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All the ideas for 'Frege's Concept of Numbers as Objects', 'Logic [1897]' and 'Phaedo'

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58 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom makes virtue and true goodness possible [Plato]
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 / 5. Aims of Philosophy / b. Philosophy as transcendent
Philosophy is a purification of the soul ready for the afterlife [Plato]
2. Reason / A. Nature of Reason / 3. Pure Reason
In investigation the body leads us astray, but the soul gets a clear view of the facts [Plato]
2. Reason / A. Nature of Reason / 7. Status of Reason
The greatest misfortune for a person is to develop a dislike for argument [Plato]
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]
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 / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
If you add one to one, which one becomes two, or do they both become two? [Plato]
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
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]
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]
8. Modes of Existence / A. Relations / 2. Internal Relations
If Simmias is taller than Socrates, that isn't a feature that is just in Simmias [Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
We must have a prior knowledge of equality, if we see 'equal' things and realise they fall short of it [Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
There is only one source for all beauty [Plato]
Other things are named after the Forms because they participate in them [Plato]
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 / E. Objects over Time / 9. Ship of Theseus
The ship which Theseus took to Crete is now sent to Delos crowned with flowers [Plato]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / b. Recollection doctrine
If we feel the inadequacy of a resemblance, we must recollect the original [Plato]
People are obviously recollecting when they react to a geometrical diagram [Plato]
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
To achieve pure knowledge, we must get rid of the body and contemplate things with the soul [Plato]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
Psychological logic can't distinguish justification from causes of a belief [Frege]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
To investigate the causes of things, study what is best for them [Plato]
15. Nature of Minds / A. Nature of Mind / 8. Brain
Do we think and experience with blood, air or fire, or could it be our brain? [Plato]
16. Persons / D. Continuity of the Self / 1. Identity and the Self
One soul can't be more or less of a soul than another [Plato]
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]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
It is a mistake to think that the most violent pleasure or pain is therefore the truest reality [Plato]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
War aims at the acquisition of wealth, because we are enslaved to the body [Plato]
26. Natural Theory / C. Causation / 2. Types of cause
Fancy being unable to distinguish a cause from its necessary background conditions! [Plato]
27. Natural Reality / E. Cosmology / 1. Cosmology
If the Earth is spherical and in the centre, it is kept in place by universal symmetry, not by force [Plato]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Whether the soul pre-exists our body depends on whether it contains the ultimate standard of reality [Plato]