Combining Texts

All the ideas for 'The Nature of Mathematical Knowledge', 'Vagueness' and 'The Emotions'

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69 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
The personal view can still be objective, so I call sciences 'impersonal', rather than objective [Goldie]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Logical connectives have the highest precision, yet are infected by the vagueness of true and false [Russell, by Williamson]
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 / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
Since natural language is not precise it cannot be in the province of logic [Russell, by Keefe/Smith]
Vagueness is only a characteristic of representations, such as language [Russell]
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 / 4. Other Minds / c. Knowing other minds
We know other's emotions by explanation, contagion, empathy, imagination, or sympathy [Goldie]
Empathy and imagining don't ensure sympathy, and sympathy doesn't need them [Goldie]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher]
18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions
Unlike moods, emotions have specific objects, though the difference is a matter of degree [Goldie]
Emotional intentionality as belief and desire misses out the necessity of feelings [Goldie]
A long lasting and evolving emotion is still seen as a single emotion, such as love [Goldie]
'Having an emotion' differs from 'being emotional' [Goldie]
18. Thought / A. Modes of Thought / 3. Emotions / b. Types of emotion
Some Aborigines have fifteen different words for types of fear [Goldie]
18. Thought / A. Modes of Thought / 3. Emotions / c. Role of emotions
Emotional responses can reveal to us our values, which might otherwise remain hidden [Goldie]
If we have a 'feeling towards' an object, that gives the recognition a different content [Goldie]
When actions are performed 'out of' emotion, they appear to be quite different [Goldie]
It is best to see emotions holistically, as embedded in a person's life narrative [Goldie]
If emotions are 'towards' things, they can't be bodily feelings, which lack aboutness [Goldie]
18. Thought / A. Modes of Thought / 3. Emotions / d. Emotional feeling
If reasons are seen impersonally (as just causal), then feelings are an irrelevant extra [Goldie]
We have feelings of which we are hardly aware towards things in the world [Goldie]
An emotion needs episodes of feeling, but not continuously [Goldie]
Moods can focus as emotions, and emotions can blur into moods [Goldie]
18. Thought / A. Modes of Thought / 3. Emotions / e. Basic emotions
Emotions are not avocado pears, with a rigid core and changeable surface [Goldie]
A basic emotion is the foundation of a hierarchy, such as anger for types of annoyance [Goldie]
Early Chinese basic emotions: joy, anger, sadness, fear, love, disliking, and liking [Goldie]
Cross-cultural studies of facial expressions suggests seven basic emotions [Goldie]
18. Thought / A. Modes of Thought / 3. Emotions / f. Emotion and reason
Some emotions are direct responses, and neither rational nor irrational [Goldie]
Emotional thought is not rational, but it can be intelligible [Goldie]
18. Thought / A. Modes of Thought / 3. Emotions / g. Controlling emotions
Learning an evaluative property like 'dangerous' is also learning an emotion [Goldie]
We call emotions 'passions' because they are not as controlled as we would like [Goldie]
Emotional control is hard, but we are responsible for our emotions over long time periods [Goldie]
Emotions are not easily changed, as new knowledge makes little difference, and akrasia is possible [Goldie]
Emotional control is less concerned with emotional incidents, and more with emotional tendencies [Goldie]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
Akrasia can be either overruling our deliberation, or failing to deliberate [Goldie]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
Justifying reasons say you were right; excusing reasons say your act was explicable [Goldie]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
Character traits are both possession of and lack of dispositions [Goldie]
We over-estimate the role of character traits when explaining behaviour [Goldie]
Psychologists suggest we are muddled about traits, and maybe they should be abandoned [Goldie]
27. Natural Reality / G. Biology / 3. Evolution
Our capabilities did not all evolve during the hunter gathering period [Goldie]