the father of Charles II and was executed. Now the, when it is strictly used, involves uniqueness … Thus for our purposes we take the as involving uniqueness. (Russell, OD)

Russell’s Positive Proposal The F is G (x)(Fx & (y)(Fyy=x) & Gx) MINIMAL: There is at least one F MAXIMAL: There is at most one F ATTRIBUTION: Something that is F is G

Russell’s Positive Proposal Problem: how do we say that a propositional function is satisfied by exactly one object? Answer: by rendering it as a definite description! • The Present King of Denmark is human <Forsomex, xistheP.K.o.D, and, forall y, ifyisthe P.K. o. D., theny=x, andx is human>

Russell’s Positive Proposal Everything, nothing, and something, are not assumed to have any meaning in isolation, but a meaning is assigned to every proposition in which they occur. This is the principle of the theory of denoting I wish to advocate: that denoting phrases never have any meaning in themselves, but that every proposition in whose verbal expression they occur has a meaning. (Russell, OD) These terms do not express particular but rather general thoughts – you don’t need a particular object in mind to express a proposition involving one of the above.

Russell’s Positive Proposal (i) Every number has a successor Is there some object that corresponds to the subject – i.e., is there an ‘every number’ that is the referent? Upshot: while there is no propositional constituent corresponding to ‘everything’, ‘something’, and ‘nothing’, we know how to understand the propositions expressed by sentences involving them!

Russell’s Positive Proposal By ‘denoting phrase’ I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present king of England, the centre of mass of the Solar System at the first instant of the twentieth century, the revolution of the earth around the sun, the revolution of the sun around the earth. Thus a phrase is denoting solely in virtue of its form. (‘On Denoting’, 479)

Russell’s Positive Proposal So, we know that there are certain denoting phrases which can be involved in propositions and – more importantly – we can understand these propositions even though we don’t know what is denoted by the phrases themselves (which is convenient since there sometimes isn’t even such a thing, e.g. ‘every number’). This gives us the following point: • Definite descriptions, like all other denoting phrases, are quantifierexpressions, rather than referring expressions

Russell’s Positive Proposal In ‘On Denoting’, Russell suggests treating empty names as disguised descriptions: A proposition about Apollo means what we get by substituting what the classical dictionary tells us is meant by Apollo, say ‘the sun-god’. All propositions in which Apollo occurs are to be interpreted by the above rules for denoting phrases. (Russell, OD) • Apollo helped kill Achilles • There is an x such that, x is a sun-god, and, for all objects y, if y is a sun-god, then y=x, and x helped kill Achilles.

Russell’s Positive Proposal The upshot of this move is that, if the above argumentation is true, we can understand and evaluate for truth propositions involving empty names: • <Apollohelped kill Achilles> is false because there is no such x which satisfies the definite description! Similarly, we can say that • <The Present King of France is bald> is false!

Russell’s Positive Proposal But the Russell of ‘Descriptions’ is more radical: therein, we are told that it is ‘a very rash assumption’ to regard ‘Socrates’, ‘Plato’, and ‘Aristotle’ as (genuine) names. In fact: We may even go so far as to say that, in all such knowledge as can be expressed in words—with the exception of ‘this’ and ‘that’ and a few other words of which the meaning varies on different occasions—no names, in the strict sense, occur, but what seem like names are really descriptions. (Russell, Descriptions)

Russell’s Positive Proposal In other words: every singular term is in fact a concealed definite description! • Lionel Messi is the greatest living footballer • The Argentinian striker who plays for Barcelona is the greatest living footballer • There is an x such that, x is an Argentinian striker who plays for Barcelona, and, for all objects y, if y is an Argentinian striker who plays for Barcelona, then y=x, and x is the greatest living footballer Note: we’d have to unpack ‘Barcelona’ too…

Einführung in die Theoretische Philosophie: Sprachphilosophie