4 ideas
| 8754 | Logic is dependent on mathematics, not the other way round [Heyting, by Shapiro] |
| Full Idea: Heyting (the intuitionist pupil of Brouwer) said that 'logic is dependent on mathematics', not the other way round. | |
| From: report of Arend Heyting (Intuitionism: an Introduction [1956]) by Stewart Shapiro - Thinking About Mathematics 7.3 | |
| A reaction: To me, this claim makes logicism sound much more plausible, as I don't see how mathematics could get beyond basic counting without a capacity for logical thought. Logic runs much deeper, psychologically and metaphysically. |
| 22137 | Observation can force rejection of some part of the initial set of claims [Duhem, by Boulter] |
| Full Idea: Logic and observation alone do not force a scientist to reject a scientific claim if experimental observations so not turn out as expected. The scientist must reject something of the initial set of claims, but that is a matter of choice. | |
| From: report of Pierre Duhem (The Aim and Structure of Physical Theory [1906]) by Stephen Boulter - Why Medieval Philosophy Matters 2 | |
| A reaction: This is a key point against any simplified Popperian notion of falsification. Tiny observations can't kill huge well supported theories. |
| 18197 | Experiments only test groups of hypotheses, and can't show which one is wrong [Duhem] |
| Full Idea: The physicist can never subject an isolated hypothesis to experimental test, but only a whole group of hypotheses; when the experiment is in disagreement with his predictions ...it does not designate which one should be changed. | |
| From: Pierre Duhem (The Aim and Structure of Physical Theory [1906], p.187), quoted by Penelope Maddy - Naturalism in Mathematics II.2 | |
| A reaction: This is the idea frequently invoked by Quine, in support of his holistic view of scientific knowledge (along with Neurath's Boat). |
| 1590 | The just man does not harm his enemies, but benefits everyone [Plato] |
| Full Idea: First, Socrates, you told me justice is harming your enemies and helping your friends. But later it seemed that the just man, since everything he does is for someone's benefit, never harms anyone. | |
| From: Plato (Clitophon [c.372 BCE], 410b) | |
| A reaction: Socrates certainly didn't subscribe to the first view, which is the traditional consensus in Greek culture. In general Socrates agreed with the views later promoted by Jesus. |