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All the ideas for 'fragments/reports', 'Constructibility and Mathematical Existence' and 'Frege's Concept of Numbers as Objects'

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100 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom for one instant is as good as wisdom for eternity [Chrysippus]
1. Philosophy / A. Wisdom / 2. Wise People
Wise men should try to participate in politics, since they are a good influence [Chrysippus, by Diog. Laertius]
1. Philosophy / C. History of Philosophy / 1. History of Philosophy
We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C]
1. Philosophy / D. Nature of Philosophy / 4. Divisions of Philosophy
Three branches of philosophy: first logic, second ethics, third physics (which ends with theology) [Chrysippus]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
Chrysippus said the uncaused is non-existent [Chrysippus, by Plutarch]
2. Reason / C. Styles of Reason / 1. Dialectic
The best way to understand a philosophical idea is to defend it [Wright,C]
2. Reason / D. Definition / 7. Contextual Definition
The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K]
3. Truth / B. Truthmakers / 10. Making Future Truths
The causes of future true events must exist now, so they will happen because of destiny [Chrysippus, by Cicero]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
Graspable presentations are criteria of facts, and are molded according to their objects [Chrysippus, by Diog. Laertius]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
How could you ever know that the presentation is similar to the object? [Sext.Empiricus on Chrysippus]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
We could talk of open sentences, instead of sets [Chihara, by Shapiro]
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Every proposition is either true or false [Chrysippus, by Cicero]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck]
There are five Peano axioms, which can be expressed informally [Wright,C]
Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C]
What facts underpin the truths of the Peano axioms? [Wright,C]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Sameness of number is fundamental, not counting, despite children learning that first [Wright,C]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K]
Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend]
Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck]
It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Number platonism says that natural number is a sortal concept [Wright,C]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Treating numbers adjectivally is treating them as quantifiers [Wright,C]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA]
The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C]
The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C]
The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
7. Existence / A. Nature of Existence / 2. Types of Existence
The idea that 'exist' has multiple senses is not coherent [Wright,C]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Chrysippus says action is the criterion for existence, which must be physical [Chrysippus, by Tieleman]
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
There are simple and complex facts; the latter depend on further facts [Chrysippus, by Cicero]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C]
7. Existence / E. Categories / 3. Proposed Categories
Stoics categories are Substrate, Quality, Disposition, and Relation [Chrysippus, by Pasnau]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Contextually defined abstract terms genuinely refer to objects [Wright,C, by Dummett]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
Sortal concepts cannot require that things don't survive their loss, because of phase sortals [Wright,C]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
Dion and Theon coexist, but Theon lacks a foot. If Dion loses a foot, he ousts Theon? [Chrysippus, by Philo of Alexandria]
9. Objects / E. Objects over Time / 2. Objects that Change
Change of matter doesn't destroy identity - in Dion and Theon change is a condition of identity [Chrysippus, by Long/Sedley]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
Dogs show reason in decisions made by elimination [Chrysippus, by Sext.Empiricus]
16. Persons / F. Free Will / 4. For Free Will
Chrysippus allows evil to say it is fated, or even that it is rational and natural [Plutarch on Chrysippus]
16. Persons / F. Free Will / 5. Against Free Will
A swerve in the atoms would be unnatural, like scales settling differently for no reason [Chrysippus, by Plutarch]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
Everything is fated, either by continuous causes or by a supreme rational principle [Chrysippus, by Diog. Laertius]
Chrysippus is wrong to believe in non-occurring future possibilities if he is a fatalist [Plutarch on Chrysippus]
16. Persons / F. Free Will / 6. Determinism / b. Fate
The Lazy Argument responds to fate with 'why bother?', but the bothering is also fated [Chrysippus, by Cicero]
Fate is an eternal and fixed chain of causal events [Chrysippus]
When we say events are fated by antecedent causes, do we mean principal or auxiliary causes? [Chrysippus]
16. Persons / F. Free Will / 7. Compatibilism
