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All the ideas for 'reports', 'Logic in Mathematics' and 'Action'

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36 ideas

2. Reason / D. Definition / 3. Types of Definition
A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege]
2. Reason / D. Definition / 10. Stipulative Definition
Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta]
2. Reason / E. Argument / 6. Conclusive Proof
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
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
Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege]
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
'Theorems' are both proved, and used in proofs [Frege]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Tracing inference backwards closes in on a small set of axioms and postulates [Frege]
The essence of mathematics is the kernel of primitive truths on which it rests [Frege]
A truth can be an axiom in one system and not in another [Frege]
Axioms are truths which cannot be doubted, and for which no proof is needed [Frege]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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
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
Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege]
18. Thought / B. Mechanics of Thought / 5. Mental Files
We need definitions to cram retrievable sense into a signed receptacle [Frege]
We use signs to mark receptacles for complex senses [Frege]
19. Language / A. Nature of Meaning / 6. Meaning as Use
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
Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege]
A thought is the sense expressed by a sentence, and is what we prove [Frege]
19. Language / D. Propositions / 5. Unity of Propositions
The parts of a thought map onto the parts of a sentence [Frege]
20. Action / A. Definition of Action / 1. Action Theory
Actions include: the involuntary, the purposeful, the intentional, and the self-consciously autonomous [Wilson/Schpall]
20. Action / A. Definition of Action / 4. Action as Movement
Maybe bodily movements are not actions, but only part of an agent's action of moving [Wilson/Schpall]
Is the action the arm movement, the whole causal process, or just the trying to do it? [Wilson/Schpall]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
To be intentional, an action must succeed in the manner in which it was planned [Wilson/Schpall]
If someone believes they can control the lottery, and then wins, the relevant skill is missing [Wilson/Schpall]
We might intend two ways to acting, knowing only one of them can succeed [Wilson/Schpall]
20. Action / B. Preliminaries of Action / 1. Intention to Act / c. Reducing intentions
On one model, an intention is belief-desire states, and intentional actions relate to beliefs and desires [Wilson/Schpall]
20. Action / B. Preliminaries of Action / 1. Intention to Act / d. Group intentions
Groups may act for reasons held by none of the members, so maybe groups are agents [Wilson/Schpall]
If there are shared obligations and intentions, we may need a primitive notion of 'joint commitment' [Wilson/Schpall]
20. Action / C. Motives for Action / 2. Acting on Beliefs / b. Action cognitivism
Strong Cognitivism identifies an intention to act with a belief [Wilson/Schpall]
Weak Cognitivism says intentions are only partly constituted by a belief [Wilson/Schpall]
Strong Cognitivism implies a mode of 'practical' knowledge, not based on observation [Wilson/Schpall]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
Maybe the explanation of an action is in the reasons that make it intelligible to the agent [Wilson/Schpall]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Causalists allow purposive explanations, but then reduce the purpose to the action's cause [Wilson/Schpall]
It is generally assumed that reason explanations are causal [Wilson/Schpall]
25. Social Practice / D. Justice / 3. Punishment / c. Deterrence of crime
The greatest deterrence for injustice is if uninjured parties feel as much indignation as those who are injured [Solon, by Diog. Laertius]