[extropy-chat] Identity (was: Survival tangent)

[Ian Goddard]

Jef Allbright wrote:

> Where is it logically shown that all persons must 
> have unique identity?


 The classical definition of 'identity' in logic is
found in the second-order statement quantifying over
objects (x, y) and properties of objects (P):

  AxAy[(x = y) <-> AP(Px <-> Py)]

Literally: for all objects x and y, x is y if and only
if for all properties P, P is a property of x if and
only if P is a property of y. More simply: x is y just
in case every property of x is a property of y and
vice versa. 

 Now, given the logical definition of 'identity', if
there is a perfect copy of my brain with all its
encoded contents and possible states, that copy still
lacks at least: (1) the property of being 'the
original', (2) the property of being in the location
that the original is, and (3) the property of being
encoded on the physical substrate that the original is
encoded on. Ergo, there exists at least one property
that the original has but the copy lacks, and thus, by
the definition of 'identity', any claim that "the
original = the copy" is false. QED



> Slawomir, A and B are symbols representing 
> antecedent and consequent in the form of a 
> syllogism.  The particulars don't matter if the 
> form is logically invalid. 
> In this particular case, A->B corresponds to the 
> statement "any person is defined by values, beliefs
> and memories".  This does not imply the statement 
> B->A corresponding to "any values, beliefs and 
> memories define a person" because not all values, 
> beliefs and memories are associated with any given 
> person.  It's not symmetrical.


 By denoting 'Any person', your statement "Any person
is defined by values, beliefs and memories"
*quantifies* over the set of all people. So the
proposed formula of propositional logic 'A->B' is not
an indicated model. The statement instead points to a
quantified model in predicate logic, something more
like: "For all x, if x is a person, then x is defined
by values, beliefs and memories." 

 Consider also, in that statement you quantify over
the set of all people, but in your interpretation of
its converse 'B->A' you quantify over the set of all
values, beliefs, and memories, saying: "Any values,
beliefs and memories define a person." Apart from my
previous observation about 'identity', I'm not taking
a side in all aspects of the discussion, but it might
be helpful to explicitly articulate the analytic model
you're proposing. ~Ian


http://IanGoddard.net

"A proposition can be true or false only in virtue of
being a picture of reality." - Wittgenstein


 



 
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