27 ideas
1815 | Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius] |
1812 | All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius] |
1811 | Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius] |
1813 | All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius] |
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
6303 | Sets are positions in patterns [Resnik] |
6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
12132 | Indiscernibility is a necessary and sufficient condition for identity [Brody] |
15834 | Brody bases sortal essentialism on properties required throughout something's existence [Brody, by Mackie,P] |
12140 | Modern emphasis is on properties had essentially; traditional emphasis is on sort-defining properties [Brody] |
11895 | A sortal essence is a property which once possessed always possessed [Brody, by Mackie,P] |
12141 | Maybe essential properties are those which determine a natural kind? [Brody] |
12137 | De re essentialism standardly says all possible objects identical with a have a's essential properties [Brody] |
12142 | Essentially, a has P, always had P, must have had P, and has never had a future without P [Brody] |
12143 | An object having a property essentially is equivalent to its having it necessarily [Brody] |
12144 | Essentialism is justified if the essential properties of things explain their other properties [Brody] |
12139 | Mereological essentialism says that every part that ensures the existence is essential [Brody] |
12135 | Interrupted objects have two first moments of existence, which could be two beginnings [Brody] |
12130 | a and b share all properties; so they share being-identical-with-a; so a = b [Brody] |
12138 | Identity across possible worlds is prior to rigid designation [Brody] |
8850 | Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M] |
1814 | Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius] |