display all the ideas for this combination of texts
2 ideas
| 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'? |
| 11261 | Puzzles arise when reasoning seems equal on both sides [Aristotle] |
| Full Idea: The equality of opposite reasonings is the cause of aporia; for it is when we reason on both [sides of a question] and it appears to us that everything can come about either way, that we are in a state of aporia about which of the two ways to take up. | |
| From: Aristotle (Topics [c.331 BCE], 145b17), quoted by Vassilis Politis - Aristotle and the Metaphysics 3.1 | |
| A reaction: Other philosophers give up on the subject in this situation, but I love Aristotle because he takes this to be the place where philosophy begins. |