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All the ideas for 'Frege's Concept of Numbers as Objects', 'A Discourse on Method' and 'Why Medieval Philosophy Matters'

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66 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]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Slow and accurate thought makes the greatest progress [Descartes]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Most things in human life seem vain and useless [Descartes]
Almost every daft idea has been expressed by some philosopher [Descartes]
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Science rests on scholastic metaphysics, not on Hume, Kant or Carnap [Boulter]
2. Reason / A. Nature of Reason / 4. Aims of Reason
Methodical thinking is cautious, analytical, systematic, and panoramic [Descartes, by PG]
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]
2. Reason / F. Fallacies / 4. Circularity
Clear and distinct conceptions are true because a perfect God exists [Descartes]
3. Truth / A. Truth Problems / 8. Subjective Truth
Truth is clear and distinct conception - of which it is hard to be sure [Descartes]
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]
8. Modes of Existence / D. Universals / 2. Need for Universals
Thoughts are general, but the world isn't, so how can we think accurately? [Boulter]
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]
10. Modality / A. Necessity / 6. Logical Necessity
Logical possibility needs the concepts of the proposition to be adequate [Boulter]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
We can believe a thing without knowing we believe it [Descartes]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
In morals Descartes accepts the conventional, but rejects it in epistemology [Roochnik on Descartes]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
In thinking everything else false, my own existence remains totally certain [Descartes]
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
I aim to find the principles and causes of everything, using the seeds within my mind [Descartes]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Understanding, rather than imagination or senses, gives knowledge [Descartes]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
I was searching for reliable rock under the shifting sand [Descartes]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
When rebuilding a house, one needs alternative lodgings [Descartes]
14. Science / A. Basis of Science / 3. Experiment
Only experiments can settle disagreements between rival explanations [Descartes]
Experiments don't just observe; they look to see what interventions change the natural order [Boulter]
14. Science / B. Scientific Theories / 1. Scientific Theory
Science begins with sufficient reason, de-animation, and the importance of nature [Boulter]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
Little reason is needed to speak, so animals have no reason at all [Descartes]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
Our concepts can never fully capture reality, but simplification does not falsify [Boulter]
16. Persons / B. Nature of the Self / 3. Self as Non-physical
I am a thinking substance, which doesn't need a place or material support [Descartes]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
I can deny my body and the world, but not my own existence [Descartes]
Reason is universal in its responses, but a physical machine is constrained by its organs [Descartes]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
The soul must unite with the body to have appetites and sensations [Descartes]
18. Thought / B. Mechanics of Thought / 6. Artificial Thought / c. Turing Test
A machine could speak in response to physical stimulus, but not hold a conversation [Descartes]
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]
19. Language / E. Analyticity / 3. Analytic and Synthetic
Aristotelians accept the analytic-synthetic distinction [Boulter]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
The facts about human health are the measure of the values in our lives [Boulter]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
Greeks elevate virtues enormously, but never explain them [Descartes]
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
God has established laws throughout nature, and implanted ideas of them within us [Descartes]