And numbers are not even countable objects in the first place, they are imaginary, so such a count, counting imaginary things, is a false count. Therefore natural numbers ought not be thought of as countable. — Metaphysician Undercover
First, there is no general definition of number in mathematics.
— fishfry
That's because numbers are not objects, and therefore they cannot be described or identified as such. And since they cannot be identified, they cannot be counted. — Metaphysician Undercover
What is your definition of number?
— fishfry
It is a value representing a quantity. — Metaphysician Undercover
Not in math. After all, some numbers have neither quantity nor order, like 3+5i3+5i in the complex numbers. No quantity, no order, but a perfectly respectable number. You take this point, I hope. And are you claiming a philosopher would deny the numbertude of 3+5i3+5i? You won't be able to support that claim.
— fishfry
Yes, that's a symptom of the problem I explained to TIDF. — Metaphysician Undercover
Once we decide that numbers are objects which can be counted, then we need to devise a numbering system to count them. So we create a new type of number. Then we might want to count these numbers, as objects as well, so we need to devise another numbering system, and onward, ad infinitum. Instead of falling into this infinite regress of creating new types of imaginary objects (numbers), mathemajicians ought to just recognize that numbers are not countable, and work on something useful. — Metaphysician Undercover
Of course I'm wrong mathematically, I'm arguing against accepted mathematical principles. — Metaphysician Undercover
But the question is one of truth and falsity. Are numbers objects which can be counted, rendering a true result to a count, or are they just something in your imagination, and if you count them and say "I have ten", you don't really have ten, a false count is what you really have? — Metaphysician Undercover
fractions for dividing up a pumpkin pie — fishfry
I've answered that already a few times. To have a non-empty count, of course there exist the objects counted, and in you example, these objects are books. — TonesInDeepFreeze
Now I'm answering yet again, there is no no-empty count if there are not objects counted.
Now, are you going to continue asking me this over and over again? — TonesInDeepFreeze
I can count the captains of the starship Enterprise even though they're imaginary. — fishfry
Curious to know: If you deny complex numbers do you likewise deny quantum physics, which has the imaginary unit i in its core equation? — fishfry
If you count "1", then it is implied that there is one thing (an object) counted. Do you, or do you not agree with this?
— Metaphysician Undercover
Agree. — TonesInDeepFreeze
I think you agree with me on the necessity of having two objects to make the use of "2" or "second", a true or valid use. — Metaphysician Undercover
To have a count of one, there must be an object which is counted. In order for the count to be a valid count, there must be something which is counted. — Metaphysician Undercover
Do you agree that there must be some of these things (objects) which are classed as "books", for us to have a true count.
— Metaphysician Undercover
I've answered that already a few times. To have a non-empty count, of course there exist the objects counted, and in you example, these objects are books. — TonesInDeepFreeze
Do you agree that there is no activity of counting if there is no objects counted?
