Combining Texts

All the ideas for 'Idea for a Universal History', 'Thoughts without Laws' and 'Logic in Mathematics'

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26 ideas

2. Reason / A. Nature of Reason / 3. Pure Reason
21054 Reason enables the unbounded extension of our rules and intentions [Kant]
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]
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]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
12582 The function of beliefs is to produce beliefs-that-p when p [Millikan]
16. Persons / F. Free Will / 2. Sources of Free Will
21053 The manifest will in the world of phenomena has to conform to the laws of nature [Kant]
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]
24. Political Theory / D. Ideologies / 6. Liberalism / d. Liberal freedom
21055 Our aim is a constitution which combines maximum freedom with strong restraint [Kant]
21056 The vitality of business needs maximum freedom (while avoiding harm to others) [Kant]
25. Social Practice / D. Justice / 1. Basis of justice
21057 The highest ideal of social progress is a universal cosmopolitan existence [Kant]