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All the ideas for 'fragments/reports', 'Principia Mathematica' and 'Outlines of Pyrrhonism'

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64 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Even pointing a finger should only be done for a reason [Epictetus]
1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
You cannot divide anything into many parts, because after the first division you are no longer dividing the original [Sext.Empiricus]
2. Reason / E. Argument / 6. Conclusive Proof
Proof moves from agreed premises to a non-evident inference [Sext.Empiricus]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro]
We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead]
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead]
Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
A valid hypothetical syllogism is 'that which does not begin with a truth and end with a falsehood' [Sext.Empiricus]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel]
5. Theory of Logic / L. Paradox / 7. Paradoxes of Time
Since Socrates either died when he was alive (a contradiction) or died when he was dead (meaningless), he didn't die [Sext.Empiricus]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / a. Defining numbers
Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes]
Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman]
The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
If an argument has an absurd conclusion, we should not assent to the absurdity, but avoid the absurd argument [Sext.Empiricus]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / c. Representative realism
Whether honey is essentially sweet may be doubted, as it is a matter of judgement rather than appearance [Sext.Empiricus]
12. Knowledge Sources / B. Perception / 5. Interpretation
How can the intellect know if sensation is reliable if it doesn't directly see external objects? [Sext.Empiricus]
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
We distinguish ambiguities by seeing what is useful [Sext.Empiricus]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
The basis of scepticism is the claim that every proposition has an equal opposing proposition [Sext.Empiricus]
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
The necks of doves appear different in colour depending on the angle of viewing [Sext.Empiricus]
The same oar seems bent in water and straight when out of it [Sext.Empiricus]
The same tower appears round from a distance, but square close at hand [Sext.Empiricus]
If we press the side of an eyeball, objects appear a different shape [Sext.Empiricus]
13. Knowledge Criteria / E. Relativism / 1. Relativism
How can we judge between our impressions and those of other animals, when we ourselves are involved? [Sext.Empiricus]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
Water that seems lukewarm can seem very hot on inflamed skin [Sext.Empiricus]
Some actions seem shameful when sober but not when drunk [Sext.Empiricus]
If we had no hearing or sight, we would assume no sound or sight exists, so there may be unsensed qualities [Sext.Empiricus]
Sickness is perfectly natural to the sick, so their natural perceptions should carry some weight [Sext.Empiricus]
If we enjoy different things, presumably we receive different impressions [Sext.Empiricus]
13. Knowledge Criteria / E. Relativism / 4. Cultural relativism
Even if all known nations agree on a practice, there may be unknown nations which disagree [Sext.Empiricus]
With us it is shameful for men to wear earrings, but among Syrians it is considered noble [Sext.Empiricus]
14. Science / C. Induction / 3. Limits of Induction
If you don't view every particular, you may miss the one which disproves your universal induction [Sext.Empiricus]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
If we utter three steps of a logical argument, they never exist together [Sext.Empiricus]
The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B]
A judgement is a complex entity, of mind and various objects [Russell/Whitehead]
The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead]
The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead]
Only the act of judging completes the meaning of a statement [Russell/Whitehead]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
26. Natural Theory / C. Causation / 4. Naturalised causation
Some say that causes are physical, some say not [Sext.Empiricus]
26. Natural Theory / C. Causation / 7. Eliminating causation
Knowing an effect results from a cause means knowing that the cause belongs with the effect, which is circular [Sext.Empiricus]
Cause can't exist before effect, or exist at the same time, so it doesn't exist [Sext.Empiricus]
If there were no causes then everything would have been randomly produced by everything [Sext.Empiricus]
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
Causes are either equal to the effect, or they link equally with other causes, or they contribute slightly [Sext.Empiricus]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
If time and place are infinitely divided, it becomes impossible for movement ever to begin [Sext.Empiricus]
Does the original self-mover push itself from behind, or pull itself from in front? [Sext.Empiricus]
If all atoms, times and places are the same, everything should move with equal velocity [Sext.Empiricus]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
If motion and rest are abolished, so is time [Sext.Empiricus]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
Time must be unlimited, but past and present can't be non-existent, and can't be now, so time does not exist [Sext.Empiricus]
27. Natural Reality / D. Time / 3. Parts of Time / c. Intervals
How can time be divisible if we can't compare one length of time with another? [Sext.Empiricus]
28. God / A. Divine Nature / 2. Divine Nature
How can we agree on the concept of God, unless we agree on his substance or form or place? [Sext.Empiricus]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
The existence of God can't be self-evident or everyone would have agreed on it, so it needs demonstration [Sext.Empiricus]
29. Religion / D. Religious Issues / 3. Problem of Evil / d. Natural Evil
If God foresaw evil he would presumably prevent it, and if he only foresees some things, why those things? [Sext.Empiricus]