Can the mind think about non-existing things?

[dhuisjen2]

I confess to being something of a dualist, or maybe even a more abstract multiplist than that. God exists and God is not a physical phenomenon. Nor is (IMHO) is God a mental phenomenon built on physical phenomena, like the green elephant.

Karl Popper talks about three levels of reality: 1) physical reality (such as the rust on my Mazda); 2) mental realities (such as my distrust for my ex-mother-in-law) and 3) socially constructed realities (such as the ASCII code). I would add a fourth in terms of absolute metaphysical foundations: God and His laws.

These are easiest to relate to in terms of mathematical realities. For example pi can be calculated out to billions of places, but you will never find a physical circle with perfectly demonstrates the true value of pi as far as it can be calculated. Nor is the value of pi the result of personal perceptions, nor is it dependant on interpersonal communications.

The problem in talking about this fourth dimension of reality is that it can easily get caught up in a discussion of Platonic ideals. In simple terms, has God made man(kind) in his own image, or visa-versa, or both.

Thus, for me, the hard part is not to be able to think about things beyond what we can abstact from the physical world ; the hard part is assigning a place within the various levels of reality to each particular cognitive phenomenon.

 

[quatona]

Real in this context refers to existence. Evil is unloving acts, not unmatched expectations.

But that´s just for mind readers. What I experience as real is that my expectations, desires and wishes are matched or not matched. The rest would be pure speculation.

 

[quatona]

I'll frame my question in three parts:

1) What is a non-existing thing?

In my understanding no "thing" exists. Distinguishing something as "thing" is a process of my mind. The "thing" is the product of this process.
If we define the products of our minds to be existing, then, yes, "things" exist.

2)Is it limited only to physical existence?

Is what limited to physical existence? I´m afraid I don´t understand the question.

3) Can the mind think about non-existing things?

Yes, this is exactly what and all that the mind does all the time.

 

[Born_to_Lose_Live_to_Win]

Is what limited to physical existence? I´m afraid I don´t understand the question.

Is the definition of a non-existent "thing"(for pragmatic reasons) limited to those that cannot be externally perceived by the senses but exist only in the mind?

Yes, this is exactly what and all that the mind does all the time.

I agree, but in a different way. The mind is able to think about non-existent things because existence underlies these thoughts. Something actual is thought of as something else.

 

[quatona]

Is the definition of a non-existent "thing"(for pragmatic reasons) limited to those that cannot be externally perceived by the senses but exist only in the mind?

No, not in my view. "Things" are just products of our minds, no matter whether we perceive "things" by our senses or by mere intellect.

I agree, but in a different way. The mind is able to think about non-existent things because existence underlies these thoughts. Something actual is thought of as something else.

I don´t think there is such as "something actual" (as opposed to "something else"). Whatever we identify as "thing", this is merely a product of our minds.

 

[StrugglingSceptic]

I'll frame my question in three parts:

1) What is a non-existing thing?

A hypothetical object whose properties are not instantiated.

2)Is it limited only to physical existence?

No. The largest prime number is non-existant.

3) Can the mind think about non-existing things?

Yes. To prove that the largest prime number is non-existant, I can temporarily consider such an object and obtain a contradiction.

The fact that a one with an infinite number of zeros behind it is no closer to the end of the infinite number string than any other number makes the concept absurd and unfathomable. The concept breaks down and we realize we never had a concept of it to begin with. We only had the illusion of a concept.

We have consistent mathematical formulations of infinity. An infinite set is a set which can be put in one-to-one correspondence with a strict subset of itself. We even have infinite numbers: transfinite cardinals and ordinals. None of these objects are absurd or unfathomable. They are precisely defined and conclusions about them have been rigorously derived within set theories.

 

[TeddyKGB]

Yes. To prove that the largest prime number is non-existant, I can temporarily consider such an object and obtain a contradiction.

There is no object to consider, temporarily or otherwise. "The largest prime number" is a contradiction in terms, made so by prior conditions.

 

[Lifesaver]

We can think of non-existing things as long as they are not logically contradictory. If they are, then they are not things at all, in fact, and we can't even properly refer to them.

Existing entities can be physical or non-physical, that is, corporeal or incorporeal. Your desire to drink some water, for example, is incorporeal, even though it has corporeal causes.

 

[StrugglingSceptic]

There is no object to consider, temporarily or otherwise. "The largest prime number" is a contradiction in terms, made so by prior conditions.

Did you even read my post? Yes. It is a contradiction, but such a (hypothetical) object may be considered for the purpose of deriving a contradiction. There is nothing wrong with a mathematical proof beginning with "suppose there is a largest prime p". Proofs frequently begin with these kinds of statement.

 

[TeddyKGB]

Did you even read my post? Yes. It is a contradiction, but such a (hypothetical) object may be considered for the purpose of deriving a contradiction. There is nothing wrong with a mathematical proof beginning with "suppose there is a largest prime p". Proofs frequently begin with these kinds of statement.

That is a modality. In the original case a contradiction is arrived at via reductio ad absurdum; no object need be considered.

 

[StrugglingSceptic]

That is a modality.

As I have stated already -- the object is hypothetical.

In the original case a contradiction is arrived at via reductio ad absurdum; no object need be considered.

The object is considered, for the purposes of carrying through the proof by contradiction. A better example is the standard proof that the square root of two is irrational:

Suppose there exist integers p and q such that (p/q)^2=2.

The integers p and q do not exist, but their existence is considered (supposed) for the purposes of deriving a contradiction.

