Can we logically prove that anything exists?

Question

Suppose I want to prove that negative numbers exist. Well, I could easily do that using a mathematical proof. However, all I would be doing is adding another logical object to a list of known logical objects, none of which appear outside in the real world. It's a bit like proving that you lost in a game of chess by invoking the rules.

Using logic or mathematics to prove things does not relate to the real world directly. You cannot prove objects exist in the real world by using logic because no matter how cunning you are, it still might be the case that the objects do not exist. It is possible that no physical objects exist, but that would not affect your logic.

This explains why all attempts to prove God exists fail. You can't do it just by using logic. You could demonstrate that God exists, but nobody has managed to do that under laboratory conditions. All we have are stories that contradict each other.

So my question is: Can we logically prove that anything exists?

Answer 1

IMO, there are two related but different issues here.

We prove statements : in math and logic we prove a theorem from axioms. There is no way of proving a statement "from scratch", i.e. without assumptions.

The basics of "deductive sciences" are well-known since Aristotle and the same A discussed the issue of infinite regress in the foundations of knowledge.

Every theory (including math and logical ones) can prove the existence of something only in the context of the axioms presupposed by the theory itself.

The same for the deductive arguments about the existence of God; see e.g. Spinoza's Ethics : it deduces the existence of God from axioms and definitions.

In conclusion, there is no absolute (i.e. unconditional, not relying on some assumptions) proof that something exists.

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A different topic regards facts : we do not prove e.g. the fact that Napoleon was the Emperor of France from some axiomatic theory of Emperors.

We can assert it because it is a well-known historical fact.

In a similar way, we may appeal to the Bible and say that it provides historical grounds for the existence of God.

But, in both cases, they are not "logical proofs" at all.

Answer 2

"If a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubts, he shall end in certainties." — Bacon, Francis, Graham Rees, and Lisa Jardine. The Oxford Francis Bacon. Clarendon Press, 1996.

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"If you tried to doubt everything you would not get as far as doubting anything. The game of doubting itself presupposes certainty." — Wittgenstein, Ludwig, et al. On certainty. Vol. 174. Oxford: Blackwell, 1969.

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One argument is as such: To absolutely doubt anything and everything, thus namely radical skepticism, results in destroying your basis of inference of radical skepticism by the very nature of doubting itself.

The point I am trying to make is that the very act of doubting can be argued to have tautological implications, such as the Wittgenstein quote above.

(https://plato.stanford.edu/entries/logic-epistemic/)

I use the term, tautological, in the non-pejorative sense as used in epistemology and/or formal logic.

(https://en.wikipedia.org/wiki/Tautology_(logic))

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A related exposition of Immanuel Kant's views on this matter was written here on Stack Exchange:--

(https://philosophy.stackexchange.com/a/42465/30380)

Kant continues Descartes' quest for reducing doubt of knowledge.

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"To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection." — Poincaré, Henri. Science and hypothesis. Science Press, 1905.

Answer 3

I would agree with your suggestion: with logic alone, we cannot prove the existence of anything ... we need to make at least some observation.

Indeed, Descartes needed to note that he had thoughts (through introspection, a kind of internal observation) in order to prove the existence of those very thoughts (and, consequently, himself ... as the thought-haver)

Also, a quick note on the existence of mathematical objects. When mathematicians talk about existence (there exist perfect numbers; there does not exist a largest prime number, etc.), they are indeed not talking about 'real world' kind of existence, but rather are talking about logical consistency with some set of axioms. That is, mathematicians simply postulate the (logical) consistency of objects (e,.g. numbers), and then see what logically follows ... and what follows from, e.g. the Peano Axioms, is that there are perfect numbers, but no largest prime numbers. But yeah, in the end, this kind of 'mathematical existence' is not the same as the kind of 'real word existence' as we normally think of it, you're right.

Answer 4

We can't prove that negative numbers exist using mathematical proof; they are simply implications of our axioms.

Similarly, in life, nothing can be proven. But this begs the question: what would we gain from proving existence? Sure it would provide closure and confirmation of universal truths, but how would it benefit society in any way?

I agree, however, that it is very interesting to think about how many things we believe will never be and, more importantly, can never be proven.

Answer 5

The Italian philosopher Umberto Eco offered a funny and insightful answer to this question:

Perché c’è dell’essere piuttosto che nulla? Perché sì.

Translated, it means: "Why is there something instead of nothing? Because."

One can be skeptical about everything, even about skepticism itself, as suggested by Vladimir Nabokov in Transparent things:

Men have learned to live with a black burden, a huge aching hump: the supposition that "reality" may be only a "dream." How much more dreadful it would be if the very awareness of your being aware of reality's dreamlike nature were also a dream, a built-in hallucination!

