The Law of Identity is Refuted by Time/Change

[Magnus Anderson]

Says the guy who thinks adding a thing to itself gives you two things.

That's not what I think. Rather, it is you who think that if we can't do the above -- which is indeed impossible to do -- that it is impossible to apply a binary function to one and the same portion of reality.

Basic Definitions

For the sake of convenience, let's not talk about functions in general. The word "function" is a bit too broad for our needs since it can represent almost any kind of relation between two things. Let's focus on causal functions instead.

A causal function is a process that determines the state of one portion of reality ( "output" ) based on the state of other portions of reality ( "inputs". )

The arity of a function is the number of inputs it has. Unary have 1. Binary have 2. Ternary have 3. And so on.

Arity is an arbitrary, linguistic, choice. For every function that has n arguments, where n is greater than 0, there is an equivalent function that has m arguments where m is greater than 0 and different from n.

One and the same portion of reality can be an input to a function more than once.

Your Argument

Your claim is that a binary casual function cannot be applied to one and the same portion of reality.

This is based on your premise that you cannot add a thing to itself.

And I agree with your premise. But I disagree that your conclusion follows from it.

And that's why I keep insisting that you present your full reasoning, not merely bits and pieces of it.

The Problem

The problem is that you're blind to all the other ways that a binary casual function can be applied to one and the same portion of reality. Unlike the method that you keep talking about over and over again, many of these other methods that you DO NOT talk about are logically possible.

Computers can do it just fine, and they do it all the time, but you obviously find it difficult to see it ( even though you're a freak obsessed with computers. )

So let's pick a different example.

Imagine a universe where space and time are infinite in all directions. Imagine a single moment in time where there is nothing in the universe other than 1 apple. Now, consider the one and only law that governs this universe, "The number of apples in the entire universe on any given day is equal to the the number of apples in the entire universe 1 day earlier multiplied by 2." If "n" is the number of apples in the universe today, then "sum( n, n )" is a function invocation that determines the number of apples tomorrow.

The function that is being invoked is a binary function that is applied to one and the same portion of reality. The fact that it refers to one and the same portion of reality does not make it unary.

"sum( n, n )" is equivalent to "mul( n, 2 )" which is equivalent to "twoTimes( n )". They are 3 different invocations of 3 different functions that for the same "n" produce the same output. They are, in effect, 3 different ways to represent one and the same function.

The number of arguments a function has is an arbitrary, linguistic, choice. As a computer programming freak, you should understand these things without me having to spell them out for you. But then again, you have no respect for language, so why would you understand these things?

For every function that has more than 1 argument, there is an equivalent function that has exactly 1 argument.

In computer programming, one way to fight an argument bloat, which is a situation where a function has too many arguments, is via argument bundling, i.e. by combining all of the arguments into a single configuration object. Argument bundling effectively reduces the number of arguments to 1 without changing the behavior of the function. In functional programming, there is a thing called "currying" where functions with multiple arguments are broken down into functions that accept only 1 argument. In functional languages, "sum( a, b )" would be "sum( a )( b )". Instead of having one binary function, you'd have two unary functions.

Question

Is a process of comparing 2 different apples to see if they are equal a binary function or a unary one?

Are 2 apples 2 objects or 1 object?

Who decides?

[Magnus Anderson]

Question #2

Is a process of comparing an apple to itself to see if it's equal to itself a unary function or a binary one?

Is 1 apple 1 object?
Or is it 2 objects e.g. 2 halves of an apple?
Or is it 3 objects e.g. 3 halves of an apple?

[Skepdick]

Now, binary recursion affords us exactly four categories of Grammar called a Grammar Matrix. Each member has an historically established name: Common Grammar, Arithmetic, Algebra and Geometry. Something like 5 - 0 = 5. If A - n = A, then n = 0.

So, show everyone that you can do the same line of reasoning in at least one other grammar beside common grammar.

Duh!

Why not just regular recursion; or co-recursion? You can have as many categories as you want or need. None,1, 2 or infinitely many.

Your "Grammar Matrix" is missing quite a few disciplines.

You do not read much, study much, or think much do you? By biological fact, as Plato noted, what can you actually name? Here is another hint, how many parts of speech does even the definition of a thing tell you exists? How many parts of speech does a computer use to process all information/

Good god man, get a thought!

When it comes to information processing, you might want practice your arguments on the own computer. See if it will change its behavior.

"get a thought" (says the man without any original ones).

Yes, arguments change a computer's behaviour. That's how programming works. That's what programs do. They instruct behaviour.

[Skepdick]

That's not what I think.

Why are you lying?

that it is impossible to apply a binary function to one and the same portion of reality.

Way to misunderstand. You can't use a single resource twice. Try eating the same apple twice.

A binary function requires TWO resources.
If you have only ONE resource; you have to DUPLICATE your resource in order to use it TWICE.

This is a trivial idea, man. It's copying/replication.

Basic Definitions

blah blah blah

Definitions don't matter. We are talking about how logical operations behave.

Can you apply a binary function to a single object; or not?
Can you compare (binary function) a single apple to itself?

And the answer is trivial. No, you can't. Because you need to copy the apple to get two apples.

Question

Is a process of comparing 2 different apples to see if they are equal a binary function or a unary one?

That's not the question.

The question is whether the process of comparing a single apple to itself is a "binary" process.