— Metaphysician Undercover
Now I'm answering yet again, there is no no-empty count if there are not objects counted. — TonesInDeepFreeze
Therefore the number 5 loses its meaning if it does not refer to five of something counted, books in this case. — Metaphysician Undercover
In everyday understanding, when we count, we associate one thing with 1, then the next thing with 2, etc. — TonesInDeepFreeze
To have a count of one, there must be an object which is counted. In order for the count to be a valid count, there must be something which is counted. — Metaphysician Undercover
The count of two is justified by the existence of two such objects — Metaphysician Undercover
If no books are counted, do you consider this to be a count? — Metaphysician Undercover
do you agree that it is necessary that there is a thing counted
— Metaphysician Undercover
To have a count (in sense (1)), you need something to count. (Except in the base case, there is the empty count.) — TonesInDeepFreeze
I'm asking you if you believe there is such a thing as an empty count — Metaphysician Undercover
you are counting hypothetical doors, symbolic representations of doors — Metaphysician Undercover
If you present this as a true count of actual captains of an actual starship, you'd be engaged in deception. — Metaphysician Undercover
And that parenthetical is simply to make clear that in this context we're not talking about the technical notion of an empty count. We're talking about counts that start at 1. — TonesInDeepFreeze
If there is a count that reaches 1, then there exists at least one object counted, and if there is a count that reaches 2, then there exist at least two objects counted. — TonesInDeepFreeze
Your original and ongoing question regarded the context in which there are books on the shelf. You didn't ask me about the notion of an empty count. — TonesInDeepFreeze
But about the empty count: It's a technical set theoretical matter. It's not intended that the use of the word 'count' in 'empty count' corresponds to our everyday English senses of 'count'. I happily agree that it's an odd use of the word 'count'. If you don't like the notion, then that's okay in this context, because the representation with a bijection doesn't depend on the notion. — TonesInDeepFreeze
We are not claiming it is a count of actual captains. — TonesInDeepFreeze
Why do you keep avoiding the question? — Metaphysician Undercover
within a logical system you cannot change the "sense" of a word without the fallacy of equivocation — Metaphysician Undercover
If we are going to say that zero objects is a countable number of objects, then we need a definition of "count" which is consistent with this. — Metaphysician Undercover
None. We know that there are zero, without counting any. — Metaphysician Undercover
if we can assign such a value to imaginary things in a similar way, we need a principle to establish equality, or compatibility, between observed things and imaginary things. This is required to use negative numbers. — Metaphysician Undercover
That's what I would call a false count, because it's hypothetical. It's like if you look at an architect's blueprints, and count how many doors are on the first floor of a planned building. You are not really counting doors, you are counting hypothetical doors, symbolic representations of doors, in the architect's design. Likewise, if you count how many people are in a work of fiction, these people are hypothetical people, so you are not really counting people, you are counting symbolic representations. We can count representations, but they are counted as symbols, like the architect's representation of a door, may be counted as a specific type of symbol. And when you count captains of the Enterprise, you are likewise counting symbolic representations. If you present this as a true count of actual captains of an actual starship, you'd be engaged in deception. You are not counting captains of a starship, only symbolic representations. — Metaphysician Undercover
Yes, I think quantum physics uses a very primitive, and completely mistaken representation of space and time. That's why it has so many interpretative difficulties. — Metaphysician Undercover
I want to be clear in my mind. Is this your position on the subject? — fishfry
Read my last post. — Metaphysician Undercover
Then why do you ask me to repeat myself? — Metaphysician Undercover
Then why do you ask me to repeat myself? — Metaphysician Undercover
I'm thinking that I've read your last post. — fishfry
Look, I think it's very important for a rigorous mathematics to distinguish between counting real things, and counting imaginary things. — Metaphysician Undercover
This is because we have no empirical criteria by which we can determine what qualifies as a thing or not, when the things are imaginary. — Metaphysician Undercover
Therefore we can only count representations of the imaginary things, which exist as symbols. — Metaphysician Undercover
So we are not really counting the imaginary things, but symbols or representations of them, and we have empirical criteria by which we judge the symbols and pretend to count the imaginary things represented by the symbols. — Metaphysician Undercover
But this is not really counting because there are no things being counted. We simply assume that the symbol represents a thing, or a number of things, so we count them as things when there really aren't any things there at all. — Metaphysician Undercover
So counting imaginary things by means of symbols is completely different from counting real things because one symbol can represent numerous things, like "5" represents a number of things. — Metaphysician Undercover
And we aren't really counting things, we are inferring from the symbol that there is an imaginary thing, or number of things represented by the symbol, to be counted. — Metaphysician Undercover
So it's a matter of faith, that the imaginary things represented by the symbol, are really there to counted. — Metaphysician Undercover
But of course they really are not there, because they are imaginary, so it's false faith. — Metaphysician Undercover
So we are not really counting the imaginary things, but symbols or representations of them — Metaphysician Undercover
But this is not really counting because there are no things being counted. — Metaphysician Undercover
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