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...
"Lost in symbols, hey!", me too really, I wonder if one can can get rid of that symbolic approach to mathematics and use instead of them understandabl...
Yes, it can! If you followed by tribe example, you'll see that you can do that! consider 4 to be the name of the set of all four member sets, now you ...
I understand the general difficulty in having both 4 symbols in "4+4" representing the same object, its indeed not that easy to fathom. I'll try to gi...
Well, you definitely have some point of view here. But model theory is not altogether useless. It's easier to understand mathematical theories as spea...
Plain deletion is a partial answer. You won't get the same result! dichotomous optimistic realism adds hope and value, something that just deletion wo...
Yes, I agree to that. Anyhow, my point was that if one wants to understand applicability of formal systems, then definitely you'll need people outside...
Yes! I'm speaking about those of course. I'm not speaking about tracing the bulk of mathematics technically into one MATHEMATICAL system, which is oft...
We'll, I think the "real answer" to that is that WE DON"T KNOW. So in the face of our ignorance of what would happen, we are free to be optimistic and...
Yes, I agree. I generally agree with ALL of that posting really. And sorry for confusion about your stance from the conventions, I see know what are y...
I should add, that I'm really amazed by the last posting. Really strange. In this posting you appear to know exactly the official stuff about identity...
OK, what you are saying in this last posting is understandable, I in some sense agree with most of it. There is something nice in your conception abou...
No! Unless these differences are indescribable by formulation of the language. Once you are in a logical theory then what decides identity of somethin...
Equality is in the least sense an equivalence relation and that's it, it doesn't necessarily satisfy the substitution schema. However when logicians a...
this is also a good book. Look how does he use "identity" interchangeably with equality. https://www.math.uni-bielefeld.de/~frettloe/papers/wikibuch.p...
What? that's really strange. You need to first read it and then know about it then you should decide whether its worthy or not. You need to get a good...
No of course we don't agree. The usual formulation is for 2 to be a constant (zero place function symbol), that's the usual convention. Now there are ...
I wrote to you the identity relation in ZFC. I already wrote that explicitly it is the reflexive and substitution axiom schema, those are the identity...
hmmm...., let me think about that, I'm really not sure if "identity" really arise in mathematical system per se. But if you consider first order logic...
In set theory, yes that is the case. But of course you can reject set theoretic interpretation of arithmetic. But fishfry is saying the truth about se...
No! There is! Please see my message that just precedes this, where I've pin pointed where is that object and I showed you all denotations involved. Bu...
Those are present in Peano arithmetic in a very clear manner. You can review a full treatment of them. That they are not fixed rule of mathematics, mi...
I read the whole of your message about why symbols must denote other objects etc.. Its nice and very DEEEEEEEEEEP, indeed; and I won't differ with you...
This is indeed a plausible stance! But I think formalists won't agree. I still think that we can have distinctions between numbers even if they are me...
That's a fantastic explanation of Formalism. I know that you don't like it, well, but by the way its really a nice account explaining my intentions. Y...
What you are saying is definitely intelligible and sane, there is no problem with it. Although I might disagree with you about self referring terms, b...
2 is referring to an object (which is itself here), but to identify it in relation other symbols by using the particulars of a certain language (for e...
No problem with two 2's in 2 + 2 being denoting different objects, since they can be interpreted as denoting themselves and they are of course distinc...
I thought we got over that point. I agreed with you that "=" is NOT necessarily the identity function, so why you are returning the discussion backwar...
Well, that is not completely right. I understand very well that "=" can be understood as equivalence relation, I concede to that. I personally would p...
I didn't say that + would make 3 and 5 into one object, I said it will send them to one object, if I did say that it makes them into one object, then ...
Because the rules of arithmetic and and the arbitrary definitions dictates that! I showed you how formally this can run in a prior comment on a system...
There is another problem with miracles, that is how can we know that they are outside the capacity of those stranger beings? I mean those beings are m...
Yes + sends objects denoted by the symbols it occurs between, to some object. The objects denoted by the symbols the symbol of + is written in between...
Finally you are nearly getting what I mean. Yes exactly I'll re-iterate what you wrote because it captures what I said in a very good manner, but I'll...
That's really strange. Just see the example of 'The mother of Jesus and James", this sentence is denoting a single object that is Mary, also Jesus in ...
I generally agree to the subjectivity matter about religious experience. But here I'm dealing with what I might label as "responsible stance" in front...
Those are not my claims. Please read about the syntax of first order logic which is the background logic used in foundational systems of mathematics. ...
Agreed. But for those who request some kind of referential interpretation for the symbols, i.e. semantics, it would be nice to try figure that out as ...
No the operator + doesn't express a relationship between the objects those symbols are denoting, for example lets take the expression "3 + 5" you seem...
all of this is wrong. + is a binary function symbol which means it is a ternary relation symbol, it is a relation between three occurrences of symbols...
Agreed. And I mentioned this to MU. I said that one can indeed interpret the '=' sign as some equivalence relation, no doubt, like that of synonymy, o...
I introduced the object k as an intermediate clarification step, of course it is not mentioned by 2+2. I just want you to answer this question does th...
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