42 ideas
6675 | The heart has its reasons of which reason knows nothing [Pascal] |
9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
9896 | A prime number is one which is measured by a unit alone [Dummett] |
18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
9895 | A number is a multitude composed of units [Dummett] |
9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
9869 | Realism is just the application of two-valued semantics to sentences [Dummett] |
9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
22011 | The first principles of truth are not rational, but are known by the heart [Pascal] |
19413 | If we know what is good or rational, our knowledge is extended, and our free will restricted [Leibniz] |
9849 | Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett] |
9850 | An argument for conceptual priority is greater simplicity in explanation [Dummett] |
9873 | Abstract terms are acceptable as long as we know how they function linguistically [Dummett] |
9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait] |
9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
9833 | To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett] |
9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
6681 | We only want to know things so that we can talk about them [Pascal] |
6676 | Painting makes us admire things of which we do not admire the originals [Pascal] |
6680 | It is a funny sort of justice whose limits are marked by a river [Pascal] |
6677 | Imagination creates beauty, justice and happiness, which is the supreme good [Pascal] |
6678 | We live for the past or future, and so are never happy in the present [Pascal] |
20732 | If man considers himself as lost and imprisoned in the universe, he will be terrified [Pascal] |
6682 | Majority opinion is visible and authoritative, although not very clever [Pascal] |
6679 | It is not good to be too free [Pascal] |
18257 | Why should the limit of measurement be points, not intervals? [Dummett] |
7455 | Pascal knows you can't force belief, but you can make it much more probable [Pascal, by Hacking] |
7457 | Pascal is right, but relies on the unsupported claim of a half as the chance of God's existence [Hacking on Pascal] |
7456 | The libertine would lose a life of enjoyable sin if he chose the cloisters [Hacking on Pascal] |
6684 | If you win the wager on God's existence you win everything, if you lose you lose nothing [Pascal] |