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Single Idea 18080
[filed under theme 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
]
Full Idea
We have only to keep in mind that to find a tangent means to draw a line that connects two points of a curve at an infinitely small distance.
Gist of Idea
A tangent is a line connecting two points on a curve that are infinitely close together
Source
Gottfried Leibniz (works [1690]), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.1
Book Ref
Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.234
A Reaction
[The quote can be tracked through Kitcher's footnote]
The
58 ideas
from 'works'
9147
|
Number cannot be defined as addition of ones, since that needs the number; it is a single act of abstraction
[Fine,K on Leibniz]
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18081
|
Nature uses the infinite everywhere
[Leibniz]
|
18080
|
A tangent is a line connecting two points on a curve that are infinitely close together
[Leibniz]
|
7561
|
Substances are essentially active
[Leibniz, by Jolley]
|
7565
|
Leibniz proposes monads, since there must be basic things, which are immaterial in order to have unity
[Leibniz, by Jolley]
|
8110
|
Leibniz identified beauty with intellectual perfection
[Leibniz, by Gardner]
|
10419
|
If relations can be reduced to, or supervene on, monadic properties of relata, they are not real
[Leibniz, by Swoyer]
|
12035
|
Leibniz bases pure primitive entities on conjunctions of qualitative properties
[Leibniz, by Adams,RM]
|
13091
|
Leibnizian substances add concept, law, force, form and soul
[Leibniz, by Cover/O'Leary-Hawthorne]
|
12715
|
Leibniz strengthened hylomorphism by connecting it to force in physics
[Leibniz, by Garber]
|
11878
|
Leibniz's view (that all properties are essential) is extreme essentialism, not its denial
[Leibniz, by Mackie,P]
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11862
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Leibniz was not an essentialist
[Leibniz, by Wiggins]
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16504
|
Two eggs can't be identical, because the same truths can't apply to both of them
[Leibniz]
|
8650
|
Things are the same if one can be substituted for the other without loss of truth
[Leibniz]
|
13828
|
Necessary truths are those provable from identities by pure logic in finite steps
[Leibniz, by Hacking]
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4307
|
A reason must be given why contingent beings should exist rather than not exist
[Leibniz]
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15883
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Leibniz narrows down God's options to one, by non-contradiction, sufficient reason, indiscernibles, compossibility
[Leibniz, by Harré]
|
18822
|
Each monad expresses all its compatible monads; a possible world is the resulting equivalence class
[Leibniz, by Rumfitt]
|
7837
|
Leibniz proposed possible worlds, because they might be evil, where God would not create evil things
[Leibniz, by Stewart,M]
|
13080
|
Leibniz has a counterpart view of de re counterfactuals
[Leibniz, by Cover/O'Leary-Hawthorne]
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19332
|
For Leibniz, divine understanding grasps every conceivable possibility
[Leibniz, by Perkins]
|
5509
|
Leibniz said dualism of mind and body is illusion, and there is only mind
[Leibniz, by Martin/Barresi]
|
7568
|
Leibniz is an idealist insofar as the basic components of his universe are all mental
[Leibniz, by Jolley]
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19354
|
Leibniz introduced the idea of degrees of consciousness, essential for his monads
[Leibniz, by Perkins]
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7841
|
We think we are free because the causes of the will are unknown; determinism is a false problem
[Leibniz]
|
5510
|
Leibniz has a panpsychist view that physical points are spiritual
[Leibniz, by Martin/Barresi]
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7564
|
Occasionalism give a false view of natural laws, miracles, and substances
[Leibniz, by Jolley]
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19372
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Concepts are ordered, and show eternal possibilities, deriving from God
[Leibniz, by Arthur,R]
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13467
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Leibniz was the first modern to focus on sentence-sized units (where empiricists preferred word-size)
[Leibniz, by Hart,WD]
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19365
|
Limited awareness leads to bad choices, and unconscious awareness makes us choose the bad
[Leibniz, by Perkins]
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7569
|
Humans are moral, and capable of reward and punishment, because of memory and self-consciousness
[Leibniz, by Jolley]
|
7574
|
Natural law theory is found in Aquinas, in Leibniz, and at the Nuremberg trials
[Leibniz, by Jolley]
|
12728
|
Leibniz rejected atoms, because they must be elastic, and hence have parts
[Leibniz, by Garber]
|
12713
|
Forms have sensation and appetite, the latter being the ability to act on other bodies
[Leibniz, by Garber]
|
13087
|
The essence of a thing is its real possibilities
[Leibniz, by Cover/O'Leary-Hawthorne]
|
12701
|
Leibniz moved from individuation by whole entity to individuation by substantial form
[Leibniz, by Garber]
|
13105
|
The laws-of-the-series plays a haecceitist role
[Leibniz, by Cover/O'Leary-Hawthorne]
|
7560
|
Leibniz struggled to reconcile bodies with a reality of purely soul-like entities
[Jolley on Leibniz]
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16683
|
Leibniz eventually said resistance, rather than extension, was the essence of body
[Leibniz, by Pasnau]
|
12725
|
Leibniz wanted to explain motion and its laws by the nature of body
[Leibniz, by Garber]
|
3889
|
God's existence is either necessary or impossible
[Leibniz, by Scruton]
|
7842
|
Leibniz was closer than Spinoza to atheism
[Leibniz, by Stewart,M]
|
19359
|
Leibniz aims to give coherent rational support for empiricism
[Leibniz, by Perkins]
|
13086
|
Metaphysics is a science of the intelligible nature of being
[Leibniz, by Cover/O'Leary-Hawthorne]
|
16897
|
Reason is the faculty for grasping apriori necessary truths
[Leibniz, by Burge]
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16710
|
Leibniz tried to combine mechanistic physics with scholastic metaphysics
[Leibniz, by Pasnau]
|
3346
|
For Leibniz rationality is based on non-contradiction and the principle of sufficient reason
[Leibniz, by Benardete,JA]
|
3347
|
Leibniz said the principle of sufficient reason is synthetic a priori, since its denial is not illogical
[Leibniz, by Benardete,JA]
|
8627
|
Leibniz is inclined to regard all truths as provable
[Leibniz, by Frege]
|
7859
|
Leibniz had an unusual commitment to the causal completeness of physics
[Leibniz, by Papineau]
|
15307
|
Leibniz uses 'force' to mean both activity and potential
[Leibniz]
|
13092
|
The essence of substance is the law of its changes, as in the series of numbers
[Leibniz]
|
19374
|
Microscopes and the continuum suggest that matter is endlessly divisible
[Leibniz]
|
19375
|
The continuum is not divided like sand, but folded like paper
[Leibniz, by Arthur,R]
|
16507
|
The law within something fixes its persistence, and accords with general laws of nature
[Leibniz]
|
16513
|
Identity of a substance is the law of its persistence
[Leibniz]
|
13078
|
Relations aren't in any monad, so they are distributed, so they are not real
[Leibniz]
|
13084
|
How can things be incompatible, if all positive terms seem to be compatible?
[Leibniz]
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