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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Virtues of the Mind' and 'Logic (Encyclopedia I)'

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98 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Unlike knowledge, wisdom cannot be misused [Zagzebski]
1. Philosophy / A. Wisdom / 2. Wise People
Wisdom is the property of a person, not of their cognitive state [Zagzebski, by Whitcomb]
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 / 6. Metaphysics as Conceptual
Logic is metaphysics, the science of things grasped in thoughts [Hegel]
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 / C. Styles of Reason / 1. Dialectic
Dialectic is the moving soul of scientific progression, the principle which binds science together [Hegel]
Dialectic is seen in popular proverbs like 'pride comes before a fall' [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 / 2. Aims of Definition
Precision is only one of the virtues of a good definition [Zagzebski]
2. Reason / E. Argument / 1. Argument
Objection by counterexample is weak, because it only reveals inaccuracies in one theory [Zagzebski]
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]
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 / D. Assumptions for Logic / 2. Excluded Middle
Excluded middle is the maxim of definite understanding, but just produces contradictions [Hegel]
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]
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]
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]
7. Existence / E. Categories / 1. Categories
Even simple propositions about sensations are filled with categories [Hegel]
Thought about particulars is done entirely through categories [Hegel]
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 / B. Unity of Objects / 2. Substance / a. Substance
The one substance is formless without the mediation of dialectical concepts [Hegel]
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]
11. Knowledge Aims / A. Knowledge / 2. Understanding
Modern epistemology is too atomistic, and neglects understanding [Zagzebski]
Epistemology is excessively atomic, by focusing on justification instead of understanding [Zagzebski]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
Truth is valuable, but someone knowing the truth is more valuable [Zagzebski]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
Some beliefs are fairly voluntary, and others are not at all so [Zagzebski]
11. Knowledge Aims / A. Knowledge / 5. Aiming at Truth
Knowledge either aims at a quantity of truths, or a quality of understanding of truths [Zagzebski]
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 / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
For internalists Gettier situations are where internally it is fine, but there is an external mishap [Zagzebski]
Gettier problems are always possible if justification and truth are not closely linked [Zagzebski]
We avoid the Gettier problem if the support for the belief entails its truth [Zagzebski]
Gettier cases arise when good luck cancels out bad luck [Zagzebski]
13. Knowledge Criteria / B. Internal Justification / 1. Epistemic virtues
Intellectual virtues are forms of moral virtue [Zagzebski]
Intellectual and moral prejudice are the same vice (and there are other examples) [Zagzebski]
We can name at least thirteen intellectual vices [Zagzebski]
A reliable process is no use without the virtues to make use of them [Zagzebski]
A justified belief emulates the understanding and beliefs of an intellectually virtuous person [Zagzebski]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
Epistemic perfection for reliabilism is a truth-producing machine [Zagzebski]
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
Humean scepticism, unlike ancient Greek scepticism, accepts the truth of experience as basic [Hegel]
16. Persons / C. Self-Awareness / 2. Knowing the Self
The self is known as much by its knowledge as by its action [Zagzebski]
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 / A. Modes of Thought / 3. Emotions / d. Emotional feeling
The feeling accompanying curiosity is neither pleasant nor painful [Zagzebski]
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]
20. Action / C. Motives for Action / 1. Acting on Desires
Motives involve desires, but also how the desires connect to our aims [Zagzebski]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
Modern moral theory concerns settling conflicts, rather than human fulfilment [Zagzebski]
22. Metaethics / C. The Good / 1. Goodness / i. Moral luck
Moral luck means our praise and blame may exceed our control or awareness [Zagzebski]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
Nowadays we doubt the Greek view that the flourishing of individuals and communities are linked [Zagzebski]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
Every moral virtue requires a degree of intelligence [Zagzebski]
Virtue theory is hopeless if there is no core of agreed universal virtues [Zagzebski]
A virtue must always have a corresponding vice [Zagzebski]
Eight marks distingush skills from virtues [Zagzebski, by PG]
Virtues are deep acquired excellences of persons, which successfully attain desire ends [Zagzebski]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
Virtue theory can have lots of rules, as long as they are grounded in virtues and in facts [Zagzebski]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
We need phronesis to coordinate our virtues [Zagzebski]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
For the virtue of honesty you must be careful with the truth, and not just speak truly [Zagzebski]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
The courage of an evil person is still a quality worth having [Zagzebski]
26. Natural Theory / C. Causation / 1. Causation
Old metaphysics tried to grasp eternal truths through causal events, which is impossible [Hegel]
28. God / A. Divine Nature / 2. Divine Nature
If God is the abstract of Supremely Real Essence, then God is a mere Beyond, and unknowable [Hegel]
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]
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]