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All the ideas for 'Axiomatic Theories of Truth (2005 ver)', 'reports' and 'Frege's Concept of Numbers as Objects'

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70 ideas

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]
2. Reason / A. Nature of Reason / 7. Status of Reason
Reason is a more powerful persuader than gold [Democritus (attr)]
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 / A. Truth Problems / 2. Defining Truth
Truth definitions don't produce a good theory, because they go beyond your current language [Halbach]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach]
If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach]
Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach]
Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationists say truth merely serves to express infinite conjunctions [Halbach]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
To prove the consistency of set theory, we must go beyond set theory [Halbach]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach]
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach]
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 / c. Neo-logicism
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]
Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA]
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]
7. Existence / A. Nature of Existence / 2. Types of Existence
The idea that 'exist' has multiple senses is not coherent [Wright,C]
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]
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]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
A concept is only a sortal if it gives genuine identity [Wright,C]
'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [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]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
Beauty is merely animal without intelligence [Democritus (attr)]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Behave well when alone, and feel shame in you own eyes [Democritus (attr)]
22. Metaethics / B. Value / 2. Values / d. Health
Good breeding in men means having a good character [Democritus (attr)]
22. Metaethics / B. Value / 2. Values / g. Love
Virtuous love consists of decorous desire for the beautiful [Democritus (attr)]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
We should only choose pleasures which are concerned with the beautiful [Democritus (attr)]
Good and true are the same for everyone, but pleasures differ [Democritus (attr)]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
Only accept beneficial pleasures [Democritus (attr)]
22. Metaethics / C. The Good / 3. Pleasure / d. Sources of pleasure
The great pleasures come from the contemplation of noble works [Democritus (attr)]
Moderation brings more pleasures, and so increases pleasure [Democritus (attr)]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
Immoderate desire is the mark of a child, not an adult [Democritus (attr)]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
It is as brave to master pleasure as to overcome the enemy [Democritus (attr)]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Virtue doesn't just avoid evil, but also doesn't desire it [Democritus (attr)]
A bad life is just a drawn-out death [Democritus (attr)]
Be virtuous from duty, not from fear [Democritus (attr)]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Repentance of shameful deeds is salvation [Democritus (attr)]
Virtue comes more from practice than from nature [Democritus (attr)]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / i. Absolute virtues
One must avoid even speaking of evil deeds [Democritus (attr)]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
The wrongdoer is more unfortunate than the person wronged [Democritus (attr)]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
The endless desire for money is a crueller slavery than poverty [Democritus (attr)]
Small appetite makes poverty equal to wealth [Democritus (attr)]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
It is better to have one intelligent friend than many unintelligent [Democritus (attr)]
23. Ethics / D. Deontological Ethics / 2. Duty
It is a great thing, when one is in adversity, to think of duty [Democritus (attr)]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
It is better to be poor in a democracy than be rich without freedom [Democritus (attr)]