How can objects be nonexisting?

Question

A square circle. Obviously, this is contradictory, but i feel odd saying it doesnt exist as well. thats not the bestw ay to say it.

but, then again, whatg do we even mean in mathematics or logic by proving that an object doesnt exist or isnt real? what does this even mean?

lets consider that type theorists and constructivists amongst others believe only those things which are true can be constructed, which are logical in sense and can be understood. and of ocurse the word logic can be a bit broader than maybe just classical logic butstill it remains to be seen that it is something which must be capable ofbeing understood. something false can never be constructed or conceived at all.

is it just another way of saying true an false? a square circle may exist, but it cannot really be constructed, and yet it is still the idea itself. it exists.

if i say that a thing does not exist and i prove so mathematically, then would this just mean that it is itself just soemthing of which is not valid? if i prove square circles dont exist, what does this even mean? does it just mean it is inconceivable?

Answer 1

The core of your difficulty- and of countless other questions on the same subject- is that you are confusing different senses of the word 'exist'. Your problem should go away if you separate the different meanings of exist. Here are two... 1) My left foot exists, in the sense that it has a physical presence- people can see and touch it, for example. 2) My middle foot exists as an idea in my head and in yours and in the minds of other people reading this answer, but it does not exist in the sense that my left foot does.

If I say no solution exists to the Squornat equation, I am using the word exist in a way that is neither an instance of 1) nor of 2)- instead I am using the word exist to mean 3) that you cannot specify values for the variables in the equation such that one side of the equation has the same value as the other.

Now, clearly a solution to the Sqornat equation can exist in the sense 2), ie as an idea, but it cannot exist in the sense 3). Likewise a square circle can exist in the sense 2), but it cannot exist in the sense 1).

You will find that every (perhaps I should say almost every) question about whether or not things exist boils down to confusion resulting from the ambiguous nature of the word.

Answer 2

You can use Husserl to understand this:

When we perceive, desire, or think, we always do so with reference to something. This means that thinking is always thinking-about-something. This "aboutness" is called intentionality.

The act can be directed, like an arrow, towards an intentional object that exists or towards an imaginary or abstract content, for instance. This content does not exist, but nevertheless, since thinking or imagining is always about something, the content itself is not reducible to the mere act in which it appears. This is why chimeras or fictional characters possess that "objectivity" and doctoral theses can be written about them with meaningful standars. And yet, they are not existent entities. So being > existence.

Husserl wrote about this in his Logical Investigations, and later in Ideas Pertaining to a Pure Phenomenology and Phenomenological Philosophy.

Brentano, Alexius Meinong and Frege also wrote about this. And the Scholastics also wrote about this, calling it entia rationis or "beings of reason". Suárez for instance discussed it in the 1st and 54th of his Metaphysical Disputations when he asks what the proper object of metaphysics is.

I know it may seem shocking that something without existence can nonetheless be irreducible to mere psychic subjectivity, but mathematics is a clear example of this.

However, Husserl will tell you that not every apparent content is always intentional. In fact, a square circle is an impossible object to conceive and therefore it is difficult to think that, in itself, it has an intentional term.

Answer 3

A square circle. Obviously, this is contradictory, but i feel odd saying it doesnt exist as well

There is only one sense to the word "exist", so I can only be using the same sense throughout.

The descriptive phrase "square circle" exists, and I am quite confident everybody would agree on that.

It seems also certain that no (physical) object could possibly be a square circle and that reasonable people all agree on that. So, we can also say that square circles don't exist in the physical world. If you disagree, please exhibit one such.

Finally, there is no (mental) concept of the square circle. The proof of that is that we are unable to conceive of a square circle. We can easily think of the linguistic description, i.e. "square circle", but cannot conceive what the description "square circle" would be the description of. Anyone who would claim that they can, I will not believe them, and they won't be able to prove they can.

So, the linguistic description exists, but the physical object and the concept don't. So much for language!

Proving that a description, such as "square circle", is self-contradictory, doesn't necessarily prove 100% that the thing doesn't exist, but even if it does, it is anyway beyond our ability to conceive of it, and so there is nothing sensible or rational that anyone can say about it except that it is self-contradictory. Given this, it seems only reasonable to let it go without remorse.

Still, considering self-contradictory descriptions seems to help us think about our own rationality, and as such, it may be a useful exercise.

Answer 4

As it was said above, the term 'exists' has different meanings. you don't need to appeal to mathematics to understand it, because - as I understand your question - you're not concerned with the mathematical meaning of it, but rather with the ontological one. you want to know what we're saying when we hold a belief in the form of a positive or negative common-sensical existential, like "there is no unicorn". I think the meaning of such statements is straightforward. x exists iff the world contains x. The square circle doesn't exist means the World doesn't contain something that is a square circle. The World is defined as a universe that is the Truthmaker of negative Existential. This is the most straightforward way to deal with the ontological meaning of Existence. Many philosophers tackled the problem, but believe me when I tell you that is the most intuitive response.