Destiny is only a predisposing cause, not a sufficient cause [Chrysippus, by Plutarch]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C]
A concept is only a sortal if it gives genuine identity [Wright,C]
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
A milder claim is that understanding requires some evidence of that understanding [Wright,C]
19. Language / B. Reference / 1. Reference theories
If apparent reference can mislead, then so can apparent lack of reference [Wright,C]
19. Language / C. Assigning Meanings / 3. Predicates
We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C]
19. Language / D. Propositions / 1. Propositions
A proposition is what can be asserted or denied on its own [Chrysippus]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
Passions are judgements; greed thinks money is honorable, and likewise drinking and lust [Chrysippus, by Diog. Laertius]
20. Action / C. Motives for Action / 5. Action Dilemmas / c. Omissions
The highest degree of morality performs all that is appropriate, omitting nothing [Chrysippus]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Stoics say that beauty and goodness are equivalent and linked [Chrysippus, by Diog. Laertius]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Fate initiates general causes, but individual wills and characters dictate what we do [Chrysippus]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Human purpose is to contemplate and imitate the cosmos [Chrysippus]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Stoics say justice is a part of nature, not just an invented principle [Chrysippus, by Diog. Laertius]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
Only nature is available to guide action and virtue [Chrysippus]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Live in agreement, according to experience of natural events [Chrysippus]
22. Metaethics / C. The Good / 1. Goodness / d. Good as virtue
Living happily is nothing but living virtuously [Chrysippus, by Plutarch]
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
Pleasure is not the good, because there are disgraceful pleasures [Chrysippus, by Diog. Laertius]
Justice can be preserved if pleasure is a good, but not if it is the goal [Chrysippus, by Plutarch]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
There are shameful pleasures, and nothing shameful is good, so pleasure is not a good [Chrysippus, by Diog. Laertius]
23. Ethics / A. Egoism / 2. Hedonism
People need nothing except corn and water [Chrysippus, by Plutarch]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
All virtue is good, but not always praised (as in not lusting after someone ugly) [Chrysippus]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
Chrysippus says virtue can be lost (though Cleanthes says it is too secure for that) [Chrysippus, by Diog. Laertius]
Chrysippus says nothing is blameworthy, as everything conforms with the best nature [Chrysippus, by Plutarch]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
Rational animals begin uncorrupted, but externals and companions are bad influences [Chrysippus, by Diog. Laertius]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
Justice, the law, and right reason are natural and not conventional [Chrysippus, by Diog. Laertius]
25. Social Practice / F. Life Issues / 6. Animal Rights
We don't have obligations to animals as they aren't like us [Chrysippus, by Diog. Laertius]
Justice is irrelevant to animals, because they are too unlike us [Chrysippus, by Diog. Laertius]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
Covers are for shields, and sheaths for swords; likewise, all in the cosmos is for some other thing [Chrysippus]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
The later Stoics identified the logos with an air-fire compound, called 'pneuma' [Chrysippus, by Long]
Fire is a separate element, not formed with others (as was previously believed) [Chrysippus, by Stobaeus]
Stoics say earth, air, fire and water are the primary elements [Chrysippus, by Plutarch]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
The past and the future subsist, but only the present exists [Chrysippus, by Plutarch]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
The present does not exist, so our immediate experience is actually part past and part future [Chrysippus, by Plutarch]
Time is continous and infinitely divisible, so there cannot be a wholly present time [Chrysippus, by Stobaeus]
28. God / A. Divine Nature / 3. Divine Perfections
Stoics say that God the creator is the perfection of all animals [Chrysippus, by Diog. Laertius]
28. God / A. Divine Nature / 6. Divine Morality / a. Divine morality
The origin of justice can only be in Zeus, and in nature [Chrysippus]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
Stoics teach that law is identical with right reason, which is the will of Zeus [Chrysippus, by Diog. Laertius]
The source of all justice is Zeus and the universal nature [Chrysippus]
29. Religion / B. Monotheistic Religion / 1. Monotheistic Religion
Stoics teach that God is a unity, variously known as Mind, or Fate, or Jupiter [Chrysippus, by Diog. Laertius]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
Death can't separate soul from body, because incorporeal soul can't unite with body [Chrysippus]
29. Religion / D. Religious Issues / 3. Problem of Evil / d. Natural Evil
There is a rationale in terrible disasters; they are useful to the whole, and make good possible [Chrysippus]