33 ideas
| 4465 | Note that "is" can assert existence, or predication, or identity, or classification [PG] |
| 4686 | Fallacies are errors in reasoning, 'formal' if a clear rule is breached, and 'informal' if more general [PG] |
| 7415 | Question-begging assumes the proposition which is being challenged [PG] |
| 7414 | What is true of a set is also true of its members [PG] |
| 6696 | The Ad Hominem Fallacy criticises the speaker rather than the argument [PG] |
| 4687 | Minimal theories of truth avoid ontological commitment to such things as 'facts' or 'reality' [PG] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 6516 | Monty Hall Dilemma: do you abandon your preference after Monty eliminates one of the rivals? [PG] |
| 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] |
| 22518 | The actual must be possible, because it occurred [Aristotle] |
| 24054 | Everything has a probability, something will happen, and probabilities add up [PG] |
| 3875 | If reality is just what we perceive, we would have no need for a sixth sense [PG] |
| 3876 | If my team is losing 3-1, I have synthetic a priori knowledge that they need two goals for a draw [PG] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 7734 | Maybe a mollusc's brain events for pain ARE of the same type (broadly) as a human's [PG] |
| 7735 | Maybe a frog's brain events for fear are functionally like ours, but not phenomenally [PG] |
| 16566 | Poetry is more philosophic than history, as it concerns universals, not particulars [Aristotle] |
| 3877 | Utilitarianism seems to justify the discreet murder of unhappy people [PG] |
| 6126 | Life is Movement, Respiration, Sensation, Nutrition, Excretion, Reproduction, Growth (MRS NERG) [PG] |
| 3873 | An omniscient being couldn't know it was omniscient, as that requires information from beyond its scope of knowledge [PG] |
| 3874 | How could God know there wasn't an unknown force controlling his 'free' will? [PG] |