9545
|
Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara]
|
|
Full Idea:
Near the end of his life, Frege completely abandoned his logicism, and came to the conclusion that the source of our arithmetical knowledge is what he called 'the Geometrical Source of Knowledge'.
|
|
From:
report of Gottlob Frege (Sources of Knowledge of Mathematics [1922]) by Charles Chihara - A Structural Account of Mathematics Intro n3
|
|
A reaction:
We have, rather crucially, lost touch with the geometrical origins of arithmetic (such as 'square' numbers), which is good news for the practice of mathematics, but probably a disaster for the philosophy of the subject.
|
13764
|
Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington]
|
|
Full Idea:
Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? Are they non-truth-functional, like 'because' or 'before'? Do the values of A and B, in some cases, leave open the value of 'If A,B'?
|
|
From:
Dorothy Edgington (Conditionals [2001], 17.1)
|
|
A reaction:
I would say they are not truth-functional, because the 'if' asserts some further dependency relation that goes beyond the truth or falsity of A and B. Logical ifs, causal ifs, psychological ifs... The material conditional ⊃ is truth-functional.
|
13765
|
'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington]
|
|
Full Idea:
If it were possible to have A true, B false, and If A,B true, it would be unsafe to infer B from A and If A,B: modus ponens would thus be invalid. Hence 'If A,B' must entail ¬(A & ¬B).
|
|
From:
Dorothy Edgington (Conditionals [2001], 17.1)
|
|
A reaction:
This is a firm defence of part of the truth-functional view of conditionals, and seems unassailable. The other parts of the truth table are open to question, though, if A is false, or they are both true.
|