40 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] |
| 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] |
| 13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski] |
| 13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski] |
| 13336 | A language containing its own semantics is inconsistent - but we can use a second language [Tarski] |
| 13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
| 13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
| 13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |
| 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] |
| 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] |
| 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] |
| 22645 | Understanding by means of causes is useless if they are not reduced to a minimum number [James] |
| 22653 | Early Christianity says God recognises the neglected weak and tender impulses [James] |