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All the ideas for 'Must We Believe in Set Theory?st1=George Boolos', 'An Introduction to Political Philosophy (Rev)' and 'Intro to Contemporary Epistemology'

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94 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
As coherence expands its interrelations become steadily tighter, culminating only in necessary truth [Dancy,J]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
The correspondence theory also has the problem that two sets of propositions might fit the facts equally well [Dancy,J]
3. Truth / D. Coherence Truth / 1. Coherence Truth
If one theory is held to be true, all the other theories appear false, because they can't be added to the true one [Dancy,J]
Rescher says that if coherence requires mutual entailment, this leads to massive logical redundancy [Dancy,J]
3. Truth / D. Coherence Truth / 2. Coherence Truth Critique
Even with a tight account of coherence, there is always the possibility of more than one set of coherent propositions [Dancy,J]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
The logic of ZF is classical first-order predicate logic with identity [Boolos]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
A few axioms of set theory 'force themselves on us', but most of them don't [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
Mathematics and science do not require very high orders of infinity [Boolos]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
7. Existence / D. Theories of Reality / 2. Realism
Realism says that most perceived objects exist, and have some of their perceived properties [Dancy,J]
8. Modes of Existence / D. Universals / 1. Universals
It is lunacy to think we only see ink-marks, and not word-types [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
I am a fan of abstract objects, and confident of their existence [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
A pupil who lacks confidence may clearly know something but not be certain of it [Dancy,J]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
If senses are fallible, then being open to correction is an epistemological virtue [Dancy,J]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / a. Naïve realism
Naïve direct realists hold that objects retain all of their properties when unperceived [Dancy,J]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
Scientific direct realism says we know some properties of objects directly [Dancy,J]
Maybe we are forced from direct into indirect realism by the need to explain perceptual error [Dancy,J]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / c. Representative realism
Indirect realism depends on introspection, the time-lag, illusions, and neuroscience [Dancy,J, by PG]
Internal realism holds that we perceive physical objects via mental objects [Dancy,J]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Phenomenalism includes possible experiences, but idealism only refers to actual experiences [Dancy,J]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
Eliminative idealists say there are no objects; reductive idealists say objects exist as complex experiences [Dancy,J]
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
Extreme solipsism only concerns current experience, but it might include past and future [Dancy,J]
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
Knowing that a cow is not a horse seems to be a synthetic a priori truth [Dancy,J]
12. Knowledge Sources / B. Perception / 1. Perception
Perception is either direct realism, indirect realism, or phenomenalism [Dancy,J]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
We can't grasp the separation of quality types, or what a primary-quality world would be like [Dancy,J]
For direct realists the secondary and primary qualities seem equally direct [Dancy,J]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
We can be looking at distant stars which no longer actually exist [Dancy,J]
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
It is not clear from the nature of sense data whether we should accept them as facts [Dancy,J]
12. Knowledge Sources / B. Perception / 7. Causal Perception
Appearances don't guarantee reality, unless the appearance is actually caused by the reality [Dancy,J]
Perceptual beliefs may be directly caused, but generalisations can't be [Dancy,J]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
If perception and memory are indirect, then two things stand between mind and reality [Dancy,J]
Memories aren't directly about the past, because time-lags and illusions suggest representation [Dancy,J]
Phenomenalism about memory denies the past, or reduces it to present experience [Dancy,J]
I can remember plans about the future, and images aren't essential (2+3=5) [Dancy,J]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
Foundations are justified by non-beliefs, or circularly, or they need no justification [Dancy,J]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
For internalists we must actually know that the fact caused the belief [Dancy,J]
Internalists tend to favour coherent justification, but not the coherence theory of truth [Dancy,J]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Foundationalism requires inferential and non-inferential justification [Dancy,J]
Foundationalists must accept not only the basic beliefs, but also rules of inference for further progress [Dancy,J]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
If basic beliefs can be false, falsehood in non-basic beliefs might by a symptom [Dancy,J]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
Beliefs can only be infallible by having almost no content [Dancy,J]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Coherentism gives a possible justification of induction, and opposes scepticism [Dancy,J]
Idealists must be coherentists, but coherentists needn't be idealists [Dancy,J]
