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Single Idea 12374
[filed under theme 14. Science / A. Basis of Science / 2. Demonstration
]
Full Idea
If you understand something demonstratively, it must hold from necessity, so it is plain that your demonstration must proceed through a middle term which is necessary.
Gist of Idea
Demonstrations must be necessary, and that depends on the middle term
Source
Aristotle (Posterior Analytics [c.327 BCE], 75a13)
Book Ref
Aristotle: 'Posterior Analytics (2nd ed)', ed/tr. Barnes,Jonathan [OUP 1993], p.11
A Reaction
How can a middle 'term' be necessary, if it is not a proposition? Presumably Socrates is necessarily a man, and men are necessarily mortal, so it is the predication which is necessary.
The
27 ideas
with the same theme
[proving physical facts by observation and reason]:
16647
|
Demonstration starts from a definition of essence, so we can derive (or conjecture about) the properties
[Aristotle]
|
24048
|
Demonstrations move from starting-points to deduced conclusions
[Aristotle]
|
12309
|
There cannot be a science of accidentals, but only of general truths
[Aristotle]
|
11386
|
Demonstrations about particulars must be about everything of that type
[Aristotle]
|
17310
|
Aristotle gets asymmetric consequence from demonstration, which reflects real causal priority
[Aristotle, by Koslicki]
|
21359
|
Aristotle doesn't actually apply his theory of demonstration to his practical science
[Leroi on Aristotle]
|
24068
|
Demonstration is more than entailment, as the explanatory order must match the causal order
[Aristotle, by Koslicki]
|
12365
|
We can know by demonstration, which is a scientific deduction leading to understanding
[Aristotle]
|
1667
|
Premises must be true, primitive and immediate, and prior to and explanatory of conclusions
[Aristotle]
|
12371
|
A demonstration is a deduction which proceeds from necessities
[Aristotle]
|
10918
|
Demonstrative understanding rests on necessary features of the thing in itself
[Aristotle]
|
12374
|
Demonstrations must be necessary, and that depends on the middle term
[Aristotle]
|
1674
|
All demonstration is concerned with existence, axioms and properties
[Aristotle]
|
12148
|
Demonstrations are syllogisms which give explanations
[Aristotle]
|
1679
|
Universal demonstrations are about thought; particular demonstrations lead to perceptions
[Aristotle]
|
1680
|
Demonstration is better with fewer presuppositions, and it is quicker if these are familiar
[Aristotle]
|
12147
|
The principles of demonstrations are definitions
[Aristotle]
|
12383
|
There must be definitions before demonstration is possible
[Aristotle]
|
1691
|
Aim to get definitions of the primitive components, thus establishing the kind, and work towards the attributes
[Aristotle]
|
20779
|
Demonstration derives what is less clear from what is clear
[Stoic school, by Diog. Laertius]
|
16577
|
Induction is not demonstration, because not all of the instances can be observed
[Buridan]
|
19243
|
If each inference slightly reduced our certainty, science would soon be in trouble
[Peirce]
|
16799
|
Inductive inference is not proof, but weighing evidence and probability
[Lipton]
|
16798
|
We infer from evidence by working out what would explain that evidence
[Lipton]
|
22110
|
Demonstration provides depth of understanding and explanation (rather than foundations)
[Kretzmann/Stump]
|
15111
|
In demonstration, the explanatory order must mirror the causal order of the phenomena
[Koslicki]
|
15115
|
In a demonstration the middle term explains, by being part of the definition
[Koslicki]
|