ONT Re: Logic Of Relatives
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LOR. Discussion Note 17
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HC = Howard Callaway
JA = Jon Awbrey
JA: In closing, observe that the teridentity relation has turned up again
in this context, as the second comma-ing of the universal term itself:
1,, = B:B:B +, C:C:C +, D:D:D +, E:E:E +, I:I:I +, J:J:J +, O:O:O.
HC: I see that you've come around to a mention of teridentity again, Jon.
Still, if I recall the prior discussions, then no one doubts that we
can have a system of notation in which teridentity appears (I don't
actually see it here).
Perhaps we could get at the root of the misunderstanding
if you tell me why you don't actually see the concept of
teridentity being exemplified here.
If it's only a matter of having lost the context of the
present discussion over the break, then you may find the
previous notes archived at the distal ends of the ur-links
that I append below (except for the first nine discussion
notes that got lost in a disk crash at the Arisbe Dev site).
HC: Also, I think we can have a system of notation in which
teridentity is needed. Those points seem reasonably clear.
The advantage of a concept is the integration of a species of manifold.
The necessity of a concept is the incapacity to integrate it otherwise.
Of course, no one should be too impressed with a concept that
is only the artifact of a particular system of representation.
So before we accord a concept the status of addressing reality,
and declare it a term of some tenured office in our intellects,
we would want to see some evidence that it helps us to manage
a reality that we cannot see a way to manage any other way.
Granted.
Now how in general do we go about an investiture of this sort?
That is the big question that would serve us well to consider
in the process of the more limited investigation of identity.
Indeed, I do not see how it is possible to answer the small
question if no understanding is reached on the big question.
HC: What remains relatively unclear is why we should need a system of notation
in which teridentity appears or is needed as against one in which it seems
not to be needed -- since assertion of identity can be made for any number
of terms in the standard predicate calculus.
This sort of statement totally non-plusses me.
It seems like a complete non-sequitur or even
a contradiction in terms to me.
The question is about the minimal adequate resource base for
defining, deriving, or generating all of the concepts that we
need for a given but very general type of application that we
conventinally but equivocally refer to as "logic". You seem
to be saying something like this: We don't need 3-identity
because we have 4-identity, 5-identity, 6-identity, ..., in
the "standard predicate calculus". The question is not what
concepts are generated in all the generations that follow the
establishment of the conceptual resource base (axiom system),
but what is the minimal set of concepts that we can use to
generate the needed collection of concepts. And there the
answer is, in a way that is subject to the usual sorts of
mathematical proof, that 3-identity is the minimum while
2-identity is not big enough to do the job we want to do.
Jon Awbrey
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LOR. Logic Of Relatives
01. http://suo.ieee.org/ontology/msg04416.html
02. http://suo.ieee.org/ontology/msg04417.html
03. http://suo.ieee.org/ontology/msg04418.html
04. http://suo.ieee.org/ontology/msg04419.html
05. http://suo.ieee.org/ontology/msg04421.html
06. http://suo.ieee.org/ontology/msg04422.html
07. http://suo.ieee.org/ontology/msg04423.html
08. http://suo.ieee.org/ontology/msg04424.html
09. http://suo.ieee.org/ontology/msg04425.html
10. http://suo.ieee.org/ontology/msg04426.html
11. http://suo.ieee.org/ontology/msg04427.html
12. http://suo.ieee.org/ontology/msg04431.html
13. http://suo.ieee.org/ontology/msg04432.html
14. http://suo.ieee.org/ontology/msg04435.html
15. http://suo.ieee.org/ontology/msg04436.html
16. http://suo.ieee.org/ontology/msg04437.html
17. http://suo.ieee.org/ontology/msg04438.html
18. http://suo.ieee.org/ontology/msg04439.html
19. http://suo.ieee.org/ontology/msg04440.html
20. http://suo.ieee.org/ontology/msg04441.html
21. http://suo.ieee.org/ontology/msg04442.html
22. http://suo.ieee.org/ontology/msg04443.html
23. http://suo.ieee.org/ontology/msg04444.html
24. http://suo.ieee.org/ontology/msg04445.html
25. http://suo.ieee.org/ontology/msg04446.html
26. http://suo.ieee.org/ontology/msg04447.html
27. http://suo.ieee.org/ontology/msg04448.html
28. http://suo.ieee.org/ontology/msg04449.html
29. http://suo.ieee.org/ontology/msg04450.html
30. http://suo.ieee.org/ontology/msg04451.html
31. http://suo.ieee.org/ontology/msg04452.html
32. http://suo.ieee.org/ontology/msg04453.html
33. http://suo.ieee.org/ontology/msg04454.html
34. http://suo.ieee.org/ontology/msg04456.html
35. http://suo.ieee.org/ontology/msg04457.html
36. http://suo.ieee.org/ontology/msg04458.html
37. http://suo.ieee.org/ontology/msg04459.html
38. http://suo.ieee.org/ontology/msg04462.html
39. http://suo.ieee.org/ontology/msg04464.html
40. http://suo.ieee.org/ontology/msg04473.html
41. http://suo.ieee.org/ontology/msg04478.html
LOR. Logic of Relatives -- Discussion Notes
10. http://suo.ieee.org/ontology/msg04460.html
11. http://suo.ieee.org/ontology/msg04461.html
12. http://suo.ieee.org/ontology/msg04471.html
13. http://suo.ieee.org/ontology/msg04472.html
14. http://suo.ieee.org/ontology/msg04475.html
15. http://suo.ieee.org/ontology/msg04476.html
16. http://suo.ieee.org/ontology/msg04477.html
17. http://suo.ieee.org/ontology/msg04479.html
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