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All the ideas for 'Logic (Encyclopedia I)', 'Frege philosophy of mathematics' and 'A Survey of Metaphysics'

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118 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
True philosophy aims at absolute unity, while our understanding sees only separation [Hegel]
1. Philosophy / D. Nature of Philosophy / 6. Hopes for Philosophy
Free thinking has no presuppositions [Hegel]
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
The ideal of reason is the unification of abstract identity (or 'concept') and being [Hegel]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
Older metaphysics naively assumed that thought grasped things in themselves [Hegel]
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Metaphysics is concerned with the fundamental structure of reality as a whole [Lowe]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
Logic is metaphysics, the science of things grasped in thoughts [Hegel]
Maybe such concepts as causation, identity and existence are primitive and irreducible [Lowe]
1. Philosophy / G. Scientific Philosophy / 2. Positivism
If all that exists is what is being measured, what about the people and instruments doing the measuring? [Lowe]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
We must break up the rigidity that our understanding has imposed [Hegel]
2. Reason / A. Nature of Reason / 3. Pure Reason
Let thought follow its own course, and don't interfere [Hegel]
2. Reason / A. Nature of Reason / 5. Objectivity
Categories create objective experience, but are too conditioned by things to actually grasp them [Hegel]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
If truth is just non-contradiction, we must take care that our basic concepts aren't contradictory [Hegel]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
It is more extravagant, in general, to revise one's logic than to augment one's ontology [Lowe]
2. Reason / C. Styles of Reason / 1. Dialectic
Dialectic is seen in popular proverbs like 'pride comes before a fall' [Hegel]
Dialectic is the moving soul of scientific progression, the principle which binds science together [Hegel]
Socratic dialectic is subjective, but Plato made it freely scientific and objective [Hegel]
Older metaphysics became dogmatic, by assuming opposed assertions must be true and false [Hegel]
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
3. Truth / A. Truth Problems / 2. Defining Truth
Superficial truth is knowing how something is, which is consciousness of bare correctness [Hegel]
3. Truth / A. Truth Problems / 5. Truth Bearers
In Hegel's logic it is concepts (rather than judgements or propositions) which are true or false [Hegel, by Scruton]
3. Truth / A. Truth Problems / 7. Falsehood
In the deeper sense of truth, to be untrue resembles being bad; badness is untrue to a thing's nature [Hegel]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
The deeper sense of truth is a thing matching the idea of what it ought to be [Hegel]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Excluded middle is the maxim of definite understanding, but just produces contradictions [Hegel]
5. Theory of Logic / L. Paradox / 3. Antinomies
The idea that contradiction is essential to rational understanding is a key modern idea [Hegel]
Tenderness for the world solves the antinomies; contradiction is in our reason, not in the essence of the world [Hegel]
Antinomies are not just in four objects, but in all objects, all representations, all objects and all ideas [Hegel]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
An infinite series of tasks can't be completed because it has no last member [Lowe]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
It might be argued that mathematics does not, or should not, aim at truth [Lowe]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
A prime number is one which is measured by a unit alone [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A number is a multitude composed of units [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The identity of a number may be fixed by something outside structure - by counting [Dummett]
Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
7. Existence / A. Nature of Existence / 4. Abstract Existence
Nominalists deny abstract objects, because we can have no reason to believe in their existence [Lowe]
7. Existence / B. Change in Existence / 1. Nature of Change
Change can be of composition (the component parts), or quality (properties), or substance [Lowe]
Four theories of qualitative change are 'a is F now', or 'a is F-at-t', or 'a-at-t is F', or 'a is-at-t F' [Lowe, by PG]
7. Existence / B. Change in Existence / 4. Events / a. Nature of events
Numerically distinct events of the same kind (like two battles) can coincide in space and time [Lowe]
7. Existence / B. Change in Existence / 4. Events / b. Events as primitive
Maybe modern physics requires an event-ontology, rather than a thing-ontology [Lowe]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
Maybe an event is the exemplification of a property at a time [Lowe]
Events are changes in the properties of or relations between things [Lowe]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett]
7. Existence / D. Theories of Reality / 2. Realism
Realism is just the application of two-valued semantics to sentences [Dummett]
7. Existence / E. Categories / 1. Categories
Thought about particulars is done entirely through categories [Hegel]
Even simple propositions about sensations are filled with categories [Hegel]
7. Existence / E. Categories / 3. Proposed Categories
The main categories of existence are either universal and particular, or abstract and concrete [Lowe]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
Trope theory says blueness is a real feature of objects, but not the same as an identical blue found elsewhere [Lowe]
Maybe a cushion is just a bundle of tropes, such as roundness, blueness and softness [Lowe]
Tropes seem to be abstract entities, because they can't exist alone, but must come in bundles [Lowe]
8. Modes of Existence / D. Universals / 1. Universals
The category of universals can be sub-divided into properties and relations [Lowe]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism assumes unmediated mental contact with objects [Dummett]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
Nominalists believe that only particulars exist [Lowe]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
'Is non-self-exemplifying' is a predicate which cannot denote a property (as it would be a contradiction) [Lowe]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
If 'blueness' is a set of particulars, there is danger of circularity, or using universals, in identifying the set [Lowe]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
The existence of abstract objects is a pseudo-problem [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Abstract objects nowadays are those which are objective but not actual [Dummett]
It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
