The problem is that in many instances, like in "4+4=8", it cannot signify the same object — Metaphysician Undercover
as I said I'm not good with symbols, so I just get lost trying to figure out what you're saying. — Metaphysician Undercover
Now we have the situation: A || B to mean tribe A is married to tribe B (according to rules above).
Now this is a predicative formulation, why, because A||B is a "proposition", it something that can be true or false, and the symbol || is denoting a "binary relation", so it is a "predicate" symbol. — Zuhair
Notice that we can have the situation were tribe S can marry itself!!! so we can have S || S
Notice that S occurred twice in the proposition "S || S" but still it denotes ONE object, although this object is a totality of many individuals, however that whole of many individuals is considered here as one object. So repeated occurrence of the symbol symbol in an expression doesn't denote different denotation, no here S repeatedly occurred in "S || S" but it still carries the same denotation, namely tribe S. — Zuhair
P(S||S) = Q
Now we have two distinct occurrence of the symbol S on the left, but still it has the SAME denotational coverage! Both symbols of S denote the same object that is " TRIBE "S" ". — Zuhair
ou have divided S into the subgroups MS and FS, and you ought to say that MS is married to FS. And now the mathemagician's shell trick of equivocation has been exposed. You claim that the same thing lies under each S, but in reality half of tribe S is under one S, and the other half of tribe S is under the other S. This is the only way to speak of S being married to S. This is verified from the fact that Q, the progeny of this union, is only half of C, the progeny of the union of A and B. — Metaphysician Undercover
No, the laws of the country doesn't specify a tribe of one gender, tribes can only be named if they have 50 women and 50 men. Notice the definition of marriage between tribes doesn't say what's the total number of marriages, so although you have 50 marriages between tribe S and itself, and 100 marriages between tribes A and B when they are different, still both cases are concealed by the laws, and both receive the same description of being "married tribes". — Zuhair
Of course there would be some hidden details no doubt, but the point is that there are indeed hidden difference, but since the definitions involved are blind to those differences they would pass the same. Like when we say for example "MAN" this denotes a lot of grown up males, but there are still many differences but all fall under the same SHELL. — Zuhair
So imagine there are four chairs, and we represent those four chairs with the symbol "4". — Metaphysician Undercover
We're not talking about chairs. Four chairs over here are different than the four chairs over there. — fishfry
Once again you are avoiding the question. We are talking about 4 + 4 = 8. You claim the two instances of '4' represent or stand for or refer to or mean two different things. — fishfry
You have claimed that mathematicians use the word equality when they really mean congruence, equivalence, or isomorphism. — fishfry
I ask you to introspect on the point that if you can't come up with specific examples, perhaps you don't understand your own ideas as well as you think you do. — fishfry
No, you're not paying attention fishfry — Metaphysician Undercover
n other words, there is equivocation in the meaning of "S". Do you see this? "S is married to S" doesn't mean the whole tribe is married to itself, as consistency with "A is married to B" would imply, it actually means that half the tribe is married to the other half. Therefore each S in this case signifies half the tribe, whereas "S" was originally used to represent the whole tribe. — Metaphysician Undercover
But you are right in fact. I am not paying the slightest attention to your argument. — fishfry
Bottom line I have no idea what you're talking about. — fishfry
50 men of tribe S are married to 50 women of tribe S,
AND
50 women of tribe S are married to 50 men of tribe S." — Zuhair
Your use of "AND" as a conjunction between the two expressions above provides the necessary ambiguity for your equivocation. "S is married to S" can refer to one situation only. Yet you use two distinct expressions. Since you allow that "S is married to S" represents the two distinct situations expressed above, the charge of equivocation is justified. — Metaphysician Undercover
Not it is NOT justified! Because we are using the "AND" in the GENERAL case of definition of marriage between any tribes A,B (whether A, and B are the same tribe or not), the general rule is:
IF
[50 men of tribe A are married to 50 women of tribe B
AND
50 women of tribe A are married to 50 men of tribe B]
THEN
A || B — Zuhair
Just substitute S instead of A and S instead of B, and you get the conclusion S || S. No equivocation at all. — Zuhair
I assume then, that you still do not understand the distinction I made between what a symbol means, and what it refers to, or stands for. Perhaps if you read up on the kind/token distinction, that will help you. — Metaphysician Undercover
Thus '4' is a reference set to match one to one to an unknown set to determine its 'size' or quantity. — sandman
The reference set, eg. the set of integers, is a mental construct, used in the process of counting, a practical convenience. Counting is the most fundamental process of measurement, the answer to 'how many'. The nature/identity of the elements is a matter of definition, what attributes must the elements have to be a member of a set. — sandman
You are refusing to acknowledge the equivocation in your use of "AND" in the rule. — Metaphysician Undercover
This suggests it is the process, not the object that is without limit. — sandman
IF the statement (50 men of tribe A are married to 50 women of tribe B) is TRUE
AND the statement (50 women of tribe A are married to 50 men of tribe B) is TRUE
THEN the statement "tribe A is married to tribe B" is TRUE.
