# Philosophical Logic. LECTURE SEVEN MICHAELMAS 2017 Dr Maarten Steenhagen

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1 Philosophical Logic LECTURE SEVEN MICHAELMAS 2017 Dr Maarten Steenhagen

2 Last week Lecture 1: Necessity, Analyticity, and the A Priori Lecture 2: Reference, Description, and Rigid Designation Lecture 3: What Could Meaning Mean? Lecture 4: Natural Language Lecture 5: Formal Translations Lecture 6: Conditionals Lecture 7: Deeper into the Lecture 8: Quantification and Existence

3 Today 1. The problem of non-existence 2. Denoting and referring 3. The logical form of the 4. Solving puzzles

4 The problem of nonexistence

5 The present king of France is bald.

6 Propositional functions Introduction to Mathematical Philosophy 1919, p. 156

7 Propositional functions Russell suggests that a phrase like is bald on its own introduces a propositional function: Bx Bx is incomplete and not a meaningful statement. It contains undetermined values (the variable x lacks a value) When values are assigned to these elements, the expression becomes a proposition Bx +! gives Anna is bald

8 Talking about nothing But given that there is no present king of France, we lack a value in The present king of France is bald The present king of France is bald now seems a meaningless statement! The whole sentence is meaningless because part of it lacks meaning Consider also the seemingly true The present king of France does not exist

9 Can we really talk about nothing? Parmenides of Elea (5th C. BCE): "It is necessary to say and to think that what is is; for [only] what is is and nothing is not. These things I bid you ponder." (Poem, Fr. 6) Bertrand Russell ( ): "if a word can be used significantly it must mean something, not nothing, and therefore what the word means must in some sense exist" (A History of Western Philosophy, 1945:50).

10 Three solutions Metaphysical, Metasemantic, Semantic

11 Metaphysical solution There is some non-existing object that the phrase the present king of France refers to View attributed to Alexius Meinong ( ), who contrasted objects that have being and objects that do not have being We can now say that the value of Bx can be something that lacks being, e.g. the present king of France

12 Metaphysical solution Problem for the metaphysical solution: allows us to prove contradictions If the present King of France picks out some non-existent King, then the existent present King of France must pick out some nonexistent King as well But then the following statement must be true: The existent present King of France does not exist But that is a contradiction like The barking dog does not bark

13 Metasemantic solution We can also assume that the meaning of a name is more than just its reference Gottlob Frege ( ): every meaningful expression has a sense as well as a (possible) reference The sense of an expression is the mode of presentation of a referent So the present King of France may lack a reference, it still has sense Therefore, all parts of The present King of France is bald are meaningful; so the whole sentence can be meaningful

14 Metasemantic solution One problem with Frege s solution is that though meaningful, it implies the sentence lacks a truth value For a sentence to be true or false, all of its component variables must be assigned a referent; yet the present King of France lacks a referent, also on Frege s picture Yet Russell thinks, not unreasonably, that The present king of France is bald is not only meaningful, but also false

15 Denoting and Referring Russell s semantic solution

16 Denoting, not referring Both the metaphysical and the metasemantic solutions assumed that the present king of France functions as a name or referring expression (like Anna or Amsterdam ). The present King of France is bald Anna is bald Russell gives up this assumption: the present King of France is a denoting expression, not a referring expression

17 Denoting phrases

18 Denoting phrases Why think denoting expressions work differently? Argument from contradiction (Introduction to Mathematical Philosophy 1919, p ): Imagine I met my colleague Tim Button yesterday, and I tell you I met a colleague If a colleague is a referring expression, the phrase refers to Tim. What I say is (logically) equivalent to I met Tim. But then I should contradict myself if I said I met a colleague, but it was not Tim. Yet this sentence is not self-contradictory; it is merely false. (Contrast: I met Tim but it was not Tim ) So a colleague is here not a referring expression

19 What denoting phrases do Referring expressions introduce some object (e.g. ) to complete a propositional function Denoting expressions do something else: they make a statement about in what way a propositional function is satisfied by objects (e.g. never, sometimes, always)

20 A philosopher Example: A philosopher thought hard Is it a name? Gramatically, a philosopher seems to function as a name, just as Tim Button in Tim Button thought hard But no! Semantically, a philosopher is not a meaningful (complete) expression. The contribution of a philosopher can only be understood in light of the entire statement in which it occurs (in that respect, it s like ton though in Tim Button thought hard ) A philosopher thought hard means that the propositional function Tx ( x thought hard ) is sometimes satisfied by something that satisfies the propositional function Px ( x is a philosopher )

21 Definite and indefinite We can distinguish definite and indefinite descriptions (definite and indefinite uses of denoting phrases). Compare: A philosopher thought hard The philosopher thought hard The first is true if there is some object that is both a philosopher and thought hard (indefinite) The second is true if and only if there is a unique thing that is both a philosopher and thought hard (definite)

22 The logical form of the

23 Logical form All denoting phrases function grammatically in the same way as proper names. But sentences containing denoting phrases have a logical form that distinguishes them from sentences using only names and predicates. To represent their contribution to the meaning of a sentence, we can explicate that logical form (e.g. using FOL)

24 Logical form Nothing is red A. The function Rx is never satisfied B. x Rx A philosopher thought hard A. Tx is sometimes satisfied by something that satisfies Px B. x Px Tx

25 Logical form A philosopher thought hard A. Tx is sometimes satisfied by something that satisfies Px B. x Px Tx The philosopher thought hard A. Px is uniquely satisfied by something that satisfies Tx B. x (Px y(py y = x) Tx)

26 Solving puzzles

27 The present king of France is bald.

28 The present king of France is bald. According to Russell s semantic solution, this says that: A. Kx is uniquely satisfied by something that satisfies Bx B. x (Kx Bx y (Ky y = x)) It is (a) meaningful (though not about anything!) and (b) false

29 Another advantage Russell s theory also explains how The present King of France does not exist can be true Because The present King of France is a denoting phrase, we need not think that the sentence is made true by some present King of France Instead, the sentence simply says that nothing satisfies the function Kx x Kx

30 Yet another advantage Russell s theory explains how knowledge by description is possible

31 Next week Lecture 1: Necessity, Analyticity, and the A Priori Lecture 2: Reference, Description, and Rigid Designation Lecture 3: What Could Meaning Mean? Lecture 4: Natural Language Lecture 5: Formal Translations Lecture 6: Conditionals Lecture 7: Deeper into the Lecture 8: Quantification and Existence

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