On Aug 24, 2010, at 12:29 PM, FERENC KOVACS wrote:
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).
YEs. But my main point is that in "Every object is identical with itself" there are two objects, the object in question and "itself", your picture of the same.
Sorry, but that just is not so. The principle is a simple _expression_ of the fact that identity relation is reflexive. There is only one variable in the principle which, in any instance of the principle, can take as its value only one object.
Without two items you cannot compare anything.
Perhaps so, but the logical principle of identity has nothing whatever to do with comparing one thing with another or with the epistemological difficulties involved in, e.g., discovering that what might be thought to be two things (e.g., the morning star and the evening star, Sam Clemens and Mark Twain, etc) are in fact one and the same. Those are tremendously interesting questions on which the reflexivity of identity has no bearing whatsoever.
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.
No wonder that you cannot ground your ontologies which are derived from our experience of reality and are an additional aspect of the same through the symbols and signs we use - but in a different sense.
What I can or cannot do with my ontologies is neither here nor there. You have confused a clear and simple principle of the logic of the identity relation — that it is reflexive — with something else entirely having to do with time, space, context, experience, reality, etc. Your views on these subjects might be profoundly important, but they have nothing to do with the logical principle in question. Therefore, I am simply correcting the record.