38 ideas
9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
19115 | You can 'rebut' an argument's conclusion, or 'undercut' its premises [Antonelli] |
19119 | We infer that other objects are like some exceptional object, if they share some of its properties [Antonelli] |
19111 | Reasoning may be defeated by new premises, or by finding out more about the given ones [Antonelli] |
19114 | Should we accept Floating Conclusions, derived from two arguments in conflict? [Antonelli] |
19113 | Weakest Link Principle: prefer the argument whose weakest link is the stronger [Antonelli] |
19116 | Non-monotonic core: Reflexivity, Cut, Cautious Monotonicity, Left Logical Equivalence, Right Weakening [Antonelli] |
19117 | We can rank a formula by the level of surprise if it were to hold [Antonelli] |
19118 | People don't actually use classical logic, but may actually use non-monotonic logic [Antonelli] |
9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
19110 | In classical logic the relation |= has Monotony built into its definition [Antonelli] |
19112 | Cautious Monotony ignores proved additions; Rational Monotony fails if the addition's negation is proved [Antonelli] |
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] |
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] |
20959 | Concepts are only analytic once the predicate is absorbed into the subject [Schleiermacher] |
18257 | Why should the limit of measurement be points, not intervals? [Dummett] |