Everything, except that something exists – indeed, even a mistake or an illusion are something.

So, let's say that,

(1) Nothing exists.

it naturally follows that

(2) (1) is something

therefore

(3) Something exists.

Even if we doubt the working principles of logic, our doubts and mistakes would still be something.

Answer 6

This largely depends on what you mean by ‘logically prove that anything exists’ (and a bit on what you mean by ‘logical object’). Let’s consider two alternatives.

If you mean: ‘showing that it is a logical truth that something exists’, then the answer is no, or almost no. If a is an individual constant of given logical language, a = a is a logical truth, and so is the existential sentence ∃x x = a – which effectively say that a exists. So, it is a logical truth that something (or, some thing) exists; but that’s as far as it goes: we can’t prove the existence of a second thing, nor can we prove that the existing thing is a physical object.
Some logicians feel that even this is too much. Logic should be subject neutral, they argue, to the extent that the existence of no thing should be a logical truth. This type of approach is known as Free Logic.
On the other hand, Logicists and Neo-Logicists hold that numbers exist of logical necessity, and have tried to show that their existence follows from what they take to be laws of logic. If this can be done successfully, numbers would be 'logical objects' - but that certainly doesn't mean that their existence is trivial! This is one of the best-developed, but also one of most complex and complicated views in formal logic and philosophy of mathematics.

Alternatively, by ‘logically prove that anything exists’, you might mean: ‘prove deductively as opposed to inductively that something exists’. The next question is then what you want to prove this from, i.e.: What are the premises in your proof? If they are once again only logical truths, we are back to the above situation. However, logical truths aren’t the only truths. Take the claim ‘Proxima Centauri is a red dwarf’ as an example. This is certainly not a logical truth, but a truth nevertheless. Now, both the existence of Proxima Centauri itself, and the existence of red dwarfs, follow from this statement. Importantly, they follow by means of a logical rule of inference, or deductive rule, known as existential generalisation.
Just because we’ve used a logical rule in the proof doesn’t mean that the conclusion are truths of logic: that Proxima Centauri and red dwarfs exist, are contingent truths and not logical ones. So, we can prove deductively that something exists, even though the existence of that something isn’t itself a truth of logic. (But that's all we wanted.)
Of course, we haven’t proved the existence of something that we previously thought didn’t exist. However, Quine in his famous paper On What There Is points out that the same method will sometimes uncover ontological commitments that we previously didn’t think we had to make. In particular, he argues (roughly) that because the laws of physics involve numerical statements (like e.g. ‘The speed of light is 299.792.458 m / s’), physics commits us to the existence of numbers. This is called the Indispensability Argument.

You mention God, and proofs of the existence of God; but as it stands, I’m not sure you’re your question is specific to God’s existence. Also, people have certainly done more (whether successfully or unsuccessfully) than tell stories about God: proofs of the existence of God abound, and some even claim to be ‘logical’ or at least ‘analytic’ or ‘a priori’. – Whether these proofs are sound, is a different question, of course.

Answer 7

This isn't quite a proof, but it seems that in the act of attempting to formulate any proof at all, we must presuppose that there exists something that is capable of doing logical reasoning; otherwise, the whole endeavor would be futile. We sometimes catch mistakes in what we thought was a solid proof, and so it is not clear that we can decisively rule out the possibility that any logical thinking we have ever done is fundamentally mistaken. This is not to advocate extreme skepticism, but it does seem that to get started on any logical reasoning (or at least to have any faith in such reasoning), we have to implicitly assume that something capable of such reasoning exists.

(This seems somewhat different from the Cartesian argument that I exist, which still allows for the possibility that I am -- and perhaps everything in existence is -- in general a highly flawed logical reasoner. On the other hand, the Cartesian argument is at least an argument for directly establishing something, whereas the above is just saying that there is little point in not making a certain assumption.)

Answer 8

No you cannot prove anything exists. Kierkegaard's Absolute Paradox provides a really good example showing the redundancy.

Essentially the problem with existence is in order to prove something you have to in advance believe it exists to prove it exists. But if you think in advance it exists then it's already existing but not existing. His example is Napoleon's works. You can prove Napoleon's works exist by Napoleon, but his works cannot show his existence. Because for the works to show his existence they would need to exist before him, which they don't. By using the name "Napoleon" it means he already exists but you're trying to prove he exists by thinking in advance he exists in order to prove he exists.

If we were to remove the name "Napoleon" from the equation, then an interpretation of "him" has been formed which opens an argument for how do we know "him" refers to Napoleon and not the army General of France. We'd have no way to prove "him" referred to Napoleon.

