Combining Texts

All the ideas for 'Russell's Mathematical Logic', 'Essays on Intellectual Powers 6: Judgement' and 'Thinking and Experience'

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30 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
The existence of tensed verbs shows that not all truths are necessary truths [Reid]
2. Reason / D. Definition / 8. Impredicative Definition
Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
2. Reason / F. Fallacies / 7. Ad Hominem
An ad hominem argument is good, if it is shown that the man's principles are inconsistent [Reid]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Impredicative definitions are admitted into ordinary mathematics [Gödel]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
Some dispositional properties (such as mental ones) may have no categorical base [Price,HH]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
If someone denies that he is thinking when he is conscious of it, we can only laugh [Reid]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
The existence of ideas is no more obvious than the existence of external objects [Reid]
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
We are only aware of other beings through our senses; without that, we are alone in the universe [Reid]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
In obscure matters the few must lead the many, but the many usually lead in common sense [Reid]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
The theory of ideas, popular with philosophers, means past existence has to be proved [Reid]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
Consciousness is an indefinable and unique operation [Reid]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Before we can abstract from an instance of violet, we must first recognise it [Price,HH]
If judgement of a characteristic is possible, that part of abstraction must be complete [Price,HH]
There may be degrees of abstraction which allow recognition by signs, without full concepts [Price,HH]
There is pre-verbal sign-based abstraction, as when ice actually looks cold [Price,HH]
Intelligent behaviour, even in animals, has something abstract about it [Price,HH]
18. Thought / A. Modes of Thought / 1. Thought
Recognition must precede the acquisition of basic concepts, so it is the fundamental intellectual process [Price,HH]
18. Thought / A. Modes of Thought / 8. Human Thought
The structure of languages reveals a uniformity in basic human opinions [Reid]
18. Thought / E. Abstraction / 1. Abstract Thought
Abstractions can be interpreted dispositionally, as the ability to recognise or imagine an item [Price,HH]
If ideas have to be images, then abstract ideas become a paradoxical problem [Price,HH]
18. Thought / E. Abstraction / 2. Abstracta by Selection
The basic concepts of conceptual cognition are acquired by direct abstraction from instances [Price,HH]
If you can't distinguish the features of a complex object, your notion of it would be a muddle [Reid]
21. Aesthetics / A. Aesthetic Experience / 3. Taste
There are axioms of taste - such as a general consensus about a beautiful face [Reid]