38 ideas
16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
16878 | We must be clear about every premise and every law used in a proof [Frege] |
14273 | Conditional Proof is only valid if we accept the truth-functional reading of 'if' [Edgington] |
16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
16865 | 'Theorems' are both proved, and used in proofs [Frege] |
16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
16871 | A truth can be an axiom in one system and not in another [Frege] |
16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
13163 | Circles must be bounded, so cannot be infinite [Leibniz] |
16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
14281 | A thing works like formal probability if all the options sum to 100% [Edgington] |
14284 | Conclusion improbability can't exceed summed premise improbability in valid arguments [Edgington] |
14270 | Simple indicatives about past, present or future do seem to form a single semantic kind [Edgington] |
14269 | Maybe forward-looking indicatives are best classed with the subjunctives [Edgington] |
14275 | Truth-function problems don't show up in mathematics [Edgington] |
14274 | Inferring conditionals from disjunctions or negated conjunctions gives support to truth-functionalism [Edgington] |
14276 | The truth-functional view makes conditionals with unlikely antecedents likely to be true [Edgington] |
14290 | Doctor:'If patient still alive, change dressing'; Nurse:'Either dead patient, or change dressing'; kills patient! [Edgington] |
14271 | Non-truth-functionalist say 'If A,B' is false if A is T and B is F, but deny that is always true for TT,FT and FF [Edgington] |
14272 | I say "If you touch that wire you'll get a shock"; you don't touch it. How can that make the conditional true? [Edgington] |
14282 | On the supposition view, believe if A,B to the extent that A&B is nearly as likely as A [Edgington] |
14278 | Truth-functionalists support some conditionals which we assert, but should not actually believe [Edgington] |
14287 | Does 'If A,B' say something different in each context, because of the possibiites there? [Edgington] |
13162 | Sloth's Syllogism: either it can't happen, or it is inevitable without my effort [Leibniz] |
16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
16875 | We use signs to mark receptacles for complex senses [Frege] |
16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
16874 | The parts of a thought map onto the parts of a sentence [Frege] |
19339 | Evil is a negation of good, which arises from non-being [Leibniz] |
13164 | God only made sin possible because a much greater good can be derived from it [Leibniz] |