39 ideas
17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
17638 | If one proposition is deduced from another, they are more certain together than alone [Russell] |
17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
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] |
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] |
17629 | Which premises are ultimate varies with context [Russell] |
17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
17640 | Finding the axioms may be the only route to some new results [Russell] |
17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
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] |
17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
17639 | Believing a whole science is more than believing each of its propositions [Russell] |
17631 | Induction is inferring premises from consequences [Russell] |
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] |
17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
9111 | God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham] |
9112 | We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham] |