This is how I represent "one dollar", like that or like this, $1. Something equal to a dollar is "ten dimes", or "four quarters". I really do not believe that you can't see the difference, I think you're in denial. — Metaphysician Undercover
This is no different to what I mean when I say that they are different expressions of the same value. — Luke
You seem to think that the law of identity has some bearing on mathematics, or that A=A is somehow relevant to mathematical equations. I fail to understand what the relevance is. There would be little point using mathematical equations to state, e.g., 4=4. It seems that you just enjoy the confusion you create by treating the law of identity like a mathematical equation, or vice versa. — Luke
MY point is that "different expressions of the same value" refer to different things. — Metaphysician Undercover
"Ten dimes" refers to something different than "four quarters". — Metaphysician Undercover
There's more than [...] — Metaphysician Undercover
I don't seehow it's relevant— Metaphysician Undercover
You repeat the confusion. "Different expressions of the same value" are different wrt their expressions (or "representations"), but the same wrt their value. — Luke
es, but "ten dimes" and "four quarters" have the same value; they both "refer" to a value of one dollar. — Luke
Edit: There is no philosophical significance in pointing out that a dime is different to a quarter, or that "2" is different to "4". It goes without saying. You clearly exploit those cases where the values are the same (but the expressions are different) merely to provoke a response. — Luke
Everyone else understanding should tell you something. — jorndoe
And, if I say "2+2", you could infer that I am taking about the quantity represented by "4", but in no way am I talking about the quantity represented by "4". You simply apply some logical premise and make that conclusion. — Metaphysician Undercover
here is no "logical premise" involved; that's simply how we use mathematical equations: the equals sign means that the value on the left is equal to the value on the right. "2+2=4" is a mathematical equation. — Luke
To make the case that each side of the equation is different in a way which is unrelated to their values, i.e. in their symbols, or in what those symbols refer to, is just being a troll. Obviously, they are different in that sense; just look at the bloody symbols. That difference does not need to be pointed out. You are trolling for a response, and I won't oblige you any further. — Luke
Call it "being a troll" if you like. I look at it as a trivial matter. The problem is that the difference needed to be pointed out, because fishfry kept insisting that the very same thing is represented on the left side as the right side of the equation. — Metaphysician Undercover
it seems very obvious from this thread that many people misunderstand — Metaphysician Undercover
Af far as I can see, you're the only one that don't understand typical use of "value" (e.g., as in variables that may take values, like some/any proposition p in non-contradiction ¬(p ∧ ¬p)). I suppose, if you don't even (want to) try, then so be it. — jorndoe
I just can't see how the fact that a specific variable can be assigned different values, is at all relevant. That's simply the nature of a value, because value is relative there is a degree of arbitrariness. One dollar appears to be a constant value, but when considered within the context of the international market, it is variable. — Metaphysician Undercover
Therefore that value is "relative" to that system. — Metaphysician Undercover
Otherwise I could arbitrarily say that a chair and a table have the same value to me, therefore they are the same intelligible object. — Metaphysician Undercover
Do you even know what "value" means? It refers to the desirability of a thing, or what a thing is worth. — Metaphysician Undercover
The principles that the system is based in, the arbitrariness of the system, is a further matter. — Metaphysician Undercover
That's simply the nature of a value, because value is relative there is a degree of arbitrariness. — Metaphysician Undercover
This appears quite different to your previous comments, where the value was not relative to a mathematical system, but instead relative to you: — Luke
It is clear that you have had this meaning of "value" in mind the entire time, and have misunderstood the meaning of "value" as used in mathematics, and by most of us here. — Luke
In what sense is a mathematical value arbitrary? — Luke
The point is that it is relative to something. Whether it is relative to my own personal decision, or agreed upon decision (convention), does not change the nature of what a value is, itself. — Metaphysician Undercover
there you go again with your uncharitable interpretation for the sake of straw manning. You, yourself, introduced ambiguity onto the meaning of "value", trying to distance your use of "value" from my use of value, for the sake of your straw man, when no such separation is warranted. — Metaphysician Undercover
