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Single Idea 13166
[filed under theme 9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
]
Full Idea
Essences and essential properties do not seem to be useful in mathematical contexts, since all mathematical truths are regarded as necessary (though Kit Fine distinguishes between essential and necessary properties).
Gist of Idea
Essences are no use in mathematics, if all mathematical truths are necessary
Source
Paolo Mancosu (Explanation in Mathematics [2008], §6.1)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.14
A Reaction
I take the proviso in brackets to be crucial. This represents a distortion of notion of an essence. There is a world of difference between the central facts about the nature of a square and the peripheral inferences derivable from it.
Related Idea
Idea 11248
Necessary truths can be two-way relational, where essential truths are one-way or intrinsic [Politis]
The
22 ideas
with the same theme
[essence is different from necessary properties]:
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12262
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An 'idion' belongs uniquely to a thing, but is not part of its essence
[Aristotle]
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17246
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Some accidental features are permanent, unless the object perishes
[Hobbes]
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17191
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Nothing is essential if it is in every part, and is common to everything
[Spinoza]
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13082
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The complete concept of an individual includes contingent properties, as well as necessary ones
[Leibniz]
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13189
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A necessary feature (such as air for humans) is not therefore part of the essence
[Leibniz]
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11180
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Essentialist sentences are not theorems of modal logic, and can even be false
[Marcus (Barcan)]
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11186
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'Essentially' won't replace 'necessarily' for vacuous properties like snub-nosed or self-identical
[Marcus (Barcan)]
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11185
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'Is essentially' has a different meaning from 'is necessarily', as they often cannot be substituted
[Marcus (Barcan)]
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11993
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Jones may cease to exist without some simple property, but that doesn't make it essential
[Kung]
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12763
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Necessarily self-identical, or being what it is, or its world-indexed properties, aren't essential
[Stalnaker]
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11918
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The essence of a thing need not include everything that is necessarily true of it
[Molnar]
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13376
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We should not regard essentialism as just nontrivial de re necessity
[Jubien]
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16537
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Essence as necessary properties produces a profusion of essential properties
[Fine,K, by Lowe]
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11163
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The nature of singleton Socrates has him as a member, but not vice versa
[Fine,K]
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11164
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It is not part of the essence of Socrates that a huge array of necessary truths should hold
[Fine,K]
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11167
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Metaphysical necessity is a special case of essence, not vice versa
[Fine,K]
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9206
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We must distinguish between the identity or essence of an object, and its necessary features
[Fine,K]
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12870
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We must distinguish the de dicto 'must' of propositions from the de re 'must' of essence
[Simons]
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11248
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Necessary truths can be two-way relational, where essential truths are one-way or intrinsic
[Politis]
|
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13166
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Essences are no use in mathematics, if all mathematical truths are necessary
[Mancosu]
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10934
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Unlosable properties are not the same as essential properties
[Rami]
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16749
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Aristotelians deny that all necessary properties are essential
[Pasnau]
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