58 ideas
| 9023 | If you say that a contradiction is true, you change the meaning of 'not', and so change the subject [Quine] |
| 9012 | Talk of 'truth' when sentences are mentioned; it reminds us that reality is the point of sentences [Quine] |
| 9011 | Truth is redundant for single sentences; we do better to simply speak the sentence [Quine] |
| 9013 | We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)' [Quine] |
| 9020 | My logical grammar has sentences by predication, then negation, conjunction, and existential quantification [Quine] |
| 9028 | Maybe logical truth reflects reality, but in different ways in different languages [Quine] |
| 10014 | Quine rejects second-order logic, saying that predicates refer to multiple objects [Quine, by Hodes] |
| 10828 | Quantifying over predicates is treating them as names of entities [Quine] |
| 9024 | Excluded middle has three different definitions [Quine] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 10012 | Quantification theory can still be proved complete if we add identity [Quine] |
| 9016 | Names are not essential, because naming can be turned into predication [Quine] |
| 9015 | Universal quantification is widespread, but it is definable in terms of existential quantification [Quine] |
| 9025 | You can't base quantification on substituting names for variables, if the irrationals cannot all be named [Quine] |
| 9026 | Some quantifications could be false substitutionally and true objectually, because of nameless objects [Quine] |
| 10705 | Putting a predicate letter in a quantifier is to make it the name of an entity [Quine] |
| 9027 | A sentence is logically true if all sentences with that grammatical structure are true [Quine] |
| 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] |
| 9017 | Predicates are not names; predicates are the other parties to predication [Quine] |
| 9018 | A physical object is the four-dimensional material content of a portion of space-time [Quine] |
| 9019 | Four-d objects helps predication of what no longer exists, and quantification over items from different times [Quine] |
| 9014 | Some conditionals can be explained just by negation and conjunction: not(p and not-q) [Quine] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 8143 | Self is the rider, intellect the charioteer, mind the reins, and body the chariot [Anon (Upan)] |
| 8147 | We have an apparent and a true self; only the second one exists, and we must seek to know it [Anon (Upan)] |
| 8155 | Without speech we cannot know right/wrong, true/false, good/bad, or pleasant/unpleasant [Anon (Upan)] |
| 9009 | Single words are strongly synonymous if their interchange preserves truth [Quine] |
| 9007 | It makes no sense to say that two sentences express the same proposition [Quine] |
| 9008 | There is no rule for separating the information from other features of sentences [Quine] |
| 9010 | We can abandon propositions, and just talk of sentences and equivalence [Quine] |
| 9021 | A good way of explaining an expression is saying what conditions make its contexts true [Quine] |
| 8142 | The wise prefer good to pleasure; the foolish are drawn to pleasure by desire [Anon (Upan)] |
| 8151 | Let your teacher be a god to you [Anon (Upan)] |
| 8153 | By knowing one piece of clay or gold, you know all of clay or gold [Anon (Upan)] |
| 8154 | Originally there must have been just Existence, which could not come from non-existence [Anon (Upan)] |
| 8148 | Brahma, supreme god and protector of the universe, arose from the ocean of existence [Anon (Upan)] |
| 8144 | Brahman is the Uncaused Cause [Anon (Upan)] |
| 8152 | Earth, food, fire, sun are all forms of Brahman [Anon (Upan)] |
| 8156 | The gods are not worshipped for their own sake, but for the sake of the Self [Anon (Upan)] |
| 8157 | A man with desires is continually reborn, until his desires are stilled [Anon (Upan)] |
| 8159 | Damayata - be self-controlled! Datta - be charitable! Dayadhwam - be compassionate! [Anon (Upan)] |
| 8145 | Those ignorant of Atman return as animals or plants, according to their merits [Anon (Upan)] |
| 8149 | Charity and ritual observance distract from the highest good of religion [Anon (Upan)] |
| 8158 | Do not seek to know Brahman by arguments, for arguments are idle and vain [Anon (Upan)] |
| 8146 | The immortal in us is the part that never sleeps, and shapes our dreams [Anon (Upan)] |
| 8150 | The immortal Self and the sad individual self are like two golden birds perched on one tree [Anon (Upan)] |