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All the ideas for 'Thinking About Mathematics', 'Material Beings' and 'Intro to Contemporary Epistemology'

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110 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]
2. Reason / D. Definition / 12. Paraphrase
We could refer to tables as 'xs that are arranged tablewise' [Inwagen]
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
Rescher says that if coherence requires mutual entailment, this leads to massive logical redundancy [Dancy,J]
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]
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 / G. Formal Mereology / 1. Mereology
Mereology is 'nihilistic' (just atoms) or 'universal' (no restrictions on what is 'whole') [Inwagen, by Varzi]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
The 'Law' of Excluded Middle needs all propositions to be definitely true or definitely false [Inwagen]
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
Variables are just like pronouns; syntactic explanations get muddled over dummy letters [Inwagen]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
There are no heaps [Inwagen]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
I reject talk of 'stuff', and treat it in terms of particles [Inwagen]
7. Existence / D. Theories of Reality / 2. Realism
Realism says that most perceived objects exist, and have some of their perceived properties [Dancy,J]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
Singular terms can be vague, because they can contain predicates, which can be vague [Inwagen]
9. Objects / A. Existence of Objects / 1. Physical Objects
Material objects are in space and time, move, have a surface and mass, and are made of some stuff [Inwagen]
Maybe table-shaped particles exist, but not tables [Inwagen, by Lowe]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
Nihilism says composition between single things is impossible [Inwagen]
If there are no tables, but tables are things arranged tablewise, the denial of tables is a contradiction [Liggins on Inwagen]
Actions by artefacts and natural bodies are disguised cooperations, so we don't need them [Inwagen]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
Every physical thing is either a living organism or a simple [Inwagen]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
The statue and lump seem to share parts, but the statue is not part of the lump [Inwagen]
If you knead clay you make an infinite series of objects, but they are rearrangements, not creations [Inwagen]
9. Objects / C. Structure of Objects / 3. Matter of an Object
I assume matter is particulate, made up of 'simples' [Inwagen]
9. Objects / C. Structure of Objects / 5. Composition of an Object
If contact causes composition, do two colliding balls briefly make one object? [Inwagen]
If bricks compose a house, that is at least one thing, but it might be many things [Inwagen]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
I think parthood involves causation, and not just a reasonably stable spatial relationship [Inwagen]
We can deny whole objects but accept parts, by referring to them as plurals within things [Inwagen, by Liggins]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Special Composition Question: when is a thing part of something? [Inwagen]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
The essence of a star includes the released binding energy which keeps it from collapse [Inwagen]
9. Objects / D. Essence of Objects / 11. Essence of Artefacts
The persistence of artifacts always covertly involves intelligent beings [Inwagen]
9. Objects / E. Objects over Time / 7. Intermittent Objects
When an electron 'leaps' to another orbit, is the new one the same electron? [Inwagen]
9. Objects / E. Objects over Time / 9. Ship of Theseus
If you reject transitivity of vague identity, there is no Ship of Theseus problem [Inwagen]
9. Objects / F. Identity among Objects / 1. Concept of Identity
We should talk of the transitivity of 'identity', and of 'definite identity' [Inwagen]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
Actuality proves possibility, but that doesn't explain how it is possible [Inwagen]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Counterparts reduce counterfactual identity to problems about similarity relations [Inwagen]
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
A merely possible object clearly isn't there, so that is a defective notion [Inwagen]
Merely possible objects must be consistent properties, or haecceities [Inwagen]
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
Internal realism holds that we perceive physical objects via mental objects [Dancy,J]
Indirect realism depends on introspection, the time-lag, illusions, and neuroscience [Dancy,J, by PG]
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 / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
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]
27. Natural Reality / B. Modern Physics / 3. Chromodynamics / a. Chromodynamics
The strong force pulls, but also pushes apart if nucleons get too close together [Inwagen]
27. Natural Reality / F. Chemistry / 2. Modern Elements
Is one atom a piece of gold, or is a sizable group of atoms required? [Inwagen]
27. Natural Reality / G. Biology / 2. Life
At the lower level, life trails off into mere molecular interaction [Inwagen]
A tumour may spread a sort of life, but it is not a life, or an organism [Inwagen]
Being part of an organism's life is a matter of degree, and vague [Inwagen]
Some events are only borderline cases of lives [Inwagen]
Unlike waves, lives are 'jealous'; it is almost impossible for them to overlap [Inwagen]
One's mental and other life is centred on the brain, unlike any other part of the body [Inwagen]
The chemical reactions in a human life involve about sixteen elements [Inwagen]
Life is vague at both ends, but could it be totally vague? [Inwagen]
A flame is like a life, but not nearly so well individuated [Inwagen]
If God were to 'reassemble' my atoms of ten years ago, the result would certainly not be me [Inwagen]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
There is no reason to think that mere existence is a valuable thing [Inwagen]