Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'The Nature of Mathematical Knowledge' and 'Truth'

expand these ideas     |    start again     |     specify just one area for these texts


49 ideas

1. Philosophy / F. Analytic Philosophy / 3. Analysis of Preconditions
In "if and only if" (iff), "if" expresses the sufficient condition, and "only if" the necessary condition [Engel]
3. Truth / A. Truth Problems / 5. Truth Bearers
Are truth-bearers propositions, or ideas/beliefs, or sentences/utterances? [Engel]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
The redundancy theory gets rid of facts, for 'it is a fact that p' just means 'p' [Engel]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
We can't explain the corresponding structure of the world except by referring to our thoughts [Engel]
3. Truth / D. Coherence Truth / 1. Coherence Truth
The coherence theory says truth is an internal relationship between groups of truth-bearers [Engel]
3. Truth / D. Coherence Truth / 2. Coherence Truth Critique
Any coherent set of beliefs can be made more coherent by adding some false beliefs [Engel]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationism seems to block philosophers' main occupation, asking metatheoretical questions [Engel]
Deflationism cannot explain why we hold beliefs for reasons [Engel]
3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Maybe there is no more to be said about 'true' than there is about the function of 'and' in logic [Engel]
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 / D. Assumptions for Logic / 1. Bivalence
Deflationism must reduce bivalence ('p is true or false') to excluded middle ('p or not-p') [Engel]
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]
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 / A. Knowledge / 4. Belief / a. Beliefs
The Humean theory of motivation is that beliefs may be motivators as well as desires [Engel]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
Our beliefs are meant to fit the world (i.e. be true), where we want the world to fit our desires [Engel]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
'Evidentialists' say, and 'voluntarists' deny, that we only believe on the basis of evidence [Engel]
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 / D. Empiricism / 3. Pragmatism
Pragmatism is better understood as a theory of belief than as a theory of truth [Engel]
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]
13. Knowledge Criteria / C. External Justification / 5. Controlling Beliefs
We cannot directly control our beliefs, but we can control the causes of our involuntary beliefs [Engel]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher]
17. Mind and Body / C. Functionalism / 1. Functionalism
Mental states as functions are second-order properties, realised by first-order physical properties [Engel]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]