Are 2 apples 2 objects or 1 object?

Who decides?

Don't give a shit. That's not the question.

[Magnus Anderson]

A binary function requires TWO resources.
If you have only ONE resource; you have to DUPLICATE your resource in order to use it TWICE.

This is the kind of idiocy that results when you disregard the importance of language, namely, that all thinking operates on symbols, and thus, that there is no thinking without language.

A binary function requires two ARGUMENTS. Not two different portions of reality but two ARGUMENTS. That's what makes it binary.

How many resources is 1 apple?

Is it 1 resource, i.e. 1 apple?

Or is it 2 resources, i.e. 2 halves of the same apple?

Or is it more than that given that an average apple consists of around 6 trillion trillion molecules?

1 apple = 2 halves of the apple = 6 trillion trillion molecules.

These are 3 different but accurate descriptions of one and the same thing.

It is precisely language that allows us to accurately describe one and the same portion of reality in an infinitely many different ways.

A recovering direct realist finds it difficult to understanding this despite the fact he has distanced himself from direct realism. He still does not understand that language precedes perception. And as long as he fails to understand this simple yet very important fact, he will be stuck between direct and indirect realism, never fully embracing either.

Consider a function called "isItself". This function basically determines whether or not the given portion of reality has the same identity as itself. Of course, it always returns true. But the question is, how many arguments does it have?

The answer to that question, of course, is as many as you need.

It can be one, e.g. isItself( apple ).
It can be two, e.g. isItself( 1/2 apple, 1/2 apple ).
It can be three, e.g. isItself( 1/3 apple, 1/3 apple, 1/3 pple ).
And so on.

Do you want to represent a thing as 1 whole or as multiple parts of the whole?

It's your choice.

You've been quibbling about this shit for too long pretending as if it's somehow relevant to the topic at hand ( which it clearly isn't. )

It's called DISTRACTION.

[Magnus Anderson]

Don't give a shit. That's not the question.

You said that "isItself" is a unary function.

But is it necessarily so?

Let me write you some code.

Code: Select all

function isItself( apple ) {

  return true;

}

Here, you have one argument representing the apple.

Apple is represented as 1 whole.

Code: Select all

function isItself( appleTopHalf, appleBottomHalf ) {

  return true;

}

Here, you have two arguments representing the apple ( "appleTopHalf" and "appleBottomHalf". )

Apple is represented as 2 parts of a whole.

Is the function unary or is it binary?

Or is it an arbitrary choice?

You can hide from reality all you want but reality won't hide from you.

[Magnus Anderson]

Definitions don't matter.

Ergo, thinking does not matter either.

[Magnus Anderson]

Can you apply a binary function to a single object; or not?

Is a single object 1 object, 2 objects or is it some other number of objects? Or is it all of these?

Is a single apple 1 object or is it 2 objects, e.g. a top half and a bottom half of the apple? Or is it both?

And if 1 apple is the same as 2 halves of it, what makes it difficult for you to apply a binary function to it?

Can you compare (binary function) a single apple to itself?

Yes, you can. There's no need to make a copy of it. All you have to do is construct two accurate maps of it. Then you have to simply compare the two maps in terms of how they describe that apple. In fact, that's what you do whenever you do any comparison. You're always only comparing your maps of reality. You have no direct access to reality.

[Skepdick]

Definitions don't matter.

Ergo, thinking does not matter either.

Only an idiot like you thinks that follows. Thinking is a priori definitions.

[Magnus Anderson]

Thinking is a priori definitions.

Well, it just happens that you're wrong.

[Magnus Anderson]

Consider a function that calculates the color of the average pixel of a 3x3 bitmap image.

The bitmap image is 3x3 in size wihch means it's 3 pixels wide and 3 pixels high. That, in turn, means there are 9 pixels in total. Each pixel has a color value represented as an integer between 0 and 255.

Is the arity of such a function necessarily 1?

Here's a version of the function that takes exactly 1 argument.

Code: Select all

function avgPxColor( bitmap ) {

  let sum = 0;
  
  for ( let y = 0; y < 3; y++ ) {
    
    const row = bitmap[ y ];
    
    for ( let x = 0; x < 3; x++ ) {
    
      sum += row[ x ];
    
    }
  
  }
  
  return sum / 9;

}

And a version with 9 arguments.

Code: Select all

function avgPxColor( p00, p01, p02, p10, p11, p12, p20, p21, p22 ) {

  return (
    p00 + p01 + p02 +
    p10 + p10 + p12 +
    p20 + p21 + p22
  ) / 9;

}

[Skepdick]

Thinking is a priori definitions.

Well, it just happens that you're wrong.

OK. Then the conclusion is pretty obvious. YOU can't think outside of definitions.

That sounds like a YOU-problem.

[Skepdick]

blah blah blah

You don't even understand the difference between 1st order and 2nd order functions.

[Skepdick]

Yes, you can. There's no need to make a copy of it. All you have to do is construct two accurate maps of it.

Then you have to simply compare the two maps in terms of how they describe that apple. In fact, that's what you do whenever you do any comparison. You're always only comparing your maps of reality. You have no direct access to reality.

You don't even understand the difference between comparing apples; and comparing maps of apples?

Wow.

[Magnus Anderson]

You don't even understand the difference between 1st order and 2nd order functions.

I do. But you don't understand what understand and what I do not.