So you're saying that the way you defined "and" isn't A = A? — Skalidris

The way I defined "and" does not say "A = A."

You defined it as: "the "and" operator is an attractor that puts multiple members into one set" — Skalidris

Here's the correct translation of my verbal equation to a math equation: Given A, A (two unconnected, identical machine parts), with the entrance of the conjunction operator $∧$ we get
{$A∧A = 2A$}.

A = A is not a multiplicity of A twice; it is one A, itself.

You used multiple to define it but multiple is just a step further from "and" (if you take one element AND another, you have MULTIPLE elements). — Skalidris

No. I did not use "multiple" to define the conjunction operator. I used "attractor" to describe what it does: connect. Perhaps you'll argue that connecting is just the same as multiplying. They're related, but they're not identical. We can prove this by showing how 3+4 = 7, whereas 3x4 = 12.

Also, as you say, “multiple is just a step further from ‘and…’”. Well, one step further is a positive distance from the previous step, so the two positions are different. What this means in our context here is that

…(if you take one element AND another, you have MULTIPLE elements). — Skalidris

Your description shows us that the conjunction operator is a function that renders a connection linking multiple parts. This process that renders connected parts is distinct from the connection it produces. The connection is the result of the process. We know the two things are distinct because parts don’t connect without a process that renders the connection. An example is a truck and the trailer it pulls. The truck and the trailer don’t connect unless there’s a trailer hitch that performs the function of connecting the two.

Suppose "trailer hitch" is defined as "a connector that links truck and trailer." This definition has the same form as "...the "and" operator is an attractor that puts multiple members into one set." I want you to show how both definitions are indistinguishable from the definition of "and."

If A = B but the only meaningful way to define B (or an element within B) is B = A, it's the same as A = A. It's only meaningful in language, if you don't know the word for "and" and that someone tries to explain what that means, they can use words that you know that imply the concept "and", but that doesn't mean they've defined it in a meaningful way. — Skalidris

The underlined part of your quote is incorrect. With A = B, you've set up an equation of the type:
5 = 2+3. This is not A = A, which could be 5 = 5, or 2+3 = 2+3. A and B, as your eye can see, are not identical, as the case with A = A. Stop conflating equivalent with identical.

When you stop conflating equivalent with identical, you’ll see clearly that saying: “He tried to bother me.” differs from saying: “He tried to harass me.” The two verbs are roughly equivalent, but certainly not identical.

But if A is an element of C and that C= B∧A, defining A as C without B isn't meaningful. — Skalidris

If A is an element of C such that C = {A∧B}, then defining A as C is a non-sequitur.

For clarity, consider you have a pizza with mushrooms and bell pepper toppings. This establishes bell pepper as an element of the pizza. Does it make sense to go from there to saying bell pepper equals the pizza?

I now see that your argument denounces my definition as redundant. The issue in our debate is whether my definition is distinct from Webster’s definition of “and.” This is a very different issue from arguing that a definition is neither meaningful or useful. Since you've used these words to make your argument, claiming my definition possesses neither attribute, I've been assuming they accurately express the point of contention. They don't.

Although my definition says nothing not already said, I claim it is still distinct from Webster’s definition of “and.” My definition emphasizes “connect” within the context of set theory.

As I now think you're saying a fundamental definition cannot be redefined usefully because of redundancy, I go along with you most of the way, but not all of the way because of the issue of context. If it’s best to insert 5 into one context, whereas it’s best to insert 2+3 into another context, then that stands as a minor example of usefully spinning a fundamental definition.

No. I did not use "multiple" to define the conjunction operator. — ucarr

In other words, the "and" operator is an attractor that puts multiple members into one set — ucarr

You did, you used multiple in the definition. If you only want to used attractor, when you define attractor, you'll still have two use a word similar to multiple, several, and, connect, which all contain the same essence that's fundamental and can't be defined in a meaningful way (or, since you don't like saying that, it simply can't be explained). In other words, if you can't define/explain "and" with smaller parts it's made of, it creates the circularity, the self reference. Do you know what I mean or don't you? Because it's not clear from your response, I'm not sure about where you're going with this.

Perhaps you'll argue that connecting is just the same as multiplying. They're related, but they're not identical. We can prove this by showing how 3+4 = 7, whereas 3x4 = 12. — ucarr

Multiple isn't the same as multiplying... Just as you said here.

multiple | ˈməltəp(ə)l |
adjective
having or involving several parts, elements, or members — ucarr

The underlined part of your quote is incorrect. With A = B, you've set up an equation of the type:
5 = 2+3. This is not A = A, which could be 5 = 5, or 2+3 = 2+3. A and B, as your eye can see, are not identical, as the case with A = A. Stop conflating equivalent with identical. — ucarr

No, the problem I mention is when A = 7-2 rather than 2+3. But the analogy with numbers doesn't work because we know that we can break down 5 in a lot of ways, and the problem I mentioned is when 5 can't be broken down into smaller units, smaller operations. Basically the question "how do you make 5?" is left unanswered and the only way to "define it" is to take a "bigger" category and remove other elements from it, or to use synonyms.

Does it make sense to go from there to saying bell pepper equals the pizza? — ucarr

Bell pepper equals pizza (containing bell peppers) minus all the other elements. That's what I meant when I said "C without B", it means C minus B.

you're saying a fundamental definition cannot be redefined usefully — ucarr

Again, no, I did not say that. I mentioned the use in language here:

It's only useful if you don't know the word for A — Skalidris

If it’s best to insert 5 into one context, whereas it’s best to insert 2+3 into another context, then that stands as a minor example of usefully spinning a fundamental definition. — ucarr

Yes, trouble is that, in the context of primitive notions, you can't define 5 as an addition of smaller parts.

Physicalism Is Dead — Marc Wittmann

Thank goodness that's finally settled!


:rofl:

No. I did not use "multiple" to define the conjunction operator. — ucarr

You did, you used multiple in the definition. If you only want to used attractor, when you define attractor, you'll still have two use a word similar to multiple, several, and, connect, which all contain the same essence that's fundamental and can't be defined... — Skalidris

...if you can't define/explain "and" with smaller parts it's made of, it creates the circularity, the self reference. — Skalidris

In other words, the "and" operator is an attractor that puts multiple members into one set — ucarr

I need to change my definition as follows:

In other words, the "and" operator is a connector that links multiple things that are to be taken jointly — ucarr

The word changes do not alter the meaning of the definition except to make it a more accurate description: to connect by linking things together.

and (conjunction) -- used to connect things that are to be taken jointly

multiple (adjective) -- having several parts

When you look at the two definitions, why do you think they are one and the same?

3x4 = 12 — ucarr

Multiple isn't the same as multiplying... Just as you said here. — Skalidris

Regarding the equation with the multiplying function, why do you deny that 12 is a multiple of 3 and 4?

...the problem I mentioned is when 5 can't be broken down into smaller units, smaller operations. — Skalidris

It's true prime numbers are limited as to how they're factored, but your argument includes more than the primes.

Bell pepper equals pizza (containing bell peppers) minus all the other elements. — Skalidris

This statement says bell pepper stands alone, or B = B. B $≠$ B + P

...you're saying a fundamental definition cannot be broken down into subordinate parts — ucarr

This is true.

You're saying when the terms of a fundamental definition are not known to someone, synonymous terms of equal meaning known to that person are useful in the effort to communicate the definition to them.

This is true.