Look, it is completely arbitrary that the symbol "2" represents the quantitative value which we call "two". To remove the arbitrariness we might assume an object, a number, which "2" and "two" refer to. — Metaphysician Undercover
That two distinct things are equal, and therefore have the same value, is inherently arbitrary, but that they are distinct individuals, allowing us to number, or count them individually, is grounded in real difference. — Metaphysician Undercover
How is, e.g. the set of natural numbers, relative to your own personal decision? — Luke
Also, how can it be relative if your decision "does not change the nature of what a value is, itself"? You're talking out of both sides of your mouth. — Luke
The ambiguity exists in the language because the word "value" has more than one meaning. If you think that mathematical value, or the set of natural numbers, has anything to do with "the desirability of a thing", then you are plainly incorrect. — Luke
You're aware that we can count independently of counting things, right? — Luke
This arbitrariness of "a value" is just further evidence that having the same value does not imply being the same intelligible object. Otherwise I could arbitrarily say that a chair and a table have the same value to me, therefore they are the same intelligible object. — Metaphysician Undercover
A mathematical value is a type of "worth" — Metaphysician Undercover
No, that's clearly wrong, mathematics has to do with the desire to count and measure things. Counting and measuring are desirable things. Therefore contrary to your ignorant assertion, assigning a quantitative value to things is the result of the desirability of something, counting and measuring, because these are desirable things to do, there's a purpose to them. — Metaphysician Undercover
In general, a mathematical value may be any definite mathematical object. In elementary mathematics, this is most often a number – for example, a real number such as π or an integer such as 42.
— The value of a variable or a constant is any number or other mathematical object assigned to it.
— The value of a mathematical expression is the result of the computation described by this expression when the variables and constants in it are assigned values.
— The value of a function, given the value(s) assigned to its argument(s), is the value assumed by the function for these argument values.
For example, if the function f is defined by f(x) = 2x^2 – 3x + 1, then assigning the value 3 to its argument x yields the function value 10, since f(3) = 2·3^2 – 3·3 + 1 = 10.
And as I explained in the last post, if "1" refers to an object called "a number", then "2" cannot refer to two distinct occurrences of that same number, or else we would not have two, but only one still. — Metaphysician Undercover
Therefore that act of counting independent of counting something, is just an exercise in remembering an arbitrary ordering of symbols — Metaphysician Undercover
In general, a mathematical value may be any definite mathematical object.
1+1=1? — Luke
Right, sort of like remembering the alphabet. Are you claiming it's not possible? Just because we can count (and do simple arithmetic) independently of "things" does not imply that we cannot count things or that we never count things. — Luke
If "1'" refers to an object called a number, then "1+1" indicates two distinct instances of the same object, which is still just the same object. So "1+1" would signify only 1 object if this were the case. — Metaphysician Undercover
Therefore, to remain consistent with common usage and adhere to true principles of numerology, we must accept the conclusion that "1" does not refer to a mathematical object called a number because this would allow the representation of two distinct instances of the same object "1" to be the same as "2". But according to common usage in counting, "2" cannot refer to a second instance of the same thing. — Metaphysician Undercover
How can "two distinct instances of the same object" amount to only one object? — Luke
This is like arguing over the rules of chess with someone who doesn't know the rules. I'm done. — Luke
Rule number one, you must count distinct objects, you cannot count the same object twice. No matter how many times the same object appears in front of you, you still only have one object. — Metaphysician Undercover
Isn't this obvious to you? If I count the object as "1" at time x, then I count the very same object as 2 at time y, this is a faulty count, counting the same object twice. Two instances of seeing the very same object, therefore a faulty count if I say there's two objects. — Metaphysician Undercover
if "1" refers to an object called "a number", then "2" cannot refer to two distinct occurrences of that same number, or else we would not have two, but only one still. — Metaphysician Undercover
So we can’t add 1+1 - is that your argument? — Luke
No, "1" is a symbol. So long as each 1 represents a different object there is no problem to add 1+1 and get 2. — Metaphysician Undercover
In other words, it appears to me like mathematicians have posited a type of "object" which is metaphysically unacceptable. — Metaphysician Undercover
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