AND is specifically the logical conjunctive article, nothing more nothing less. Now let apply this to tribe S were 50 men of tribe S are married to 50 women of tribe S, we have the antecedent:
The statement (50 men of tribe S are married to 50 women of tribe S) is TRUE
AND
The statement (50 women of tribe S are married to 50 men of tribe S) is TRUE. — Zuhair
he phrase "is married to" will mean something different in "tribe A is married to tribe B", from what it means in "tribe S is married to tribe S". — Metaphysician Undercover
RULE: For every tribe A for every tribe B (A || B if and only if for every male a of A there is one female b of B such that: a m b, and for every woman a of A there is one male b of B such that: a m b). — Zuhair
Notice the "if and only if", the above statement is a DEFINITION of "||". Notice that it was symbolized by another symbol from "m" which was given to marriage between individual.
Marriage between tribes (symbolized by ||) has NO meaning by itself, it is just a string of letters, the country gave it a meaning by the statement after the "if and only if" above. So you cannot say it leads to equivocation of meaning or anything like that, because its meaning is understood to be fully traceable to the specifications building it posed by the rule, in other ways that rule is a DEFINITIONAL RULE. Without it you have no meaning of tribal marriage at all. — Zuhair
In those rigid kinds of definitions, there is no room for equivocation or the alike. These are strict rule following machinery. Equivocation is out of question here. — Zuhair
As you said, human thought is only familiar with things having boundaries. — sandman
The point is that the symbol "||" refers to a different situation in S||S than it does in A||B. Therefore the rule produces ambiguity in the use of that symbol, and the possibility of equivocation. If we assume that "||" has the same meaning in each case, we are deceived by equivocation. Therefore the rule is a faulty rule, and ought not be accepted. — Metaphysician Undercover
I'll grant you that as true. But the point is that there is ambiguity as to what "||" signifies. So, we must be careful not to equivocate.S||S is a particular case of A||B; also C||D when C, D are disjoint tribes is also a particular case of A||B. — Zuhair
This is like variation in particularities of objects fulfilling a predicate, for example the predicate "is a circle", now not all circles are really a like, they might vary in their size for example, in their colors, etc.., that doesn't affect them all being circles. No equivocation at all. — Zuhair
Similarly the relationship || between tribes has strict definition, and whenever that definition is met, then the relationship holds between the respective tribes, variations in particularities of individual actualization of that relationship are immaterial as immaterial is the size of the circle in meeting the definition of a circle. — Zuhair
The whole matter began when I wanted to coin a relation that can exist between something and itself other than the identity relation! So the relation || as I defined in the example can occur between a tribe and itself, and also can occur between distinct tribes, so its not the identity relation. As far as the "application" of relation ||, there is no equivocation at all.
So identity is not the ONLY relation that can occur between something and itself.
But
Identity is the ONLY relation that can ONLY occurs between something and itself. — Zuhair
That definition of "||" is not so strict as you seem to think. You describe it as "the relationship || between tribes", as if it is necessarily a relationship between a plurality of "tribes". — Metaphysician Undercover
Can't elaborate on my response. There is no human experience with 'infinite' unbounbded/without limit entities. Cantor was an illusionist, who fooled many people. That's it. — sandman
It doesn't indicate that those arguments must be distinct from each other.
...
A tribe is a well specified entity, it refers to the totality of specified individuals. — Zuhair
This is a well specified entity.
...
Clearly each tribe is a well defined entity... — Zuhair
Cantor was an illusionist, who fooled many people. That's it. — sandman
Individual mathematicians may have metaphysical beliefs, but those beliefs don't play a role in proofs. — Eee
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