5 ideas
| 16974 | The nature of each logical concept is given by a collection of inference rules [Correia] |
| Full Idea: The view presented here presupposes that each logical concept is associated with some fixed and well defined collection of rules of inference which characterize its basic logical nature. | |
| From: Fabrice Correia (On the Reduction of Necessity to Essence [2012], 4) | |
| A reaction: [He gives Fine's 'Senses of Essences' 57-8 as a source] He seems to have in mind natural deduction, where the rules are for the introduction and elimination of the concepts. |
| 20660 | At one level maths and nature are very similar, suggesting some deeper origin [Wolfram] |
| Full Idea: At some rather abstract level one can immediately recognise one basic similarity between nature and mathematics ...this suggests that the overall similarity between mathematics and nature must have a deeper origin. | |
| From: Stephen Wolfram (A New Kind of Science [2002], p.772), quoted by Peter Watson - Convergence 17 'Philosophy' | |
| A reaction: Personally I think mathematics has been derived by abstracting from the patterns in nature, and then further extrapolating from those abstractions. So the puzzle in nature is not the correspondence with mathematics, but the patterns. |
| 16973 | Explain logical necessity by logical consequence, or the other way around? [Correia] |
| Full Idea: One view is that logical consequence is to be understood in terms of logical necessity (some proposition holds necessarily, if some group of other propositions holds). Alternatively, logical necessity is a logical consequence of the empty set. | |
| From: Fabrice Correia (On the Reduction of Necessity to Essence [2012], 3) | |
| A reaction: I think my Finean preference is for all necessities to have a 'necessitator', so logical necessity results from logic in some way, perhaps from logical consequence, or from the essences of the connectives and operators. |
| 20659 | Space and its contents seem to be one stuff - so space is the only existing thing [Wolfram] |
| Full Idea: It seems plausible that both space and its contents should somehow be made of the same stuff - so that in a sense space becomes the only thing in the universe. | |
| From: Stephen Wolfram (A New Kind of Science [2002], p.474), quoted by Peter Watson - Convergence 17 'Philosophy' | |
| A reaction: I presume the concept of a 'field' is what makes this idea possible. |
| 1558 | Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus] |
| Full Idea: The gods pay no attention to human affairs; if they did, they would not have ignored justice, which is the greatest good for men; for we see that men do not act with justice. | |
| From: Thrasymachus (fragments/reports [c.426 BCE], B8), quoted by Hermias - Notes on Plato's 'Phaedrus' 239.22 |