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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Essays on Intellectual Powers 6: Judgement' and 'The Mind in Nature'

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57 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Ontology is highly abstract physics, containing placeholders and exclusions [Martin,CB]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
The existence of tensed verbs shows that not all truths are necessary truths [Reid]
2. Reason / F. Fallacies / 7. Ad Hominem
An ad hominem argument is good, if it is shown that the man's principles are inconsistent [Reid]
3. Truth / A. Truth Problems / 1. Truth
Truth is a relation between a representation ('bearer') and part of the world ('truthmaker') [Martin,CB]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
8. Modes of Existence / B. Properties / 9. Qualities
A property is a combination of a disposition and a quality [Martin,CB]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Properties are the respects in which objects resemble, which places them in classes [Martin,CB]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
Properties are ways particular things are, and so they are tied to the identity of their possessor [Martin,CB]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
Objects are not bundles of tropes (which are ways things are, not parts of things) [Martin,CB]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
A property that cannot interact is worse than inert - it isn't there at all [Martin,CB]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
If unmanifested partnerless dispositions are still real, and are not just qualities, they can explain properties [Martin,CB]
8. Modes of Existence / C. Powers and Dispositions / 5. Powers and Properties
Properties endow a ball with qualities, and with powers or dispositions [Martin,CB]
Qualities and dispositions are aspects of properties - what it exhibits, and what it does [Martin,CB]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
Dispositions in action can be destroyed, be recovered, or remain unchanged [Martin,CB]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / c. Dispositions as conditional
Powers depend on circumstances, so can't be given a conditional analysis [Martin,CB]
'The wire is live' can't be analysed as a conditional, because a wire can change its powers [Martin,CB]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
9. Objects / C. Structure of Objects / 1. Structure of an Object
Structural properties involve dispositionality, so cannot be used to explain it [Martin,CB]
Structures don't explain dispositions, because they consist of dispositions [Martin,CB]
9. Objects / C. Structure of Objects / 7. Substratum
I favour the idea of a substratum for properties; spacetime seems to be just a bearer of properties [Martin,CB]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Properly understood, wholes do no more causal work than their parts [Martin,CB]
9. Objects / F. Identity among Objects / 1. Concept of Identity
Only abstract things can have specific and full identity specifications [Martin,CB]
The concept of 'identity' must allow for some changes in properties or parts [Martin,CB]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
It is pointless to say possible worlds are truthmakers, and then deny that possible worlds exist [Martin,CB]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
If someone denies that he is thinking when he is conscious of it, we can only laugh [Reid]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
The existence of ideas is no more obvious than the existence of external objects [Reid]
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
We are only aware of other beings through our senses; without that, we are alone in the universe [Reid]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
In obscure matters the few must lead the many, but the many usually lead in common sense [Reid]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
The theory of ideas, popular with philosophers, means past existence has to be proved [Reid]
14. Science / D. Explanation / 4. Explanation Doubts / a. Explanation as pragmatic
Explanations are mind-dependent, theory-laden, and interest-relative [Martin,CB]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / d. Other minds by analogy
Analogy works, as when we eat food which others seem to be relishing [Martin,CB]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
Consciousness is an indefinable and unique operation [Reid]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Memory requires abstraction, as reminders of what cannot be fully remembered [Martin,CB]
18. Thought / A. Modes of Thought / 8. Human Thought
The structure of languages reveals a uniformity in basic human opinions [Reid]
18. Thought / E. Abstraction / 2. Abstracta by Selection
If you can't distinguish the features of a complex object, your notion of it would be a muddle [Reid]
21. Aesthetics / A. Aesthetic Experience / 3. Taste
There are axioms of taste - such as a general consensus about a beautiful face [Reid]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Instead of a cause followed by an effect, we have dispositions in reciprocal manifestation [Martin,CB]
Causation should be explained in terms of dispositions and manifestations [Martin,CB]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
Causal counterfactuals are just clumsy linguistic attempts to indicate dispositions [Martin,CB]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
Causal laws are summaries of powers [Martin,CB]
27. Natural Reality / C. Space / 6. Space-Time
We can't think of space-time as empty and propertyless, and it seems to be a substratum [Martin,CB]