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Single Idea 18769
[filed under theme 7. Existence / A. Nature of Existence / 2. Types of Existence
]
Full Idea
A cursory examination shows that mathematicians have no aversion to saying that this-or-that mathematical entity exists. But is this a different sense of 'existence'?
Gist of Idea
Do mathematicians use 'existence' differently when they say some entity exists?
Source
C. Anthony Anderson (Identity and Existence in Logic [2014], 2.6)
Book Ref
'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.72
A Reaction
For those of us like me and my pal Quine who say that 'exist' is univocal (i.e. only one meaning), this is a nice challenge. Quine solves it by saying maths concerns sets of objects. I, who don't like sets, am puzzled (so I turn to fictionalism...).
The
18 ideas
with the same theme
[whether there is more than one type of existence]:
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13221
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Existence is either potential or actual
[Aristotle]
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568
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Some things exist as substances, others as properties of substances
[Aristotle]
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16588
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I prefer a lack of form to mean non-existence, than to think of some quasi-existence
[Augustine]
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16664
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Everything that exists is either a substance or an accident
[Albert of Saxony]
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17174
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Outside the mind, there are just things and their properties
[Spinoza]
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17176
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The more reality a thing has, the more attributes it has
[Spinoza]
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21291
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There is no medium state between existence and non-existence
[Hume]
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4168
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Matter and intellect are inseparable correlatives which only exist relatively, and for each other
[Schopenhauer]
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19470
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Thoughts in the 'third realm' cannot be sensed, and do not need an owner to exist
[Frege]
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10241
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For Quine, there is only one way to exist
[Quine, by Shapiro]
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15535
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We can't accept a use of 'existence' that says only some of the things there are actually exist
[Lewis]
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10470
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There are only two kinds: sets, and possibilia (actual and possible particulars)
[Lewis, by Oliver]
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15520
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Existence doesn't come in degrees; once asserted, it can't then be qualified
[Lewis]
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15789
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Lewis's distinction of 'existing' from 'being actual' is Meinong's between 'existing' and 'subsisting'
[Lycan on Lewis]
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12620
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If 'exist' is ambiguous in 'chairs and numbers exist', that mirrors the difference between chairs and numbers
[Fodor]
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13884
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The idea that 'exist' has multiple senses is not coherent
[Wright,C]
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15078
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There are levels of existence, as well as reality; objects exist at the lowest level in which they can function
[Fine,K]
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18769
|
Do mathematicians use 'existence' differently when they say some entity exists?
[Anderson,CA]
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