Combining Texts

All the ideas for 'Symbolic Reasoning', 'Regressive Method for Premises in Mathematics' and 'A Dictionary of Philosophy'

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16 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell]
2. Reason / A. Nature of Reason / 6. Coherence
If one proposition is deduced from another, they are more certain together than alone [Russell]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Non-contradiction was learned from instances, and then found to be indubitable [Russell]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The null class is the class with all the non-existents as its members [MacColl, by Lackey]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Finding the axioms may be the only route to some new results [Russell]
Which premises are ultimate varies with context [Russell]
The sources of a proof are the reasons why we believe its conclusion [Russell]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Arithmetic was probably inferred from relationships between physical objects [Russell]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
Maybe 'sense-data' just help us to talk about unusual perceptual situations [Lacey]
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
Where do sense-data begin or end? Can they change? What sort of thing are they? [Lacey]
Some claim sense-data are public, and are parts of objects [Lacey]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Believing a whole science is more than believing each of its propositions [Russell]
14. Science / C. Induction / 2. Aims of Induction
Induction is inferring premises from consequences [Russell]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
The law of gravity has many consequences beyond its grounding observations [Russell]