Does “1” refer to an object called “a number”? — Luke
Does “1” refer to an object called “a number”?
— Luke
No, of course not. — Metaphysician Undercover
So "1" is not a number? — Luke
Who is claiming that "1" is an object? — Luke
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.
The point is that there is no need to posit "a number" as existing between the symbol "1", and what the symbol refers to in a particular application of mathematics. — Metaphysician Undercover
...counting numbers is nonsense... — Metaphysician Undercover
Different numerals can represent the same number (or value), such as "4" and "IV" — Luke
Also, different expressions can represent the same number (or value), such as "2x2" and "1+3". — Luke
This indicates "a number as existing between the symbol(s)...and what the symbol(s) refer to". — Luke
I have no problem with saying that a numeral represents a value. That is how we establish equality, by giving different things the same value. — Metaphysician Undercover
"2+2" and "3+1" are just symbols which cannot be said to have any particular value, or refer to any particular value. — Metaphysician Undercover
No such "number" is indicated. "2+2=3+1" is just an expression of symbols — Metaphysician Undercover
To imagine that there is an object called "a number" referred to by "2", or "3", or another type of mathematical object referred to by "2+2", or "3+1" is just an imaginary fiction — Metaphysician Undercover
Then you must concede that there exists an intermediary between a symbol (numeral) and an object: a value. A value is a number.
No, I just explain why this is not the case. Why just go and assert it anyway?
— Luke
Numerals represent numbers which are predicated of objects. — Luke
But a numeral or a number can also be an object. We can speak of three numerals or four numbers, for example. — Luke
Both expressions have a value of 4. A child could tell you that. — Luke
You still need to explain how you can count objects without first being able to count numbers. — Luke
Hold on here, you're jumping ahead of yourself. An object is one, so you cannot predicate any number other than one of an object. If you have a group or set of objects you can count them, assign a quantity or number to that group or set, but take notice that number, or quantity is actually predicated of the group or set, not of the objects themselves. — Metaphysician Undercover
Clearly a numeral is an object, as a symbol. But I do not see how a number can be an object. Number, or quantity is something predicated of a group or set of objects, so how can a number itself be an object? — Metaphysician Undercover
The expression isn't what has the value, it's what the expression refers to that has the value. — Metaphysician Undercover
The numeral "4" does not have the value, of 4, Whatever it is that we refer to with "4", in application, is what is judged to have that value. So "4" is used to refer to that group of objects which is judged to have the value of 4. — Metaphysician Undercover
First you claim that there is no intermediary between symbols and objects, but now you claim that there are both numbers and sets between them? Make up your mind. — Luke
I simply meant that numbers can also be predicated of numerals and numbers themselves. — Luke
Exactly my point. So you need to review your claim that “ there is no need to posit "a number" as existing between the symbol "1", and what the symbol refers to”. “4” refers to neither the symbol nor the objects themselves, but instead to an abstract feature/grouping of those objects: a number. — Luke
...there is no need to posit "a number" as existing between the symbol "1", and what the symbol refers to...
The value we give to the group "4", is an abstract feature, but it's a value — Metaphysician Undercover
A value is a number. Do you acknowledge that? — Luke
Given your two claims above, it looks like you now accept that the “abstract feature” of a value/number exists between the symbol and what the symbol refers to. — Luke
There is a specific type of value, a quantitative value, which people have assigned the word "number" to. You have been working hard to disassociate "quantitative value" from all other forms of value — Metaphysician Undercover
They are different meanings of the word "value", as demonstrated by the Wikipedia article I posted. If you can't accept this, then I wish you well. — Luke
This is what I object to. In no way can a value be an object. — Metaphysician Undercover
This is what I object to. In no way can a value be an object. — Metaphysician Undercover
That was four days ago. And, it's what I've been arguing for weeks. Did it take you this long to figure out that I really. mean what I say? — Metaphysician Undercover
assume you saw the phrase "mathematical object" in the Wikipedia article on value and now you want to argue over the meaning of "objects". — Luke
A mathematical object is an abstract concept arising in mathematics." — Luke
Clearly our disagreement is not in the meaning of "objects", but in the meaning of "value". You want to disassociate quantitative value from all other sorts of value, claiming that mathematical values are something completely distinct and unrelated to any other type of value. But values do not exist in that way, They exist in hierarchical structures, one type of value receiving its worth from another, like a family tree, until the whole structure is grounded in a material desire or want. Aristotle explained this in his Nichomachean Ethics, one end is for the sake of another end, which is for the sake of another, until there is a grounding. Unless you recognize that values are tied together in this way and it is unrealistic, and a misunderstanding, to separate one type of value (quantitative value) from all others, we will always disagree. — Metaphysician Undercover
There is a meaning of the word "value" which is a synonym for "number". — Luke
I'm not talking about a type of value, as in the values that people hold or in what people value. — Luke
It's just another word for a number, or the number represented by an algebraic term. — Luke
Therefore any value is a type of value and the type is determined by the scale. There is no such thing as a value which is independent from a scale of evaluation, and the scale determines the type of value. — Metaphysician Undercover
So unless you are talking about "value" in the most general sense, — Metaphysician Undercover
It's as though I am talking about the bank of a river and you keep telling me that I must be talking about a financial institution. — Luke
I said there are all different types of values. — Metaphysician Undercover
What basis is there for claiming that there is a meaning for "value" which refers to something completely independent from all other types of value — Metaphysician Undercover
1.
the regard that something is held to deserve; the importance, worth, or usefulness of something.
"your support is of great value"
the material or monetary worth of something.
"prints seldom rise in value"
face value
the worth of something compared to the price paid or asked for it.
"at £12.50 the book is good value"
2.
principles or standards of behaviour; one's judgement of what is important in life.
"they internalize their parents' rules and values"
3.
the numerical amount denoted by an algebraic term; a magnitude, quantity, or number.
"the mean value of x"
4.
Music
the relative duration of the sound signified by a note.
5.
Linguistics
the meaning of a word or other linguistic unit.
the quality or tone of a spoken sound; the sound represented by a letter.
6.
the relative degree of lightness or darkness of a particular colour.
This implies the same meaning of word "value" across all "types of values". — Luke
When I talk about this animal here, my cat, "animal" has a completely different meaning from when I talk about that animal over there, my dog. The fact that all the things called "animal" can be classed together in on group, as animals, does not mean that whenever someone refers to one of those animals, "animal" has the same meaning. I am talking about this animal here now, my cat, do you see how the meaning of "animal" is completely different from when I am talking about that animal over there, my dog. — Metaphysician Undercover
I suggested, that a "value" is related to a scale, But this does not mean that when I talk about the value of a dollar, or the value of zero degrees Celsius, "value" has the same meaning. That would be ridiculous. The meaning is determined by the scale being referred to, just like the meaning of "animal" in my example, is determined by the creature being referred to. — Metaphysician Undercover
These are the same meaning of the word "animal", with a definition such as: "a living organism that feeds on organic matter, typically having specialized sense organs and nervous system and able to respond rapidly to stimuli." — Luke
In this discussion, all we've done is digressed, from the meaning of "number" to the meaning of "value", to the meaning of "meaning". — Metaphysician Undercover
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