39 ideas
2098 | The principle of sufficient reason is needed if we are to proceed from maths to physics [Leibniz] |
2104 | No reason could limit the quantity of matter, so there is no limit [Leibniz] |
3646 | There is always a reason why things are thus rather than otherwise [Leibniz] |
19079 | For idealists reality is like a collection of beliefs, so truths and truthmakers are not distinct [Young,JO] |
19076 | Coherence theories differ over the coherence relation, and over the set of proposition with which to cohere [Young,JO] |
19077 | Two propositions could be consistent with your set, but inconsistent with one another [Young,JO] |
19078 | Coherence with actual beliefs, or our best beliefs, or ultimate ideal beliefs? [Young,JO] |
19084 | Coherent truth is not with an arbitrary set of beliefs, but with a set which people actually do believe [Young,JO] |
19083 | How do you identify the best coherence set; and aren't there truths which don't cohere? [Young,JO] |
19075 | Deflationary theories reject analysis of truth in terms of truth-conditions [Young,JO] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
19385 | All simply substances are in harmony, because they all represent the one universe [Leibniz] |
21346 | The ratio between two lines can't be a feature of one, and cannot be in both [Leibniz] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
19074 | Are truth-condtions other propositions (coherence) or features of the world (correspondence)? [Young,JO] |
19082 | Coherence truth suggests truth-condtions are assertion-conditions, which need knowledge of justification [Young,JO] |
2105 | Things are infinitely subdivisible and contain new worlds, which atoms would make impossible [Leibniz] |
2106 | The only simple things are monads, with no parts or extension [Leibniz] |
2102 | Atomism is irrational because it suggests that two atoms can be indistinguishable [Leibniz] |
20965 | Leibniz upheld conservations of momentum and energy [Leibniz, by Papineau] |
2103 | The idea that the universe could be moved forward with no other change is just a fantasy [Leibniz] |
2100 | Space and time are purely relative [Leibniz] |
2107 | No time exists except instants, and instants are not even a part of time, so time does not exist [Leibniz] |
2101 | If everything in the universe happened a year earlier, there would be no discernible difference [Leibniz] |
22894 | If time were absolute that would make God's existence dependent on it [Leibniz, by Bardon] |
2099 | The existence of God, and all metaphysics, follows from the Principle of Sufficient Reason [Leibniz] |