Combining Texts

All the ideas for 'The Case for Closure', 'Begriffsschrift' and 'Posterior Analytics'

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96 ideas

1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
Frege changed philosophy by extending logic's ability to check the grounds of thinking [Potter on Frege]
2. Reason / A. Nature of Reason / 1. On Reason
There is pure deductive reasoning, and explanatory demonstration reasoning [Aristotle, by Politis]
2. Reason / A. Nature of Reason / 6. Coherence
Maybe everything could be demonstrated, if demonstration can be reciprocal or circular [Aristotle]
2. Reason / B. Laws of Thought / 1. Laws of Thought
We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher]
2. Reason / B. Laws of Thought / 4. Contraries
Two falsehoods can be contrary to one another [Aristotle]
2. Reason / D. Definition / 4. Real Definition
Definitions are of what something is, and that is universal [Aristotle]
Definition by division needs predicates, which are well ordered and thorough [Aristotle]
An Aristotelian definition is causal [Aristotle, by Witt]
You can define objects by progressively identifying what is the same and what is different [Aristotle]
2. Reason / D. Definition / 6. Definition by Essence
What it is and why it is are the same; screening defines and explains an eclipse [Aristotle]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
An axiom is a principle which must be understood if one is to learn anything [Aristotle]
4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC
I don't use 'subject' and 'predicate' in my way of representing a judgement [Frege]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀
For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner]
The laws of logic are boundless, so we want the few whose power contains the others [Frege]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
In 1879 Frege developed second order logic [Frege, by Putnam]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Demonstrations by reductio assume excluded middle [Aristotle]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Something holds universally when it is proved of an arbitrary and primitive case [Aristotle]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Everything is either asserted or denied truly [Aristotle]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Frege replaced Aristotle's subject/predicate form with function/argument form [Frege, by Weiner]
5. Theory of Logic / G. Quantification / 1. Quantification
A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
For Frege the variable ranges over all objects [Frege, by Tait]
Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
Frege introduced quantifiers for generality [Frege, by Weiner]
Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh]
5. Theory of Logic / H. Proof Systems / 1. Proof Systems
Proof theory began with Frege's definition of derivability [Frege, by Prawitz]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Aristotle's axioms (unlike Euclid's) are assumptions awaiting proof [Aristotle, by Leibniz]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematics is concerned with forms, not with superficial properties [Aristotle]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
The essence of a triangle comes from the line, mentioned in any account of triangles [Aristotle]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A unit is what is quantitatively indivisible [Aristotle]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P]
7. Existence / A. Nature of Existence / 1. Nature of Existence
Existence is not a first-order property, but the instantiation of a property [Frege, by Read]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
To seek truth, study the real connections between subjects and attributes [Aristotle]
8. Modes of Existence / D. Universals / 2. Need for Universals
Separate Forms aren't needed for logic, but universals (one holding of many) are essential [Aristotle]
8. Modes of Existence / D. Universals / 6. Platonic Forms / d. Forms critiques
We can forget the Forms, as they are irrelevant, and not needed in giving demonstrations [Aristotle]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
Why are being terrestrial and a biped combined in the definition of man, but being literate and musical aren't? [Aristotle]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
Units are positionless substances, and points are substances with position [Aristotle]
9. Objects / D. Essence of Objects / 4. Essence as Definition
Definitions recognise essences, so are not themselves essences [Aristotle]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
The predicates of a thing's nature are necessary to it [Aristotle]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
Aristotelian essences are properties mentioned at the starting point of a science [Aristotle, by Kung]
10. Modality / A. Necessity / 2. Nature of Necessity
What is necessary cannot be otherwise [Aristotle]
10. Modality / A. Necessity / 3. Types of Necessity
A stone travels upwards by a forced necessity, and downwards by natural necessity [Aristotle]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
For Aristotle knowledge is explanatory, involving understanding, and principles or causes [Aristotle, by Witt]
'Episteme' means grasping causes, universal judgments, explanation, and teaching [Aristotle, by Witt]
