display all the ideas for this combination of philosophers
4 ideas
| 14352 | '¬', '&', and 'v' are truth functions: the truth of the compound is fixed by the truth of the components [Jackson] |
| Full Idea: It is widely agreed that '¬', '&', and 'v' are 'truth functions': the truth value of a compound sentence formed using them is fully determined by the truth value or values of the component sentences. | |
| From: Frank Jackson (Conditionals [2006], 'Equiv') | |
| A reaction: A candidate for not being a truth function might be a conditional →, where the arrow adds something over and above the propositions it connects. The relationship has an additional truth value? Does A depend on B? |
| 8312 | It is better if the existential quantifier refers to 'something', rather than a 'thing' which needs individuation [Lowe] |
| Full Idea: If we take the existential quantifier to mean 'there is at least one thing that' then its value must qualify as one thing, individuable in principle. ...So I propose to read it as 'there is something that', which implies nothing about individuability. | |
| From: E.J. Lowe (The Possibility of Metaphysics [1998], 11) | |
| A reaction: All sorts of doubts about the existential quantifier seem to be creeping in nowadays (e.g. Ideas 6067, 6069, 8250). Personally I am drawn to the sound of 'free logic', Idea 8250, which drops existential claims. This would reduce metaphysical confusion. |
| 6653 | Syntactical methods of proof need only structure, where semantic methods (truth-tables) need truth [Lowe] |
| Full Idea: Syntactical methods of proof (e.g.'natural deduction') have regard only to the formal structure of premises and conclusions, whereas semantic methods (e.g. truth-tables) consider their possible interpretations as expressing true or false propositions. | |
| From: E.J. Lowe (Introduction to the Philosophy of Mind [2000], Ch. 8) | |
| A reaction: This is highly significant, because the first method of reasoning could be mechanical, whereas the second requires truth, and hence meaning, and hence (presumably) consciousness. Is full rationality possible with 'natural deduction'? |
| 4229 | An infinite series of tasks can't be completed because it has no last member [Lowe] |
| Full Idea: It appears to be impossible to complete an infinite series of tasks, since such a series has, by definition, no last member. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.290) | |
| A reaction: This pinpoints the problem. So are there infinite tasks in a paradox of subdivision like the Achilles? |