Abstract objects need the context principle, since they can't be encountered directly [Dummett]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
Conventionalists see the world as an amorphous lump without identities, but are we part of the lump? [Lowe]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
The one substance is formless without the mediation of dialectical concepts [Hegel]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Statues can't survive much change to their shape, unlike lumps of bronze, which must retain material [Lowe]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
Essence is the essential self-positing unity of immediacy and mediation [Hegel]
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
Real cognition grasps a thing from within itself, and is not satisfied with mere predicates [Hegel]
9. Objects / E. Objects over Time / 9. Ship of Theseus
If old parts are stored and then appropriated, they are no longer part of the original (which is the renovated ship). [Lowe]
If 5% replacement preserves a ship, we can replace 4% and 4% again, and still retain the ship [Lowe]
A renovation or a reconstruction of an original ship would be accepted, as long as the other one didn't exist [Lowe]
9. Objects / F. Identity among Objects / 2. Defining Identity
Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett]
Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
Identity of Indiscernibles (same properties, same thing) ) is not Leibniz's Law (same thing, same properties) [Lowe]
10. Modality / B. Possibility / 1. Possibility
It is impossible to reach a valid false conclusion from true premises, so reason itself depends on possibility [Lowe]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
We might eliminate 'possible' and 'necessary' in favour of quantification over possible worlds [Lowe]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
The Cogito is at the very centre of the entire concern of modern philosophy [Hegel]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
Existence is just a set of relationships [Hegel]
12. Knowledge Sources / B. Perception / 1. Perception
The sensible is distinguished from thought by being about singular things [Hegel]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Sense perception is secondary and dependent, while thought is independent and primitive [Hegel]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Empiricism made particular knowledge possible, and blocked wild claims [Hegel]
Empiricism contains the important idea that we should see knowledge for ourselves, and be part of it [Hegel]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Empiricism unknowingly contains and uses a metaphysic, which underlies its categories [Hegel]
Empiricism of the finite denies the supersensible, and can only think with formal abstraction [Hegel]
The Humean view stops us thinking about perception, and finding universals and necessities in it [Hegel]
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
Humean scepticism, unlike ancient Greek scepticism, accepts the truth of experience as basic [Hegel]
14. Science / A. Basis of Science / 6. Falsification
Unfalsifiability may be a failure in an empirical theory, but it is a virtue in metaphysics [Lowe]
14. Science / D. Explanation / 1. Explanation / d. Explaining people
The behaviour of persons and social groups seems to need rational rather than causal explanation [Lowe]
16. Persons / F. Free Will / 7. Compatibilism
In abstraction, beyond finitude, freedom and necessity must exist together [Hegel]
18. Thought / A. Modes of Thought / 1. Thought
The act of thinking is the bringing forth of universals [Hegel]
18. Thought / B. Mechanics of Thought / 2. Categories of Understanding
Hegel's system has a vast number of basic concepts [Hegel, by Moore,AW]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
We don't think with concepts - we think the concepts [Hegel]
Active thought about objects produces the universal, which is what is true and essential of it [Hegel]
18. Thought / D. Concepts / 4. Structure of Concepts / i. Conceptual priority
Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett]
An argument for conceptual priority is greater simplicity in explanation [Dummett]
18. Thought / E. Abstraction / 1. Abstract Thought
Abstract terms are acceptable as long as we know how they function linguistically [Dummett]
18. Thought / E. Abstraction / 5. Abstracta by Negation
The centre of mass of the solar system is a non-causal abstract object, despite having a location [Lowe]
Concrete and abstract objects are distinct because the former have causal powers and relations [Lowe]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait]
We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett]
18. Thought / E. Abstraction / 8. Abstractionism Critique
To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
26. Natural Theory / C. Causation / 1. Causation
Old metaphysics tried to grasp eternal truths through causal events, which is impossible [Hegel]
26. Natural Theory / C. Causation / 5. Direction of causation
If the concept of a cause says it precedes its effect, that rules out backward causation by definition [Lowe]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
It seems proper to say that only substances (rather than events) have causal powers [Lowe]
The theories of fact causation and event causation are both worth serious consideration [Lowe]
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
Causal overdetermination is either actual overdetermination, or pre-emption, or the fail-safe case [Lowe]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
Causation may be instances of laws (seen either as constant conjunctions, or as necessities) [Lowe]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
Hume showed that causation could at most be natural necessity, never metaphysical necessity [Lowe]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
The normative view says laws show the natural behaviour of natural kind members [Lowe, by Mumford/Anjum]
26. Natural Theory / D. Laws of Nature / 9. Counterfactual Claims
'If he wasn't born he wouldn't have died' doesn't mean birth causes death, so causation isn't counterfactual [Lowe]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
If motion is change of distance between objects, it involves no intrinsic change in the objects [Lowe]
27. Natural Reality / C. Space / 3. Points in Space
Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract [Lowe]
Why should the limit of measurement be points, not intervals? [Dummett]
27. Natural Reality / C. Space / 5. Relational Space
If space is entirely relational, what makes a boundary, or a place unoccupied by physical objects? [Lowe]
28. God / A. Divine Nature / 2. Divine Nature
The older conception of God was emptied of human features, to make it worthy of the Infinite [Hegel]
God is the absolute thing, and also the absolute person [Hegel]
If God is the abstract of Supremely Real Essence, then God is a mere Beyond, and unknowable [Hegel]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
We establish unification of the Ideal by the ontological proof, deriving being from abstraction of thinking [Hegel]