Ideas from 'Posterior Analytics' by Aristotle [327 BCE], by Theme Structure

[found in 'Posterior Analytics (2nd ed)' by Aristotle (ed/tr Barnes,Jonathan) [OUP 1993,0-19-824089-9]].

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2. Reason / A. Nature of Reason / 1. On Reason
There is pure deductive reasoning, and explanatory demonstration reasoning [Politis]
2. Reason / A. Nature of Reason / 6. Coherence
Maybe everything could be demonstrated, if demonstration can be reciprocal or circular
2. Reason / B. Laws of Thought / 4. Contraries
Two falsehoods can be contrary to one another
2. Reason / D. Definition / 4. Real Definition
An Aristotelian definition is causal [Witt]
Definitions are of what something is, and that is universal
Definition by division needs predicates, which are well ordered and thorough
You can define objects by progressively identifying what is the same and what is different
2. Reason / D. Definition / 6. Definition by Essence
What it is and why it is are the same; screening defines and explains an eclipse
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
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Demonstrations by reductio assume excluded middle
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Something holds universally when it is proved of an arbitrary and primitive case
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Everything is either asserted or denied truly
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Aristotle's axioms (unlike Euclid's) are assumptions awaiting proof [Leibniz]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematics is concerned with forms, not with superficial properties
6. Mathematics / A. Nature of Mathematics / 2. Geometry
The essence of a triangle comes from the line, mentioned in any account of triangles
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A unit is what is quantitatively indivisible
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
To seek truth, study the real connections between subjects and attributes
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
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
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?
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
Units are positionless substances, and points are substances with position
9. Objects / D. Essence of Objects / 4. Essence as Definition
Definitions recognise essences, so are not themselves essences
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
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
Aristotelian essences are properties mentioned at the starting point of a science [Kung]
10. Modality / A. Necessity / 2. Nature of Necessity
What is necessary cannot be otherwise
10. Modality / A. Necessity / 3. Types of Necessity
A stone travels upwards by a forced necessity, and downwards by natural necessity
11. Knowledge Aims / A. Knowledge / 1. Knowledge
For Aristotle knowledge is explanatory, involving understanding, and principles or causes [Witt]
'Episteme' means grasping causes, universal judgments, explanation, and teaching [Witt]
The reason why is the key to knowledge
11. Knowledge Aims / A. Knowledge / 2. Understanding
We only understand something when we know its explanation
Some understanding, of immediate items, is indemonstrable
We understand a thing when we know its explanation and its necessity
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
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
Knowledge proceeds from principles, so it is hard to know if we know
12. Knowledge Sources / B. Perception / 1. Perception
You cannot understand anything through perception
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
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Animals may have some knowledge if they retain perception, but understanding requires reasons to be given
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
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
When you understand basics, you can't be persuaded to change your mind
14. Science / A. Basis of Science / 2. Demonstration
Premises must be true, primitive and immediate, and prior to and explanatory of conclusions
A demonstration is a deduction which proceeds from necessities
Aristotle gets asymmetric consequence from demonstration, which reflects real causal priority [Koslicki]
Aristotle doesn't actually apply his theory of demonstration to his practical science [Leroi]
We can know by demonstration, which is a scientific deduction leading to understanding
Demonstrative understanding rests on necessary features of the thing in itself
Demonstrations must be necessary, and that depends on the middle term
Demonstrations are syllogisms which give explanations
Universal demonstrations are about thought; particular demonstrations lead to perceptions
Demonstration is better with fewer presuppositions, and it is quicker if these are familiar
The principles of demonstrations are definitions
There must be definitions before demonstration is possible
Aim to get definitions of the primitive components, thus establishing the kind, and work towards the attributes
All demonstration is concerned with existence, axioms and properties
14. Science / C. Induction / 2. Aims of Induction
We learn universals from many particulars
14. Science / D. Explanation / 1. Explanation / a. Explanation
Universals are valuable because they make the explanations plain
Are particulars explained more by universals, or by other particulars?
What is most universal is furthest away, and the particulars are nearest
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
What we seek and understand are facts, reasons, existence, and identity
Explanation is of the status of a thing, inferences to it, initiation of change, and purpose
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Explanation and generality are inseparable [Wedin]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
The foundation or source is stronger than the thing it causes
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
Universals give better explanations, because they are self-explanatory and primitive
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
Perception creates primitive immediate principles by building a series of firm concepts
A perception lodging in the soul creates a primitive universal, which becomes generalised
15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
Many memories of the same item form a single experience
18. Thought / E. Abstraction / 2. Abstracta by Selection
We learn primitives and universals by induction from perceptions
19. Language / F. Communication / 3. Denial
Negation takes something away from something
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
26. Natural Theory / B. Natural Kinds / 6. Necessity of Kinds
Whatever holds of a kind intrinsically holds of it necessarily
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