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All the ideas for 'Mathematics and Indispensibility', 'fragments/reports' and 'Word and Object'

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84 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Quine's naturalistic and empirical view is based entirely on first-order logic and set theory [Quine, by Mautner]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
Enquiry needs a conceptual scheme, so we should retain the best available [Quine]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
Everything happens necessarily, and for a reason [Democritus]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Plurals can in principle be paraphrased away altogether [Quine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Any progression will do nicely for numbers; they can all then be used to measure multiplicity [Quine]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Two can't be a self-contained unit, because it would need to be one to do that [Democritus, by Aristotle]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Nearly all of mathematics has to quantify over abstract objects [Quine]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
True Being only occurs when it is completely full, with atoms and no void [Democritus, by Aristotle]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
Being does not exist more than non-being [Democritus, by Aristotle]
The non-existent exists as much as the existent, because it has causal powers [Democritus]
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
The only distinctions are Configuration (shape), Disposition (order) and Turning (position) [Democritus, by Aristotle]
7. Existence / B. Change in Existence / 1. Nature of Change
Nothing comes from non-existence, or passes into it [Democritus, by Diog. Laertius]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
All scientific tests will verify mathematics, so it is a background, not something being tested [Sober]
7. Existence / E. Categories / 4. Category Realism
The quest for ultimate categories is the quest for a simple clear pattern of notation [Quine]
7. Existence / E. Categories / 5. Category Anti-Realism
It is not possible to know what sort each thing is [Democritus]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
Either dispositions rest on structures, or we keep saying 'all things being equal' [Quine]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / d. Dispositions as occurrent
Explain unmanifested dispositions as structural similarities to objects which have manifested them [Quine, by Martin,CB]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
Quine aims to deal with properties by the use of eternal open sentences, or classes [Quine, by Devitt]
9. Objects / A. Existence of Objects / 1. Physical Objects
The notion of a physical object is by far the most useful one for science [Quine]
Physical objects in space-time are just events or processes, no matter how disconnected [Quine]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
Democritus denies reality to large objects, because atomic entities can't combine to produce new ones [Benardete,JA on Democritus]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Democritus said that substances could never be mixed, so atoms are the substances [Democritus, by Aristotle]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Mathematicians must be rational but not two-legged, cyclists the opposite. So a mathematical cyclist? [Quine]
Cyclist are not actually essentially two-legged [Brody on Quine]
9. Objects / F. Identity among Objects / 2. Defining Identity
We can paraphrase 'x=y' as a sequence of the form 'if Fx then Fy' [Quine]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
Normal conditionals have a truth-value gap when the antecedent is false. [Quine]
10. Modality / B. Possibility / 8. Conditionals / e. Supposition conditionals
Conditionals are pointless if the truth value of the antecedent is known [Quine]
10. Modality / B. Possibility / 9. Counterfactuals
We feign belief in counterfactual antecedents, and assess how convincing the consequent is [Quine]
Counterfactuals are plausible when dispositions are involved, as they imply structures [Quine]
Counterfactuals have no place in a strict account of science [Quine]
What stays the same in assessing a counterfactual antecedent depends on context [Quine]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / a. Qualities in perception
Sensible qualities can't be real if they appear different to different creatures [Democritus, by Theophrastus]
12. Knowledge Sources / B. Perception / 3. Representation
Man is separated from reality [Democritus]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
All evidence comes from senses, so they are indispensable to the mind [Democritus]
Obscure knowledge belongs to the five senses, and genuine knowledge is the other type [Democritus]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Democritus says there is either no truth, or it is concealed from us [Democritus, by Aristotle]
We actually know nothing, and opinions are mere flux [Democritus]
We in fact know nothing, but we each restructure our reality with beliefs [Democritus]
It is obviously impossible to understand the reality of each thing [Democritus]
