Are the rules of logic immutable?

[OccamsRazor]

In the past my philosophical stance was always based on a single overarching truth. This was that the laws of logic and mathematics were immutable and could not be changed for any description of reality that one may provide.

More recently I have been grappling with the question, what if the rules of logic and mathematics are not immutable but subjective or specific to our incarnation of reality?

In Michael Frayn's book The Human Touch he makes the statement:

Logic is just a system we have made up, not an inherent condition of the natural world.

Is this true? Is logic changeable?

In another thread I saw the following statement:

I don't quite know how knowing something about events inside a system from outside of the system is on the same level of impossibility as a logical impossibility. There cannot be a square circle, a rational root of a prime number or the simultaneous existence of an irresistible force and an immovable object. These are logical impossibilities..

Is this true? Could a being outside our own manisfestation of material reality not create such logical impossibilities?

I can see that here many readers of this post would begin to state that logic and mathematics were immutable. That there indeed could not exist a rational root of a prime number and these are objective truths.
This leads on to the question, how may one prove it? Bearing in mind that any proof of the immutability of logic must have its basis in logic. The question is, how can immutable logic prove istelf to objectively exist?

If we then decide that, possibly, logic is not immutable then where does this leave us? Can we ever make a metaphysical argument without firstly assuming that mathematics and logic are immutable?

[Caligar]

It depends on your point of view. Assuming the logic we use is in fact correct, then it is immutable. But there are lots of holes in our mathematic/science systems,
I.E., in mathematics -X=X, something we know not to be true but is never the less true to mathematics.

[Enrique]

The logic is made of something and by someone. If you modified those somethings the logic will be affected. We create logic. There's no square circle because we first define what a square and circle is. Can i say we even define what 'is' is?
A circle is a circle because is not a square. Then we say by some mind operation that is obvious that a circle square doesn't exist.
Can the logic only be seen as a chemical reaction in our brains determined by physics laws?

[Zorro1]

It depends on your point of view. Assuming the logic we use is in fact correct, then it is immutable. But there are lots of holes in our mathematic/science systems,
I.E., in mathematics -X=X, something we know not to be true but is never the less true to mathematics.

This is because in mathematics the same number can have different variable names. So if X=0 and -X = 0, your statement would be true. Hovever, in logic if X=0, then ~X would equal something other than 0, at the same time, in the same manner.

So, to connect the two statement about X is to equivocate on the terms. They don't mean the same thing, even though they look similar.

Z

[McCulloch]

There's no square circle because we first define what a square and circle is.
A circle is a circle because is not a square. Then we say by some mind operation that is obvious that a circle square doesn't exist.

That is wrong.
A circle is defined as all of the points on a plane that are the same distance (called the radius) from a specified point (called the center) on the plane. Notice that this definition makes no reference to a square. A circle is a circle because it fits this definition of a circle.
A square is four equal length line segments on a plane arranged end to end so that the four angles are equivalent. Notice that this definition makes no reference to a circle. A square is a square because it fits this definition.
A circle is not a square because there is nothing that simultaneously fits the definition of circle and fits the definition of square. That is not some mind operation. That is immutable logic. If logic is not immutable, how can we pretend to know anything?

Can the logic only be seen as a chemical reaction in our brains determined by physics laws?

No. Even if we did not exist to think about it and to provide words to describe it, there still would not be any square circles.

[Zorro1]

This leads on to the question, how may one prove it? Bearing in mind that any proof of the immutability of logic must have its basis in logic. The question is, how can immutable logic prove istelf to objectively exist?

The problem you are stating is, how do you prove logic without being circular? Because if you use logic to prove logic, the vicious circle is before us. But that can't be used as a disproof either, because you would also need to use logic to disprove logic. So, we see that both the affirmation and the denial of logic reguires the affirmation of logic to make either proposition. So the proposition that affirms logic is at least coherent and cohesive with the principles that all the statement to need in order to be made. The negation is self stultifying, in other words the negation, if true, negates the principles that the proposition is based on.

The problem could be futher inflated by pointing out that you can not form a thought without the use of logic. So, for any disproof to be of value, it must be presented without any form of thinking being involved.

Z

[Zorro1]

Can the logic only be seen as a chemical reaction in our brains determined by physics laws?

No. Even if we did not exist to think about it and to provide words to describe it, there still would not be any square circles.