For coherentists justification and truth are not radically different things [Dancy,J]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
If it is empirical propositions which have to be coherent, this eliminates coherent fiction [Dancy,J]
13. Knowledge Criteria / C. External Justification / 1. External Justification
Externalism could even make belief unnecessary (e.g. in animals) [Dancy,J]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
How can a causal theory of justification show that all men die? [Dancy,J]
Causal theories don't allow for errors in justification [Dancy,J]
13. Knowledge Criteria / C. External Justification / 8. Social Justification
Coherentism moves us towards a more social, shared view of knowledge [Dancy,J]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
What is the point of arguing against knowledge, if being right undermines your own argument? [Dancy,J]
14. Science / C. Induction / 6. Bayes's Theorem
Probabilities can only be assessed relative to some evidence [Dancy,J]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / d. Other minds by analogy
The argument from analogy rests on one instance alone [Dancy,J]
You can't separate mind and behaviour, as the analogy argument attempts [Dancy,J]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Verificationism (the 'verification principle') is an earlier form of anti-realism [Dancy,J]
Logical positivism implies foundationalism, by dividing weak from strong verifications [Dancy,J]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
If the meanings of sentences depend on other sentences, how did we learn language? [Dancy,J]
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
There is an indeterminacy in juggling apparent meanings against probable beliefs [Dancy,J]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
Charity makes native beliefs largely true, and Humanity makes them similar to ours [Dancy,J]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
Human beings can never really flourish in a long-term state of nature [Wolff,J]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Collective rationality is individuals doing their best, assuming others all do the same [Wolff,J]
Should love be the first virtue of a society, as it is of the family? [Wolff,J]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
For utilitarians, consent to the state is irrelevant, if it produces more happiness [Wolff,J]
Social contract theory has the attracton of including everyone, and being voluntary [Wolff,J]
Maybe voting in elections is a grant of legitimacy to the winners [Wolff,J]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
We can see the 'general will' as what is in the general interest [Wolff,J]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
How can dictators advance the interests of the people, if they don't consult them about interests? [Wolff,J]
24. Political Theory / C. Ruling a State / 3. Government / a. Government
'Separation of powers' allows legislative, executive and judicial functions to monitor one another [Wolff,J]
24. Political Theory / D. Ideologies / 1. Ideology
Political choice can be by utility, or maximin, or maximax [Wolff,J]
24. Political Theory / D. Ideologies / 2. Anarchism
A realistic and less utopian anarchism looks increasingly like liberal democracy [Wolff,J]
It is hard for anarchists to deny that we need experts [Wolff,J]
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
Utilitarianism probably implies a free market plus welfare [Wolff,J]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
A system of democracy which includes both freedom and equality is almost impossible [Wolff,J]
Democracy expresses equal respect (which explains why criminals forfeit the vote) [Wolff,J]
Democracy has been seen as consistent with many types of inequality [Wolff,J]
A true democracy could not tolerate slavery, exploitation or colonialism [Wolff,J]
24. Political Theory / D. Ideologies / 5. Democracy / b. Consultation
We should decide whether voting is for self-interests, or for the common good [Wolff,J]
Condorcet proved that sensible voting leads to an emphatically right answer [Wolff,J]
24. Political Theory / D. Ideologies / 5. Democracy / e. Democratic minorities
Occasional defeat is acceptable, but a minority that is continually defeated is a problem [Wolff,J]
25. Social Practice / A. Freedoms / 4. Free market
Market prices indicate shortages and gluts, and where the profits are to be made [Wolff,J]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Liberty principles can't justify laws against duelling, incest between siblings and euthanasia [Wolff,J]
Either Difference allows unequal liberty, or Liberty makes implementing Difference impossible [Wolff,J]
25. Social Practice / B. Equalities / 1. Grounds of equality
Utilitarians argue for equal distribution because of diminishing utility of repetition [Wolff,J]
Difference Principle: all inequalities should be in favour of the disadvantaged [Wolff,J]
25. Social Practice / B. Equalities / 2. Political equality
Political equality is not much use without social equality [Wolff,J]
25. Social Practice / C. Rights / 1. Basis of Rights
If natural rights are axiomatic, there is then no way we can defend them [Wolff,J]
Standard rights: life, free speech, assembly, movement, vote, stand (plus shelter, food, health?) [Wolff,J]
If rights are natural, rather than inferred, how do we know which rights we have? [Wolff,J]
25. Social Practice / C. Rights / 4. Property rights
Utilitarians might say property ownership encourages the best use of the land [Wolff,J]
25. Social Practice / D. Justice / 1. Basis of justice
Rights and justice are only the last resorts of a society, something to fall back on [Wolff,J]
25. Social Practice / D. Justice / 2. The Law / d. Legal positivism
Following some laws is not a moral matter; trivial traffic rules, for example [Wolff,J]