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

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38 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]
3. Truth / A. Truth Problems / 2. Defining Truth
In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson]
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 / 4. Pure Logic
There is no clear boundary between the logical and the non-logical [Tarski]
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 / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall]
Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W]
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 / 3. Axioms for Geometry
Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman]
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 / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
Jesus said learning was unnecessary, and only the spirit of the Law was needed [Jesus, by Johnson,P]
22. Metaethics / B. Value / 2. Values / g. Love
Love your enemies [Jesus]
Love thy neighbour as thyself [Jesus]
23. Ethics / B. Contract Ethics / 2. Golden Rule
Treat others as you would have them treat you [Jesus]
23. Ethics / B. Contract Ethics / 4. Value of Authority
Blessed are the merciful: for they shall obtain mercy [Jesus]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Except ye become as little children, ye shall not enter heaven [Jesus]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / h. Right feelings
If you lust after a woman, you have committed adultery [Jesus]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Blessed are the meek; for they shall inherit the earth [Jesus]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
Don't resist evil, but turn the other cheek [Jesus]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
It is almost impossible for the rich to go to heaven [Jesus]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
No one is good except God [Jesus]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Jesus turned the ideas of Hillel into a theology reduced to its moral elements [Jesus, by Johnson,P]