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All the ideas for 'Defending the Axioms', 'Four Dimensionalism' and 'Outlines of Pyrrhonism'

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73 ideas

1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
Metaphysical enquiry can survive if its conclusions are tentative [Sider]
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 / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
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 / 3. If-Thenism
Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
If two mathematical themes coincide, that suggest a single deep truth [Maddy]
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 / 5. The Infinite / g. Continuum Hypothesis
Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
7. Existence / B. Change in Existence / 2. Processes
Four-dimensionalism sees things and processes as belonging in the same category [Sider]
8. Modes of Existence / B. Properties / 6. Categorical Properties
Proper ontology should only use categorical (actual) properties, not hypothetical ones [Sider]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
If sortal terms fix the kind and the persistence conditions, we need to know what kinds there are [Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
If Tib is all of Tibbles bar her tail, when Tibbles loses her tail, two different things become one [Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Artists 'create' statues because they are essentially statues, and so lack identity with the lump of clay [Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
The stage view of objects is best for dealing with coincident entities [Sider]
9. Objects / C. Structure of Objects / 5. Composition of an Object
'Composition as identity' says that an object just is the objects which compose it [Sider]
9. Objects / D. Essence of Objects / 12. Essential Parts
Mereological essentialism says an object's parts are necessary for its existence [Sider]
9. Objects / E. Objects over Time / 3. Three-Dimensionalism
Three-dimensionalists assert 'enduring', being wholly present at each moment, and deny 'temporal parts' [Sider]
Some might say that its inconsistency with time travel is a reason to favour three-dimensionalism [Sider]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
Four-dimensionalists assert 'temporal parts', 'perduring', and being spread out over time [Sider]
4D says intrinsic change is difference between successive parts [Sider]
4D says each spatiotemporal object must have a temporal part at every moment at which it exists [Sider]
9. Objects / E. Objects over Time / 5. Temporal Parts
Temporal parts exist, but are not prior building blocks for objects [Sider]
Temporal parts are instantaneous [Sider]
How can an instantaneous stage believe anything, if beliefs take time? [Sider]
Four-dimensionalism says temporal parts are caused (through laws of motion) by previous temporal parts [Sider]
9. Objects / E. Objects over Time / 9. Ship of Theseus
The ship undergoes 'asymmetric' fission, where one candidate is seen as stronger [Sider]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
If you say Leibniz's Law doesn't apply to 'timebound' properties, you are no longer discussing identity [Sider]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Counterparts rest on similarity, so there are many such relations in different contexts [Sider]
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]
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
With us it is shameful for men to wear earrings, but among Syrians it is considered noble [Sext.Empiricus]
Even if all known nations agree on a practice, there may be unknown nations which disagree [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]
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]
If all atoms, times and places are the same, everything should move with equal velocity [Sext.Empiricus]
Maybe motion is a dynamical quantity intrinsic to a thing at a particular time [Sider]
Does the original self-mover push itself from behind, or pull itself from in front? [Sext.Empiricus]
27. Natural Reality / C. Space / 6. Space-Time
Space is 3D and lacks a direction; time seems connected to causation [Sider]
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 / g. Growing block
Between presentism and eternalism is the 'growing block' view - the past is real, the future is not [Sider]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
For Presentists there must always be a temporal vantage point for any description [Sider]
Presentists must deny truths about multiple times [Sider]
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 / 2. Passage of Time / c. Tenses and time
Talk using tenses can be eliminated, by reducing it to indexical connections for an utterance [Sider]
27. Natural Reality / D. Time / 2. Passage of Time / f. Tenseless (B) series
The B-theory is adequate, except that it omits to say which time is present [Sider]
The B-series involves eternalism, and the reduction of tense [Sider]
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]