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Re: [ontolog-forum] triadic sign relations in practice

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Tue, 24 Aug 2010 12:07:33 -0500
Message-id: <804A77FA-E49F-482A-8D6C-FB7AB8512C59@xxxxxxxx>
On Aug 24, 2010, at 3:55 AM, FERENC KOVACS wrote:
Following the law of identity an object is identical with itself if it exists at a particular place in space and a particular point of time.

Your claim here is in fact a trivial logical consequence of one of the usual logical laws of identity, namely, "Every object is identical with itself".  From this law, it follows immediately that "Every object is identical with itself IF it ...".  More formally expressed: ∀x(x=x) logically entails ∀x(φ → x=x), for any assertion φ at all about x (or even not about x).

Just for the record, in logic, the laws of identity typically refer to the reflexivity principle just noted and the principle typically known as the "indiscernibility of identicals" — informally put: "If x=y, then anything true of x is true of y."  In first order logic, this is expressed as a schema standing for infinitely many sentences:

  ∀x∀y(x=y → (φ → φ[x/y]), for any formula φ

where φ[x/y] is the result of replacing every "free" occurrence of x in φ (i.e., every occurrence that is not bound by a quantifier) with an occurrence of y.  (Every such replacement must also result in a free occurrence of y.)  In second-order logic, where one is allowed to quantify over properties, this principle can be expressed as a single sentence:

  ∀x∀y(x=y → ∀F(Fx → Fy)).

This is like duplicating an object. So therefore two seemingly identical objects are only identical with each other, if we disregard space an time parameters. This is called abstarction, disaambiguation, decontextualization, etc.

I'm not sure what you are saying here, but such metaphysical and epistemological ideas have nothing whatever to do with the logical laws of identity above, which in and of themselves are entirely independent of one's views of time, space, context, etc.


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