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All the ideas for 'Thinking About Mathematics', 'The Principles of Human Knowledge' and 'Science of Logic'

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75 ideas

1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
If we start with indeterminate being, we arrive at being and nothing as a united pair [Hegel, by Houlgate]
Thought about being leads to a string of other concepts, like becoming, quantity, specificity, causality... [Hegel, by Houlgate]
We must start with absolute abstraction, with no presuppositions, so we start with pure being [Hegel]
2. Reason / A. Nature of Reason / 5. Objectivity
Objectivity is not by correspondence, but by the historical determined necessity of Geist [Hegel, by Pinkard]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Being and nothing are the same and not the same, which is the identity of identity and non-identity [Hegel]
The so-called world is filled with contradiction [Hegel]
2. Reason / C. Styles of Reason / 1. Dialectic
Dialectic is the instability of thoughts generating their opposite, and then new more complex thoughts [Hegel, by Houlgate]
Hegel's dialectic is not thesis-antithesis-synthesis, but usually negation of negation of the negation [Hegel, by Moore,AW]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
An idea can only be like another idea [Berkeley]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
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 / A. Nature of Existence / 3. Being / d. Non-being
To grasp an existence, we must consider its non-existence [Hegel, by Houlgate]
Nothing exists, as thinkable and expressible [Hegel]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
Thinking of nothing is not the same as simply not thinking [Hegel, by Houlgate]
7. Existence / A. Nature of Existence / 4. Abstract Existence
Abstract ideas are impossible [Berkeley]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
The ground of a thing is not another thing, but the first thing's substance or rational concept [Hegel, by Houlgate]
7. Existence / D. Theories of Reality / 2. Realism
Kant's thing-in-itself is just an abstraction from our knowledge; things only exist for us [Hegel, by Bowie]
Hegel believe that the genuine categories reveal things in themselves [Hegel, by Houlgate]
7. Existence / D. Theories of Reality / 4. Anti-realism
Berkeley does believe in trees, but is confused about what trees are [Berkeley, by Cameron]
8. Modes of Existence / A. Relations / 2. Internal Relations
The nature of each category relates itself to another [Hegel]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
Universals do not have single meaning, but attach to many different particulars [Berkeley]
No one will think of abstractions if they only have particular ideas [Berkeley]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
Universals do not have any intrinsic properties, but only relations to particulars [Berkeley]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Material substance is just general existence which can have properties [Berkeley]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
A die has no distinct subject, but is merely a name for its modes or accidents [Berkeley]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
In absolute knowing, the gap between object and oneself closes, producing certainty [Hegel]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Perception is existence for my table, but also possible perception, by me or a spirit [Berkeley]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / c. Empirical idealism
The only substance is spirit, or that which perceives [Berkeley]
The 'esse' of objects is 'percipi', and they can only exist in minds [Berkeley]
When I shut my eyes, the things I saw may still exist, but in another mind [Berkeley]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
Hegel, unlike Kant, said how things appear is the same as how things are [Hegel, by Moore,AW]
Hegel's non-subjective idealism is the unity of subjective and objective viewpoints [Hegel, by Pinkard]
Hegel claimed his system was about the world, but it only mapped conceptual interdependence [Pinkard on Hegel]
The Absolute is the primitive system of concepts which are actualised [Hegel, by Gardner]
Authentic thinking and reality have the same content [Hegel]
The absolute idea is being, imperishable life, self-knowing truth, and all truth [Hegel]
The absolute idea is the great unity of the infinite system of concepts [Hegel, by Moore,AW]
The 'absolute idea' is when all the contradictions are exhausted [Hegel, by Bowie]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
No one can, by abstraction, conceive extension and motion of bodies without sensible qualities [Berkeley]
Motion is in the mind, since swifter ideas produce an appearance of slower motion [Berkeley]
Figure and extension seem just as dependent on the observer as heat and cold [Berkeley]
12. Knowledge Sources / B. Perception / 3. Representation
Berkeley's idealism resulted from fear of scepticism in representative realism [Robinson,H on Berkeley]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Knowledge is of ideas from senses, or ideas of the mind, or operations on sensations [Berkeley]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Hegel's 'absolute idea' is the interdependence of all truths to justify any of them [Hegel, by Bowie]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / a. Other minds
Berkeley's idealism gives no grounds for believing in other minds [Reid on Berkeley]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
I know other minds by ideas which are referred by me to other agents, as their effects [Berkeley]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
If animals have ideas, and are not machines, they must have some reason [Berkeley]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
Berkeley replaced intentionality with an anti-abstractionist imagist theory of thought [Berkeley, by Robinson,H]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
The mind creates abstract ideas by considering qualities separated from their objects [Berkeley]
I can only combine particulars in imagination; I can't create 'abstract' ideas [Berkeley]
16. Persons / D. Continuity of the Self / 7. Self and Thinking
Ideas are perceived by the mind, soul or self [Berkeley]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Every concept depends on the counter-concepts of what it is not [Hegel, by Bowie]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
Language is presumably for communication, and names stand for ideas [Berkeley]
19. Language / D. Propositions / 4. Mental Propositions
I can't really go wrong if I stick to wordless thought [Berkeley]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
When we explicate the category of being, we watch a new category emerge [Hegel, by Houlgate]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / a. Early Modern matter
No one can explain how matter affects mind, so matter is redundant in philosophy [Berkeley]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
We discover natural behaviour by observing settled laws of nature, not necessary connections [Berkeley]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
The laws of nature are mental regularities which we learn by experience [Berkeley]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
If properties and qualities arise from an inward essence, we will remain ignorant of nature [Berkeley]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
All motion is relative, so a single body cannot move [Berkeley]
27. Natural Reality / D. Time / 1. Nature of Time / c. Idealist time
I cannot imagine time apart from the flow of ideas in my mind [Berkeley]
29. Religion / D. Religious Issues / 3. Problem of Evil / a. Problem of Evil
Particular evils are really good when linked to the whole system of beings [Berkeley]