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Full Idea
The logician drops 'if-then' in favour of '→' without ever entertaining the mistaken idea that they are synonymous.
Gist of Idea
The logician's '→' does not mean the English if-then
Source
Willard Quine (Mr Strawson on Logical Theory [1953], V)
Book Ref
Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.150
A Reaction
[Quine uses the older horseshoe symbol] The conditional in English is not well understood, whereas the symbol is unambiguous. A warning to myself, since I have a tendency to translate symbols into English all the time. [p.156 'implies' is worse!]
Related Idea
Idea 8204 Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead]
| 22435 | The logician's '→' does not mean the English if-then [Quine] |
| 9512 | We write the 'negation' of P (not-P) as ¬ [Lemmon] |
| 9511 | We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon] |
| 9508 | The sign |- may be read as 'therefore' [Lemmon] |
| 9509 | That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon] |
| 9510 | That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon] |
| 9513 | We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P) [Lemmon] |
| 9514 | If A and B are 'interderivable' from one another we may write A -||- B [Lemmon] |
| 12005 | The symbol 'ι' forms definite descriptions; (ιx)F(x) says 'the x which is such that F(x)' [Forbes,G] |
| 7799 | Proposition logic has definitions for its three operators: or, and, and identical [Girle] |