Combining Texts

All the ideas for 'Letter to Herodotus', 'Necessary Beings' and 'Introduction to Zermelo's 1930 paper'

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52 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
You cannot understand what exists without understanding possibility and necessity [Hale]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
If we are to use words in enquiry, we need their main, unambiguous and uncontested meanings [Epicurus]
2. Reason / D. Definition / 6. Definition by Essence
A canonical defintion specifies the type of thing, and what distinguish this specimen [Hale]
3. Truth / A. Truth Problems / 8. Subjective Truth
Observation and applied thought are always true [Epicurus]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The two Barcan principles are easily proved in fairly basic modal logic [Hale]
With a negative free logic, we can dispense with the Barcan formulae [Hale]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale]
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
Maybe conventionalism applies to meaning, but not to the truth of propositions expressed [Hale]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems [Hale]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale]
7. Existence / A. Nature of Existence / 1. Nature of Existence
Nothing comes to be from what doesn't exist [Epicurus]
If disappearing things went to nothingness, nothing could return, and it would all be gone by now [Epicurus]
7. Existence / B. Change in Existence / 1. Nature of Change
The totality is complete, so there is no room for it to change, and nothing extraneous to change it [Epicurus]
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
Interesting supervenience must characterise the base quite differently from what supervenes on it [Hale]
7. Existence / D. Theories of Reality / 6. Physicalism
Astronomical movements are blessed, but they don't need the help of the gods [Epicurus]
7. Existence / D. Theories of Reality / 8. Facts / c. Facts and truths
There is no gap between a fact that p, and it is true that p; so we only have the truth-condtions for p [Hale]
8. Modes of Existence / B. Properties / 8. Properties as Modes
The perceived accidental properties of bodies cannot be conceived of as independent natures [Epicurus]
Accidental properties give a body its nature, but are not themselves bodies or parts of bodies [Epicurus]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
A 'body' is a conception of an aggregate, with properties defined by application conditions [Epicurus]
9. Objects / C. Structure of Objects / 5. Composition of an Object
If a chair could be made of slightly different material, that could lead to big changes [Hale]
9. Objects / D. Essence of Objects / 9. Essence and Properties
Bodies have impermanent properties, and permanent ones which define its conceived nature [Epicurus]
10. Modality / A. Necessity / 3. Types of Necessity
Absolute necessities are necessarily necessary [Hale]
'Absolute necessity' is when there is no restriction on the things which necessitate p [Hale]
Logical and metaphysical necessities differ in their vocabulary, and their underlying entities [Hale]
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessity is something which is true, no matter what else is the case [Hale]
Maybe each type of logic has its own necessity, gradually becoming broader [Hale]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
It seems that we cannot show that modal facts depend on non-modal facts [Hale]
10. Modality / C. Sources of Modality / 6. Necessity from Essence
The big challenge for essentialist views of modality is things having necessary existence [Hale]
Essentialism doesn't explain necessity reductively; it explains all necessities in terms of a few basic natures [Hale]
If necessity derives from essences, how do we explain the necessary existence of essences? [Hale]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / c. Possible but inconceivable
Above and below us will never appear to be the same, because it is inconceivable [Epicurus]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
What are these worlds, that being true in all of them makes something necessary? [Hale]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds make every proposition true or false, which endorses classical logic [Hale]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
We aim to dissolve our fears, by understanding their causes [Epicurus]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
Atoms only have shape, weight and size, and the properties which accompany shape [Epicurus]
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
Illusions are not false perceptions, as we accurately perceive the pattern of atoms [Epicurus, by Modrak]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
The soul is fine parts distributed through the body, resembling hot breath [Epicurus]
17. Mind and Body / E. Mind as Physical / 5. Causal Argument
The soul cannot be incorporeal, because then it could neither act nor be acted upon [Epicurus]
18. Thought / C. Content / 6. Broad Content
The molecules may explain the water, but they are not what 'water' means [Hale]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Totality has no edge; an edge implies a contrast beyond the edge, and there can't be one [Epicurus]
Bodies are unlimited as well as void, since the two necessarily go together [Epicurus]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
There exists an infinity of each shape of atom, but the number of shapes is beyond our knowledge [Epicurus]
Atoms just have shape, size and weight; colour results from their arrangement [Epicurus]
There cannot be unlimited division, because it would reduce things to non-existence [Epicurus]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
We aim to know the natures which are observed in natural phenomena [Epicurus]
27. Natural Reality / C. Space / 1. Void
The void cannot interact, but just gives the possibility of motion [Epicurus]
27. Natural Reality / C. Space / 4. Substantival Space
Space must exist, since movement is obvious, and there must be somewhere to move in [Epicurus]
27. Natural Reality / E. Cosmology / 10. Multiverse
There are endless cosmoi, some like and some unlike this one [Epicurus]