31 ideas
| 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] |
| 16659 | Relations do not add anything to reality, though they are real aspects of the world [Olivi] |
| 16673 | Quantity just adds union and location to the extension of parts [Olivi] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 3926 | The human heart has a natural concern for public good [Hume] |
| 3929 | No moral theory is of any use if it doesn't serve the interests of the individual concerned [Hume] |
| 3925 | Personal Merit is the possession of useful or agreeable mental qualities [Hume] |
| 3922 | Justice only exists to support society [Hume] |
| 23560 | If we all naturally had everything we could ever desire, the virtue of justice would be irrelevant [Hume] |
| 3918 | Moral philosophy aims to show us our duty [Hume] |
| 3919 | Conclusions of reason do not affect our emotions or decisions to act [Hume] |
| 3928 | Virtue just requires careful calculation and a preference for the greater happiness [Hume] |
| 3923 | No one would cause pain to a complete stranger who happened to be passing [Hume] |
| 3924 | Nature makes private affections come first, because public concerns are spread too thinly [Hume] |
| 3921 | The safety of the people is the supreme law [Hume] |
| 3927 | Society prefers helpful lies to harmful truth [Hume] |
| 3920 | If you equalise possessions, people's talents will make them unequal again [Hume] |
| 16663 | Things are limited by the species to certain modes of being [Olivi] |