Combining Texts

All the ideas for 'The Evolution of Modern Metaphysics', 'Existentialism: an introduction' and 'Logic in Mathematics'

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30 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Metaphysics is the most general attempt to make sense of things [Moore,AW]
1. Philosophy / H. Continental Philosophy / 2. Phenomenology
Phenomenologists say all experience is about something and is directed [Aho]
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]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW]
14. Science / B. Scientific Theories / 2. Aim of Science
Science has to abstract out the subjective attributes of things, focusing on what is objective [Aho]
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]
23. Ethics / F. Existentialism / 3. Angst
Anxiety, nausea, guilt and absurdity shake us up, revealing our freedom and limits [Aho]
23. Ethics / F. Existentialism / 5. Existence-Essence
Our 'existence' is how we create ourselves, unconstrained by any prior 'essence' [Aho]
23. Ethics / F. Existentialism / 6. Authentic Self
The self is constituted by its choices made within a social context [Aho]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Social contracts and markets have made society seem disconnected and artificial [Aho]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Protestantism brought the modern emphasis on inner states of the soul [Aho]
29. Religion / C. Spiritual Disciplines / 3. Buddhism
Four Noble Truths: life is suffering, caused by attachment, it is avoidable, there is a path [Aho]