Combining Texts

All the ideas for 'Science of Logic', 'Set Theory and Its Philosophy' and 'Reality without Reference'

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46 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]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Usually the only reason given for accepting the empty set is convenience [Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: There is at least one limit level [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
Nowadays we derive our conception of collections from the dependence between them [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Mereology elides the distinction between the cards in a pack and the suits [Potter]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
We can formalize second-order formation rules, but not inference rules [Potter]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
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 / 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]
8. Modes of Existence / A. Relations / 2. Internal Relations
The nature of each category relates itself to another [Hegel]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
A relation is a set consisting entirely of ordered pairs [Potter]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
10. Modality / A. Necessity / 1. Types of Modality
Priority is a modality, arising from collections and members [Potter]
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 / 3. Idealism / d. Absolute idealism
The 'absolute idea' is when all the contradictions are exhausted [Hegel, by Bowie]
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]
Authentic thinking and reality have the same content [Hegel]
The Absolute is the primitive system of concepts which are actualised [Hegel, by Gardner]
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]
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]
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 / 1. Meaning
A minimum requirement for a theory of meaning is that it include an account of truth [Davidson]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
A theory of truth tells us how communication by language is possible [Davidson]
19. Language / B. Reference / 1. Reference theories
Is reference the key place where language and the world meet? [Davidson]
With a holistic approach, we can give up reference in empirical theories of language [Davidson]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
To explain the reference of a name, you must explain its sentence-role, so reference can't be defined nonlinguistically [Davidson]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
When we explicate the category of being, we watch a new category emerge [Hegel, by Houlgate]