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
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11283
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There is pure deductive reasoning, and explanatory demonstration reasoning [Politis]
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2. Reason / A. Nature of Reason / 6. Coherence
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1672
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Maybe everything could be demonstrated, if demonstration can be reciprocal or circular
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2. Reason / B. Laws of Thought / 4. Contraries
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1684
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Two falsehoods can be contrary to one another
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2. Reason / D. Definition / 4. Real Definition
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12145
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Definitions are of what something is, and that is universal
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12384
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Definition by division needs predicates, which are well ordered and thorough
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9066
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You can define objects by progressively identifying what is the same and what is different
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12075
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An Aristotelian definition is causal [Witt]
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2. Reason / D. Definition / 6. Definition by Essence
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12382
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What it is and why it is are the same; screening defines and explains an eclipse
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
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1668
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An axiom is a principle which must be understood if one is to learn anything
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5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
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12376
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Demonstrations by reductio assume excluded middle
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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
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12373
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Something holds universally when it is proved of an arbitrary and primitive case
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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12363
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Everything is either asserted or denied truly
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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13004
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Aristotle's axioms (unlike Euclid's) are assumptions awaiting proof [Leibniz]
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6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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12377
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Mathematics is concerned with forms, not with superficial properties
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6. Mathematics / A. Nature of Mathematics / 2. Geometry
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12372
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The essence of a triangle comes from the line, mentioned in any account of triangles
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
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12369
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A unit is what is quantitatively indivisible
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8. Modes of Existence / B. Properties / 4. Intrinsic Properties
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18910
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To seek truth, study the real connections between subjects and attributes
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8. Modes of Existence / D. Universals / 2. Need for Universals
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1675
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Separate Forms aren't needed for logic, but universals (one holding of many) are essential
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8. Modes of Existence / D. Universals / 6. Platonic Forms / d. Forms critiques
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1677
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We can forget the Forms, as they are irrelevant, and not needed in giving demonstrations
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9. Objects / A. Existence of Objects / 6. Nihilism about Objects
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1687
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Why are being terrestrial and a biped combined in the definition of man, but being literate and musical aren't?
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9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
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1681
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Units are positionless substances, and points are substances with position
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9. Objects / D. Essence of Objects / 4. Essence as Definition
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12146
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Definitions recognise essences, so are not themselves essences
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9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
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17039
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The predicates of a thing's nature are necessary to it
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9. Objects / D. Essence of Objects / 8. Essence as Explanatory
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11994
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Aristotelian essences are properties mentioned at the starting point of a science [Kung]
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10. Modality / A. Necessity / 2. Nature of Necessity
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12381
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What is necessary cannot be otherwise
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10. Modality / A. Necessity / 3. Types of Necessity
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1690
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A stone travels upwards by a forced necessity, and downwards by natural necessity
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11. Knowledge Aims / A. Knowledge / 1. Knowledge
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12072
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For Aristotle knowledge is explanatory, involving understanding, and principles or causes [Witt]
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12073
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'Episteme' means grasping causes, universal judgments, explanation, and teaching [Witt]
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12378
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The reason why is the key to knowledge
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11. Knowledge Aims / A. Knowledge / 2. Understanding
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12370
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Some understanding, of immediate items, is indemonstrable
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12364
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We understand a thing when we know its explanation and its necessity
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12366
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We only understand something when we know its explanation
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11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
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1685
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No one has mere belief about something if they think it HAS to be true
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11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
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1673
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Knowledge proceeds from principles, so it is hard to know if we know
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12. Knowledge Sources / B. Perception / 1. Perception
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12379
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You cannot understand anything through perception
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12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
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16725
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Some knowledge is lost if you lose a sense, and there is no way the knowledge can be replaced
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12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
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23309
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Aristotle's concepts of understanding and explanation mean he is not a pure empiricist [Frede,M]
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1693
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Animals may have some knowledge if they retain perception, but understanding requires reasons to be given
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12. Knowledge Sources / E. Direct Knowledge / 4. Memory
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9067
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Many memories of the same item form a single experience
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13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
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1671
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Sceptics say justification is an infinite regress, or it stops at the unknowable
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13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
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1670
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When you understand basics, you can't be persuaded to change your mind
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14. Science / A. Basis of Science / 2. Demonstration
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24068
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Demonstration is more than entailment, as the explanatory order must match the causal order [Koslicki]
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17310
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Aristotle gets asymmetric consequence from demonstration, which reflects real causal priority [Koslicki]
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21359
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Aristotle doesn't actually apply his theory of demonstration to his practical science [Leroi]
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1667
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Premises must be true, primitive and immediate, and prior to and explanatory of conclusions
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12365
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We can know by demonstration, which is a scientific deduction leading to understanding
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1674
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All demonstration is concerned with existence, axioms and properties
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10918
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Demonstrative understanding rests on necessary features of the thing in itself
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12374
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Demonstrations must be necessary, and that depends on the middle term
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12148
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Demonstrations are syllogisms which give explanations
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12383
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There must be definitions before demonstration is possible
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1691
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Aim to get definitions of the primitive components, thus establishing the kind, and work towards the attributes
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12371
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A demonstration is a deduction which proceeds from necessities
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12147
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The principles of demonstrations are definitions
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1680
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Demonstration is better with fewer presuppositions, and it is quicker if these are familiar
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1679
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Universal demonstrations are about thought; particular demonstrations lead to perceptions
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14. Science / C. Induction / 2. Aims of Induction
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1683
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We learn universals from many particulars
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14. Science / D. Explanation / 1. Explanation / a. Explanation
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12380
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Universals are valuable because they make the explanations plain
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12367
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What is most universal is furthest away, and the particulars are nearest
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12385
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Are particulars explained more by universals, or by other particulars?
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14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
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1686
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What we seek and understand are facts, reasons, existence, and identity
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1689
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Explanation is of the status of a thing, inferences to it, initiation of change, and purpose
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14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
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12357
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Explanation and generality are inseparable [Wedin]
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14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
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1669
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The foundation or source is stronger than the thing it causes
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14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
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1678
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Universals give better explanations, because they are self-explanatory and primitive
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15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
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9068
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Perception creates primitive immediate principles by building a series of firm concepts
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9069
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A perception lodging in the soul creates a primitive universal, which becomes generalised
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18. Thought / E. Abstraction / 2. Abstracta by Selection
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9070
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We learn primitives and universals by induction from perceptions
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19. Language / F. Communication / 3. Denial
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12368
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Negation takes something away from something
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19. Language / F. Communication / 6. Interpreting Language / d. Metaphor
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1692
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If you shouldn't argue in metaphors, then you shouldn't try to define them either
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26. Natural Theory / B. Natural Kinds / 6. Necessity of Kinds
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12375
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Whatever holds of a kind intrinsically holds of it necessarily
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28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
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1688
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Properties must be proved, but not essence; but existents are not a kind, so existence isn't part of essence
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