Combining Texts

All the ideas for 'Mr Strawson on Logical Theory', 'True in Theory, but not in Practice' and 'The Nature of Mathematical Knowledge'

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56 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Philosophy is largely concerned with finding the minimum that science could get by with [Quine]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
Logicians don't paraphrase logic into language, because they think in the symbolic language [Quine]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
Good algorithms and theories need many occurrences of just a few elements [Quine]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL
The logician's '→' does not mean the English if-then [Quine]
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
It is important that the quantification over temporal entities is timeless [Quine]
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 / C. Ontology of Logic / 1. Ontology of Logic
Logical languages are rooted in ordinary language, and that connection must be kept [Quine]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Reduction to logical forms first simplifies idioms and grammar, then finds a single reading of it [Quine]
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 made true by the world, but is also made true by our constructions [Kitcher]
Arithmetic is an idealizing theory [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]
10. Modality / B. Possibility / 8. Conditionals / e. Supposition conditionals
Normally conditionals have no truth value; it is the consequent which has a conditional truth value [Quine]
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 / C. Capacities of Minds / 6. Idealisation
Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
If we understand a statement, we know the circumstances of its truth [Quine]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
General rules of action also need a judgement about when to apply them [Kant]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
Duty does not aim at an end, but gives rise to universal happiness as aim of the will [Kant]
23. Ethics / D. Deontological Ethics / 2. Duty
It can't be a duty to strive after the impossible [Kant]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
The will's motive is the absolute law itself, and moral feeling is receptivity to law [Kant]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
There can be no restraints on freedom if reason does not reveal some basic rights [Kant]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Personal contracts are for some end, but a civil state contract involves a duty to share [Kant]
There must be a unanimous contract that citizens accept majority decisions [Kant]
A contract is theoretical, but it can guide rulers to make laws which the whole people will accept [Kant]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
A law is unjust if the whole people could not possibly agree to it [Kant]
24. Political Theory / B. Nature of a State / 4. Citizenship
A citizen must control his own life, and possess property or an important skill [Kant]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
A lawful civil state must embody freedom, equality and independence for its members [Kant]
25. Social Practice / B. Equalities / 4. Economic equality
Citizens can rise to any rank that talent, effort and luck can achieve [Kant]
25. Social Practice / C. Rights / 3. Alienating rights
You can't make a contract renouncing your right to make contracts! [Kant]
25. Social Practice / E. Policies / 1. War / a. Just wars
The people (who have to fight) and not the head of state should declare a war [Kant]
27. Natural Reality / D. Time / 2. Passage of Time / f. Tenseless (B) series
Quine holds time to be 'space-like': past objects are as real as spatially remote ones [Quine, by Sider]