We know nothing in reality; for truth lies in an abyss [Democritus]
14. Science / B. Scientific Theories / 1. Scientific Theory
Two theories can be internally consistent and match all the facts, yet be inconsistent with one another [Quine, by Baggini /Fosl]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
Democritus was devoted to discovering causal explanations [Democritus, by Eusebius]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
Democritus says soul consists of smooth round bodies brought together in accidental collision [Democritus, by Cicero]
Atomists say soul has a rational part in the chest, and a diffused non-rational part [Democritus, by Aetius]
The soul is the same as the mind [Democritus, by Aristotle]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
Animals have a share of reason [Democritus, by Porphyry]
15. Nature of Minds / A. Nature of Mind / 8. Brain
The directive centre is located in the whole head [Democritus, by Ps-Plutarch]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
Democritus said everything happens of necessity, by natural motion of atoms [Democritus, by Cicero]
Some say there is a determinate cause for every apparently spontaneous event [Democritus, by Aristotle]
Democritus said atoms only move by their natural motions, which are therefore necessary [Democritus, by Cicero]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Democritus says spherical atoms are fire, and constitute the soul [psuche] [Democritus, by Aristotle]
Democritus says the soul is the body, and thinking is thus the mixture of the body [Democritus, by Theophrastus]
17. Mind and Body / E. Mind as Physical / 3. Eliminativism
Quine expresses the instrumental version of eliminativism [Quine, by Rey]
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
Indeterminacy of translation also implies indeterminacy in interpreting people's mental states [Dennett on Quine]
The firmer the links between sentences and stimuli, the less translations can diverge [Quine]
We can never precisely pin down how to translate the native word 'Gavagai' [Quine]
Stimulus synonymy of 'Gavagai' and 'Rabbit' does not even guarantee they are coextensive [Quine]
Dispositions to speech behaviour, and actual speech, are never enough to fix any one translation [Quine]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
We should be suspicious of a translation which implies that a people have very strange beliefs [Quine]
Weird translations are always possible, but they improve if we impose our own logic on them [Quine]
20. Action / C. Motives for Action / 1. Acting on Desires
Pleasure and pain guide our choices of good and bad [Democritus]
22. Metaethics / B. Value / 2. Values / d. Health
Wisdom creates a healthy passion-free soul [Democritus]
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
Happiness is identifying and separating the pleasures [Democritus, by Stobaeus]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
Contentment comes from moderation and proportion in life [Democritus, by Stobaeus]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
Democritus says wealth is a burden to the virtuous mind [Democritus, by Seneca]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
Atoms cling together, until a stronger necessity disperses them [Democritus, by Aristotle]
Atoms are irregular, hooked, concave, convex, and many other shapes [Democritus, by Aristotle]
'Full' and 'Void' secularised Parmenides's Being and Not-being [Democritus, by Heisenberg]
Atomists say there are only three differences - in shape, arrangement and position [Democritus, by Aristotle]
Experiences are merely convention; only atoms and the void are real [Democritus]
If only atoms are real and the rest is convention, we wouldn't bother to avoid pain [Democritus, by Diogenes of Oen.]
When atoms touch, why don't they coalesce, like water drops? [Aristotle on Democritus]
Because appearance is infinitely varied, atomists assume infinitely many shapes of atom [Democritus, by Aristotle]
There could be an atom the size of the world [Democritus, by Ps-Plutarch]
There must be atoms, to avoid the absurdity of infinite division down to nothing [Democritus, by Aristotle]
The basic atoms are without qualities - which only arise from encounters between atoms [Democritus, by Galen]
If a cone is horizontally sliced the surfaces can't be equal, so it goes up in steps [Democritus]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Greeks explained regularity by intellectual design, not by laws [Democritus, by Frede,M]
27. Natural Reality / C. Space / 1. Void
Growth and movement would not exist if there were no void to receive them [Democritus]
Democritus is wrong: in a void we wouldn't see a distant ant in exact detail [Aristotle on Democritus]
Movement is impossible in a void, because nothing can decide the direction of movement [Aristotle on Democritus]
27. Natural Reality / E. Cosmology / 1. Cosmology
There are unlimited worlds of varying sizes, some without life or water [Democritus, by Hippolytus]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
Democritus said people imagined gods as the source of what awed or frightened them [Democritus, by Sext.Empiricus]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
The soul is destroyed with the body [Democritus, by Ps-Plutarch]