6 ideas
| 17962 | The truth-maker principle is that every truth has a sufficient truth-maker [Forrest] |
| Full Idea: Item x is said to be a sufficient truth-maker for truth-bearer p just in case necessarily if x exists then p is true. ...Every truth has a sufficient truth-maker. Hence, I take it, the sum of all sufficient truth-makers is a universal truth-maker. | |
| From: Peter Forrest (General Facts,Phys Necessity, and Metaph of Time [2006], 1) | |
| A reaction: Note that it is not 'necessary', because something else might make p true instead. |
| 7726 | Aristotelian logic dealt with inferences about concepts, and there were also proposition inferences [Weiner] |
| Full Idea: Till the nineteenth century, it was a common view that Aristotelian logic could evaluate inferences whose validity was based on relations between concepts, while propositional logic could evaluate inferences based on relations between propositions. | |
| From: Joan Weiner (Frege [1999], Ch.3) | |
| A reaction: Venn diagrams relate closely to Aristotelian syllogisms, as each concept is represented by a circle, and shows relations between sets. Arrows seem needed to represent how to go from one proposition to another. Is one static, the other dynamic? |
| 10304 | Very few things in set theory remain valid in intuitionist mathematics [Bernays] |
| Full Idea: Very few things in set theory remain valid in intuitionist mathematics. | |
| From: Paul Bernays (On Platonism in Mathematics [1934]) |
| 10303 | Restricted Platonism is just an ideal projection of a domain of thought [Bernays] |
| Full Idea: A restricted Platonism does not claim to be more than, so to speak, an ideal projection of a domain of thought. | |
| From: Paul Bernays (On Platonism in Mathematics [1934], p.261) | |
| A reaction: I have always found Platonism to be congenial when it talks of 'ideals', and ridiculous when it talks of a special form of 'existence'. Ideals only 'exist' because we idealise things. I may declare myself, after all, to be a Restricted Platonist. |
| 10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
| Full Idea: Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction. | |
| From: Paul Bernays (On Platonism in Mathematics [1934], p.268) | |
| A reaction: His point is that the logicists seem to think that if you increasingly abstract from mathematics, you end up with pure logic. |
| 15432 | Structural universals might serve as possible worlds [Forrest, by Lewis] |
| Full Idea: Forrest proposed that structural universals should serve as ersatz possible worlds. | |
| From: report of Peter Forrest (Ways Worlds Could Be [1986]) by David Lewis - Against Structural Universals 'Intro' | |
| A reaction: I prefer powers to property universals. Perhaps a possible world is a maximal set of co-existing dispositions? |