Wait a minute. Enrique is committed to the atheistic cosmology that says nature, matter in motion, is all that exists. In that worldview, not only logic, but all thought is nothing more than chemical reactions based on antecedent causes. Your critique can only be made if your ability to know is independent (or trancendent) of matter in motion. That, of course, is not allowed by any atheistic cosmology.

Z

[McCulloch]

Wait a minute. Enrique is committed to the atheistic cosmology that says nature, matter in motion, is all that exists. In that worldview, not only logic, but all thought is nothing more than chemical reactions based on antecedent causes. Your critique can only be made if your ability to know is independent (or trancendent) of matter in motion. That, of course, is not allowed by any atheistic cosmology.

All thought is nothing more than chemical reactions. Without a brain (or something like a brain) to think them, there are no thoughts. If you define logic as a collection of thoughts about what can or cannot be, then, of course, logic cannot exist without brains.

But there are abstractly concepts apart from any real existence. Mathematicians deal with numbers (integers, rational, irrational, real and imaginary) without reference to what the numbers may represent or measure. The rules they discover about the numbers is independent from their ability to think about the numbers. π (pi) for instance, is an irrational number and was even before there were humans or even life to contemplate it.

If you were to define the immutable rules upon which the existence of the universe has been built on as God, then you could call me a theist (or more likely a deist). But since this is not usually an accepted definition of God, I'll remain with the atheist label.

[Enrique]

First of all, try to be patient with me as i don't know academic ways and don't have much knowledge so I can write or ask silly questions. Put a 'I think' before every sentence.

There's no square circle because we first define what a square and circle is.
A circle is a circle because is not a square. Then we say by some mind operation that is obvious that a circle square doesn't exist.

That is wrong.
A circle is defined as all of the points on a plane that are the same distance (called the radius) from a specified point (called the center) on the plane. Notice that this definition makes no reference to a square. A circle is a circle because it fits this definition of a circle.
A square is four equal length line segments on a plane arranged end to end so that the four angles are equivalent. Notice that this definition makes no reference to a circle. A square is a square because it fits this definition.
A circle is not a square because there is nothing that simultaneously fits the definition of circle and fits the definition of square. That is not some mind operation. That is immutable logic.

When you state the definition of what something is you at the same time imply what is not, you are making a reference to everything else defined. Something is because is not something else. If i have 3 elements i can define one by saying it's not the others two. I was wrong by saying that a circle is a circle because is not a square, but because it's not everything else including the square. You gave me the definition of circle and square with the help of other concepts and rules. Then you must define what those concepts and rules are. Can this iterative mechanic lead us to say that the only way to define something is by dialectic, by opposing things?
Can anything exist because can be differentiated from others?
You ommit my question if we had define what is 'is'? That's because i can't say it?

If logic is not immutable, how can we pretend to know anything?

I think that's the big point of this thread. How can we prove logic nature.

Can the logic only be seen as a chemical reaction in our brains determined by physics laws?

No. Even if we did not exist to think about it and to provide words to describe it, there still would not be any square circles.

The knowledge we generate is based our perception of the universe which is subjetive. Can we build objetivity from subjetivity? I think I'm near the dilema of what comes first: mind or universe? Does the unniverse exist if you don't?

Wait a minute. Enrique is committed to the atheistic cosmology that says nature, matter in motion, is all that exists. In that worldview, not only logic, but all thought is nothing more than chemical reactions based on antecedent causes. Your critique can only be made if your ability to know is independent (or trancendent) of matter in motion. That, of course, is not allowed by any atheistic cosmology.

I don't know what atheistic cosmology implies. I can't tell if dualism is true or false. I really don't know what my position is. I just try to enhance my knowledge

[Enrique]

'IS' has to play a significant role in logic. It can be even the fundamental unit. But there's a problem about 'IS' very related to this thread's one.
How can 'IS' being defined? I can't ask what "IS" is? I can't state 'IS' is ...
Can 'IS' be the fundamental unit of logic and in order to defined it we need other elements?
The origin of 'IS' may be assummed and passed over as they are not part of the logic world but part of our emotional world. 'IS' is(I don't know if it can be defined so) a feeling. Can 'IS' be the bridge between material and logic or thought world? Can 'IS' go further and not to be just a feeling but our primma causa? Can 'IS' be the result of I-Universe duality?