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The ontological status of an empty set 4 Years, 6 Months ago
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Let's suppose a philosophy forum was held once a week at a designated location. If only one person showed up for the meeting, would it still be a philosophy forum? If no one showed up, would it also be a philosophy forum which "exists" as an empty set with no elements?
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Re: The ontological status of an empty set 4 Years, 6 Months ago
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Only if there were posters.
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The kind of philosophy one chooses depends upon what kind of person one is. ~ J.G. Fichte
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Witt
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Re: The ontological status of an empty set 4 Years, 6 Months ago
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[quote1194876613=nanrek]
Let's suppose a philosophy forum was held once a week at a designated location. If only one person showed up for the meeting, would it still be a philosophy forum? If no one showed up, would it also be a philosophy forum which "exists" as an empty set with no elements?
[/quote1194876613]
Yes, the class of those people who think about philosophy exists even if there are no members!
The x's such that ~ExFx is the empty set, and it necessarily exists because we say so.
The x's such that ~(x=x) = (the null set).
The x's such that (x=x) = the universal set.
Like it or not!
V =df (x:x=x)
Therefore: V e V, V=V, V is included in V, etc.
See: Quine, Matematical Logic, New Foundations.
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Re: The ontological status of an empty set 4 Years, 6 Months ago
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[quote1194884395=nanrek]
Let's suppose a philosophy forum was held once a week at a designated location. If only one person showed up for the meeting, would it still be a philosophy forum? If no one showed up, would it also be a philosophy forum which "exists" as an empty set with no elements?
[/quote1194884395]
By definition a forum involves more than one person. Therefore, the answer to your question is a simple "No".
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Re: The ontological status of an empty set 4 Years, 6 Months ago
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Classical24 writes -
"By definition a forum involves more than one person. Therefore, the answer to your question is a simple "No".
_________
A forum was initially defined as a public place. I suppose it is still a public place even if it is empty.
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Re: The ontological status of an empty set 4 Years, 6 Months ago
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I'm with nanrek on this one
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A picture held us captive ...
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