Combining Texts

All the ideas for 'Sententia on 'De Caelo'', 'Logic in Mathematics' and 'Coherence: The Price is Right'

expand these ideas     |    start again     |     specify just one area for these texts

28 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
22101 Philosophy aims to know the truth about the way things are [Aquinas]
2. Reason / A. Nature of Reason / 6. Coherence
17596 Coherence problems have positive and negative restraints; solutions maximise constraint satisfaction [Thagard]
17597 Coherence is explanatory, deductive, conceptual, analogical, perceptual, and deliberative [Thagard]
17598 Explanatory coherence needs symmetry,explanation,analogy,data priority, contradiction,competition,acceptance [Thagard]
2. Reason / D. Definition / 3. Types of Definition
16877 A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege]
2. Reason / D. Definition / 10. Stipulative Definition
11219 Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta]
2. Reason / E. Argument / 6. Conclusive Proof
16878 We must be clear about every premise and every law used in a proof [Frege]
3. Truth / A. Truth Problems / 6. Verisimilitude
17602 Verisimilitude comes from including more phenomena, and revealing what underlies [Thagard]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
16867 Logic not only proves things, but also reveals logical relations between them [Frege]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
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]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
16865 'Theorems' are both proved, and used in proofs [Frege]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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]
16871 A truth can be an axiom in one system and not in another [Frege]
16870 Axioms are truths which cannot be doubted, and for which no proof is needed [Frege]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
16869 To create order in mathematics we need a full system, guided by patterns of inference [Frege]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
16864 If principles are provable, they are theorems; if not, they are axioms [Frege]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9388 Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege]
14. Science / B. Scientific Theories / 1. Scientific Theory
17601 Neither a priori rationalism nor sense data empiricism account for scientific knowledge [Thagard]
14. Science / C. Induction / 6. Bayes's Theorem
17600 Bayesian inference is forced to rely on approximations [Thagard]
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
17599 The best theory has the highest subjective (Bayesian) probability? [Thagard]
18. Thought / B. Mechanics of Thought / 5. Mental Files
16876 We need definitions to cram retrievable sense into a signed receptacle [Frege]
16875 We use signs to mark receptacles for complex senses [Frege]
19. Language / A. Nature of Meaning / 6. Meaning as Use
16879 A sign won't gain sense just from being used in sentences with familiar components [Frege]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
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]
19. Language / D. Propositions / 5. Unity of Propositions
16874 The parts of a thought map onto the parts of a sentence [Frege]