Combining Texts

All the ideas for 'New System and Explanation of New System', 'The Nature of Mathematical Knowledge' and 'The Really Hard Problem'

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43 ideas

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik]
Mathematical a priorism is conceptualist, constructivist or realist [Kitcher]
The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher]
The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers stand to measurement as natural numbers stand to counting [Kitcher]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers
Complex numbers were only accepted when a geometrical model for them was found [Kitcher]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A one-operation is the segregation of a single object [Kitcher]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
The old view is that mathematics is useful in the world because it describes the world [Kitcher]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
With infinitesimals, you divide by the time, then set the time to zero [Kitcher]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Mathematical intuition is not the type platonism needs [Kitcher]
If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher]
Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Mathematical knowledge arises from basic perception [Kitcher]
My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher]
We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher]
The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Arithmetic is an idealizing theory [Kitcher]
Arithmetic is made true by the world, but is also made true by our constructions [Kitcher]
We develop a language for correlations, and use it to perform higher level operations [Kitcher]
Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher]
If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
Reality must be made of basic unities, which will be animated, substantial points [Leibniz]
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
Abstract objects were a bad way of explaining the structure in mathematics [Kitcher]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
A priori knowledge comes from available a priori warrants that produce truth [Kitcher]
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
In long mathematical proofs we can't remember the original a priori basis [Kitcher]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher]
12. Knowledge Sources / A. A Priori Knowledge / 10. A Priori as Subjective
We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
No machine or mere organised matter could have a unified self [Leibniz]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
Research suggest that we overrate conscious experience [Flanagan]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher]
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
The soul does know bodies, although they do not influence one another [Leibniz]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
Sensations may be identical to brain events, but complex mental events don't seem to be [Flanagan]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
Morality is normative because it identifies best practices among the normal practices [Flanagan]
22. Metaethics / B. Value / 2. Values / f. Altruism
For Darwinians, altruism is either contracts or genetics [Flanagan]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
We need Eudaimonics - the empirical study of how we should flourish [Flanagan]
24. Political Theory / D. Ideologies / 9. Communism
Alienation is not finding what one wants, or being unable to achieve it [Flanagan]
27. Natural Reality / G. Biology / 2. Life
To regard animals as mere machines may be possible, but seems improbable [Leibniz]
29. Religion / C. Spiritual Disciplines / 3. Buddhism
Buddhists reject God and the self, and accept suffering as key, and liberation through wisdom [Flanagan]