Combining Texts

All the ideas for 'Perception', 'Remarks on axiomatised set theory' and 'The Nature of Mathematical Knowledge'

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62 ideas

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Axiomatising set theory makes it all relative [Skolem]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]
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 / B. Foundations for Mathematics / 1. Foundations for Mathematics
Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Mathematician want performable operations, not propositions about objects [Skolem]
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 / D. Theories of Reality / 6. Physicalism
For physicalists, the only relations are spatial, temporal and causal [Robinson,H]
8. Modes of Existence / B. Properties / 6. Categorical Properties
If reality just has relational properties, what are its substantial ontological features? [Robinson,H]
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]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / a. Naïve realism
When a red object is viewed, the air in between does not become red [Robinson,H]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / c. Representative realism
Representative realists believe that laws of phenomena will apply to the physical world [Robinson,H]
Representative realists believe some properties of sense-data are shared by the objects themselves [Robinson,H]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Phenomenalism can be theistic (Berkeley), or sceptical (Hume), or analytic (20th century) [Robinson,H]
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]
12. Knowledge Sources / B. Perception / 1. Perception
Can we reduce perception to acquisition of information, which is reduced to causation or disposition? [Robinson,H]
Would someone who recovered their sight recognise felt shapes just by looking? [Robinson,H]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / b. Primary/secondary
Secondary qualities have one sensory mode, but primary qualities can have more [Robinson,H]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
We say objects possess no intrinsic secondary qualities because physicists don't need them [Robinson,H]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
If objects are not coloured, and neither are sense-contents, we are left saying that nothing is coloured [Robinson,H]
Shape can be experienced in different ways, but colour and sound only one way [Robinson,H]
If secondary qualities match senses, would new senses create new qualities? [Robinson,H]
12. Knowledge Sources / B. Perception / 3. Representation
Most moderate empiricists adopt Locke's representative theory of perception [Robinson,H]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
Sense-data leads to either representative realism or phenomenalism or idealism [Robinson,H]
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
Sense-data do not have any intrinsic intentionality [Robinson,H]
For idealists and phenomenalists sense-data are in objects; representative realists say they resemble objects [Robinson,H]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
Sense-data are rejected because they are a veil between us and reality, leading to scepticism [Robinson,H]
12. Knowledge Sources / B. Perception / 8. Adverbial Theory
'Sense redly' sounds peculiar, but 'senses redly-squarely tablely' sounds far worse [Robinson,H]
Adverbialism sees the contents of sense-experience as modes, not objects [Robinson,H]
If there are only 'modes' of sensing, then an object can no more be red or square than it can be proud or lazy. [Robinson,H]
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]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
An explanation presupposes something that is improbable unless it is explained [Robinson,H]
If all possibilities are equal, order seems (a priori) to need an explanation - or does it? [Robinson,H]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / a. Nature of intentionality
If intentional states are intrinsically about other things, what are their own properties? [Robinson,H]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Physicalism cannot allow internal intentional objects, as brain states can't be 'about' anything [Robinson,H]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / c. Matter as extension
Locke's solidity is not matter, because that is impenetrability and hardness combined [Robinson,H]