 

[TeddyKGB]

The object is considered, for the purposes of carrying through the proof by contradiction. A better example is the standard proof that the square root of two is irrational:

Suppose there exist integers p and q such that (p/q)^2=2.

The integers p and q do not exist, but their existence is considered (supposed) for the purposes of deriving a contradiction.

For something to be an object it must have at least the potential to exist. The existence of either p or q is precluded a priori by underlying principles. A triangle whose angles add to 240 degrees is similarly a non-object. "A triangle whose angles add to 240 degrees" does not describe a potentially existing thing.

 

[spdnet75]

I'll frame my question in three parts:

1) What is a non-existing thing?
2)Is it limited only to physical existence?
3) Can the mind think about non-existing things?

I believe your question can be explained, in part by something called 'Quantum Superposition" .
If I place a coin on a table and ask you where that coin is, you would be inclined to point to it and say, "It's right there" .
The real question is, "where was that coin before you and I recognized it? "
The answer is that it was in an inordinate number of places before we both perceived it as being there.
Human beings are reality producing machines and we are the ultimate observers. So, nothing is anything or anywhere until perceived as being so by an outside observer.

 

[quatona]

I believe your question can be explained, in part by something called 'Quantum Superposition" .
If I place a coin on a table and ask you where that coin is, you would be inclined to point to it and say, "It's right there" .
The real question is, "where was that coin before you and I recognized it? "
The answer is that it was in an inordinate number of places before we both perceived it as being there.
Human beings are reality producing machines and we are the ultimate observers. So, nothing is anything or anywhere until perceived as being so by an outside observer.

 

[elman]

I believe your question can be explained, in part by something called 'Quantum Superposition" .
If I place a coin on a table and ask you where that coin is, you would be inclined to point to it and say, "It's right there" .
The real question is, "where was that coin before you and I recognized it? "
The answer is that it was in an inordinate number of places before we both perceived it as being there.
Human beings are reality producing machines and we are the ultimate observers. So, nothing is anything or anywhere until perceived as being so by an outside observer.

I think you have logically driven over the cliff. The coin's reality is not created by our observance of it. Any conclusion that says it did not exist until we perceived it is faulty.

 

[KCDAD]

I think you have logically driven over the cliff. The coin's reality is not created by our observance of it. Any conclusion that says it did not exist until we perceived it is faulty.

In the "me me me me me me" world of intellectual masturbation, if I don't experience it, then it doesn't exist. The concept of "the generalized other" is not a part of that thinking.

 

[StrugglingSceptic]

For something to be an object it must have at least the potential to exist. The existence of either p or q is precluded a priori by underlying principles.

The term a priori is redundant here since all of mathematics is a priori. And I have nowhere suggested that p and q exist. What I have said is that two hypothetical objects, p and q are being considered. If you do not believe this is what is happening, how do you understand the following

"Suppose there exist integers p and q such that (p/q)^2=2"?

Or do you believe that this statement is nonsense?

A triangle whose angles add to 240 degrees is similarly a non-object. "A triangle whose angles add to 240 degrees" does not describe a potentially existing thing.

This is only true in certain geometries, such as Euclidean and hyperbolic geometry. In elliptic geometry, there are triangles whose angles add to 240 degrees.

 

[TeddyKGB]

The term a priori is redundant here since all of mathematics is a priori. And I have nowhere suggested that p and q exist. What I have said is that two hypothetical objects, p and q are being considered. If you do not believe this is what is happening, how do you understand the following

"Suppose there exist integers p and q such that (p/q)^2=2"?

Or do you believe that this statement is nonsense?

I believe p and q are precluded based on the existing definitions of "integer" and of the functions in the equation.

This is only true in certain geometries, such as Euclidean and hyperbolic geometry. In elliptic geometry, there are triangles whose angles add to 240 degrees.

A geometry that has no spatial counterpart. Like modal logics, one can generate any number of variously constrained systems by arbitrarily denying one or more axioms. It doesn't mean those systems generate thinkable propositions or entities.

 

[StrugglingSceptic]

I believe p and q are precluded based on the existing definitions of "integer" and of the functions in the equation.

So do you think the statement is nonsense? Because such statements are typical in mathematical arguments, and this one begins the common proof that the square root of 2 is irrational. In full:

Suppose p and q are integers such that (p/q)^2=2. Let gcd(p,q)=d, and consider the integers p'=p/d and q'=q/d. Then gcd(p', q') = 1. Moreover, (p'/q')=(p/q) and so (p'/q')^2=2. Multiplying both sides by q'^2 gives

p'^2 = 2q'^2,

from which we deduce that p' must be even, since its square is even. Hence, we can write p'=2p'', which gives

(2p'')^2 = 2q'^2.

This cancels to 2(p'')^2 = q'^2, giving q' even. But then both p' and q' are even, contradicting the fact that gcd(p', q')=1. Hence, there can be no integers p and q such that (p/q)^2=2.

Again, how does this proof work, if not by considering two hypothetical objects p and q, whose properties entail a contradiction?

A geometry that has no spatial counterpart. Like modal logics, one can generate any number of variously constrained systems by arbitrarily denying one or more axioms. It doesn't mean those systems generate thinkable propositions or entities.

Which axiom is denied with modal logic? I'm sorry, but I don't think you know what you are talking about.

Elliptic geometries have physical realisations in spaces with positive curvature, the simplest example being a sphere. I believe the possibility is still open that the universe itself exhibits such a curvature.