49 ideas
22659 | It is wisdom to believe what you desire, because belief is needed to achieve it [James] |
22657 | All good philosophers start from a dumb conviction about which truths can be revealed [James] |
22647 | A complete system is just a classification of the whole world's ingredients [James] |
4465 | Note that "is" can assert existence, or predication, or identity, or classification [PG] |
22648 | A single explanation must have a single point of view [James] |
22644 | Our greatest pleasure is the economy of reducing chaotic facts to one single fact [James] |
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] |
22649 | Classification can only ever be for a particular purpose [James] |
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] |
22655 | Scientific genius extracts more than other people from the same evidence [James] |
22658 | Experimenters assume the theory is true, and stick to it as long as result don't disappoint [James] |
22654 | We can't know if the laws of nature are stable, but we must postulate it or assume it [James] |
22656 | Trying to assess probabilities by mere calculation is absurd and impossible [James] |
22646 | We have a passion for knowing the parts of something, rather than the whole [James] |
22652 | The mind has evolved entirely for practical interests, seen in our reflex actions [James] |
22651 | Dogs' curiosity only concerns what will happen next [James] |
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] |
22650 | How can the ground of rationality be itself rational? [James] |
22643 | It seems that we feel rational when we detect no irrationality [James] |
22660 | Evolution suggests prevailing or survival as a new criterion of right and wrong [James] |
3877 | Utilitarianism seems to justify the discreet murder of unhappy people [PG] |
22645 | Understanding by means of causes is useless if they are not reduced to a minimum number [James] |
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] |
22653 | Early Christianity says God recognises the neglected weak and tender impulses [James] |