The reason why is the key to knowledge [Aristotle]
11. Knowledge Aims / A. Knowledge / 2. Understanding
We understand a thing when we know its explanation and its necessity [Aristotle]
Some understanding, of immediate items, is indemonstrable [Aristotle]
We only understand something when we know its explanation [Aristotle]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
No one has mere belief about something if they think it HAS to be true [Aristotle]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
Knowledge proceeds from principles, so it is hard to know if we know [Aristotle]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne]
12. Knowledge Sources / B. Perception / 1. Perception
You cannot understand anything through perception [Aristotle]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
Some knowledge is lost if you lose a sense, and there is no way the knowledge can be replaced [Aristotle]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Animals may have some knowledge if they retain perception, but understanding requires reasons to be given [Aristotle]
Aristotle's concepts of understanding and explanation mean he is not a pure empiricist [Aristotle, by Frede,M]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
Many memories of the same item form a single experience [Aristotle]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
Sceptics say justification is an infinite regress, or it stops at the unknowable [Aristotle]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne]
We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne]
Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
When you understand basics, you can't be persuaded to change your mind [Aristotle]
14. Science / A. Basis of Science / 2. Demonstration
The principles of demonstrations are definitions [Aristotle]
There must be definitions before demonstration is possible [Aristotle]
Demonstration is more than entailment, as the explanatory order must match the causal order [Aristotle, by Koslicki]
Aristotle gets asymmetric consequence from demonstration, which reflects real causal priority [Aristotle, by Koslicki]
Aristotle doesn't actually apply his theory of demonstration to his practical science [Leroi on Aristotle]
We can know by demonstration, which is a scientific deduction leading to understanding [Aristotle]
Premises must be true, primitive and immediate, and prior to and explanatory of conclusions [Aristotle]
Demonstrative understanding rests on necessary features of the thing in itself [Aristotle]
Demonstrations must be necessary, and that depends on the middle term [Aristotle]
Demonstrations are syllogisms which give explanations [Aristotle]
Demonstration is better with fewer presuppositions, and it is quicker if these are familiar [Aristotle]
All demonstration is concerned with existence, axioms and properties [Aristotle]
Universal demonstrations are about thought; particular demonstrations lead to perceptions [Aristotle]
Aim to get definitions of the primitive components, thus establishing the kind, and work towards the attributes [Aristotle]
A demonstration is a deduction which proceeds from necessities [Aristotle]
14. Science / C. Induction / 2. Aims of Induction
We learn universals from many particulars [Aristotle]
14. Science / D. Explanation / 1. Explanation / a. Explanation
Universals are valuable because they make the explanations plain [Aristotle]
What is most universal is furthest away, and the particulars are nearest [Aristotle]
Are particulars explained more by universals, or by other particulars? [Aristotle]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
Explanation is of the status of a thing, inferences to it, initiation of change, and purpose [Aristotle]
What we seek and understand are facts, reasons, existence, and identity [Aristotle]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Explanation and generality are inseparable [Aristotle, by Wedin]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
The foundation or source is stronger than the thing it causes [Aristotle]
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
Universals give better explanations, because they are self-explanatory and primitive [Aristotle]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
Perception creates primitive immediate principles by building a series of firm concepts [Aristotle]
A perception lodging in the soul creates a primitive universal, which becomes generalised [Aristotle]
18. Thought / E. Abstraction / 2. Abstracta by Selection
We learn primitives and universals by induction from perceptions [Aristotle]
19. Language / C. Assigning Meanings / 4. Compositionality
Frege's account was top-down and decompositional, not bottom-up and compositional [Frege, by Potter]
19. Language / F. Communication / 3. Denial
Negation takes something away from something [Aristotle]
19. Language / F. Communication / 6. Interpreting Language / d. Metaphor
If you shouldn't argue in metaphors, then you shouldn't try to define them either [Aristotle]
26. Natural Theory / B. Natural Kinds / 6. Necessity of Kinds
Whatever holds of a kind intrinsically holds of it necessarily [Aristotle]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
Properties must be proved, but not essence; but existents are not a kind, so existence isn't part of essence [Aristotle]
The predicate 'exists' is actually a natural language expression for a quantifier [Frege, by Weiner]