Answer 9

Can we logically prove that anything exists?

Before answering the question, we should agree about what we're talking. Discussion upon subjective understanding is useless. My perspective comes from the systems theory.

1. Existence: this is the concept I prefer: an object system exists for a subject system if the subject can interact with the object. So, if the moon exists for me, that's because I can interact in some way with it (i.e. I receive light, I react creating a symbol in my mind for it). Ergo, existence is subjective. Right, example: God exists for some people (they say they interact with him), and doesn't exists for others. Another example: the quantum of energy started to exist as soon as we have been able to interact with it... on paper, with math. Another: cogito ergo sum means "thinking is interacting with myself, ergo, everytime I think, I exist. Problem: can we be objective about existence? Objectivity is only possible as a shared subjectivity. Even if I try to express my feelings or logical conclusions about the existence of something, they are valid for you only if you are able to be coherent with my understanding. There is no physical bounds between your mind and mine, that would be objectivity. We both follow similar (or different) thinking paths, and agree about the existence of the moon, therefore it objectively exists due our capability of having coherent subjectivities.

2. Anything, what is it? Here, you are talking about things. Again, things are mass, delimited by mental boundaries. I'm sure that you and me don't agree about what a chocolate box or a tree are. Does the tree include its water? If so, at what distance? Isn't that subjective? Where do clouds end? If that's difficult to know, then, where do rocks end? (think of it: rocks are also fuzzy ideas, but limits are defined at a smaller scale, they seem more coherent than vapor, but both are just atoms). Things can be studied by the systems theory, due to they fit perfectly the definition of system. Things can be abstract, when they have no correspondence, or a loose correspondence to matter, or concrete, if they correspond more or less to an amount of matter. But things exist only in our minds. Matter is just physical interaction (Feynman said something equivalent).

3. Logically, prove, sounds the same to me: use reason, following logic rules (the rules of nature, that we have learned and systematized, as a tool and a language: math). A logic system is just a calculator: requires of an input value to generate an output result. E.g. "if I think, I exist" is my logic; "I think" is the value I input to the system. The system tells me that I exists. So, What's the input for my logical system to assess if I can prove existence? Again, a subjective valoration. Is that valid?

So, the only possible existence raises in our mind, as a subjective idea, and can be proven using a formal construct named logic, but it requires subjective valorations as inputs. Under such constraints, it's only up to you to decide, propose a logic system and test it using observations raising from your subjective experience.

The same idea, from a different and pragmatical perspective: the present does not exist (it is just the content of our short-term memory). Then, there's only the past and the future. Of course, I cannot prove that you (or any other object) existed in the past. Even worst, I cannot prove that you (or any other object) will exist in the future. The only possible proof is memory (written or mental), and that puts us in a situation of my word against your word.

When talking about knowledge, the unconscious convention is to believe in formal science. But flat-earthers put it in doubt. Independently of them being right or wrong, skepticism is not fallacious. I myself am very skeptical about multiple issues in scientific knowledge (just look at my posts about thermodynamics).

Answer 10

Yes. You can.

You practise Solipsism.

Solipsism

Solipsism (/ˈsɒlɪpsɪzəm/ (About this soundlisten); from Latin solus, meaning 'alone', and ipse, meaning 'self')1 is the philosophical idea that only one's mind is sure to exist. As an epistemological position, solipsism holds that knowledge of anything outside one's own mind is unsure; the external world and other minds cannot be known and might not exist outside the mind. Solipsism

You use your mind to prove you exist.

I have just proven to you right now that my mind exists, by writing this message. You may doubt this, and still question that what you are seeing could just be a construct of your own mind. In which case, at least i have helped prove to you, your own mind exists.

Answer 11

I believe you are adding to the confusion by adding "logically" to the question. Can we prove that anything exists?
First of all, there is no absolute proof of any kind. However, there is proof by the preponderance of the evidence!
What this means, is that if you want to prove anything (to a given degree), you need evidence (observations), rather than logic! Of course, you could use logic to gather and present the evidence, but logic by itself, would not be enough.

Answer 12

“je pense, donc je suis“ - René Descartes, Discourse on the Method

“Cogito, ergo sum” - Latin

“I think, therefore I am” - English

What Descartes was not saying, was I think therefore I have a body. Nor, I think therefore I have a brain. What he was saying was I think therefore I am conscious and consciousness is a property of the immaterial mind, not the physical processor the brain or physical housing of the body.

Thinking, yes, is processed by humans in the brain and disciphered by it. It is stored and retrieved by the brain and in many ways our person is limited by the genetics and biology of our minds, including our physiology which is impacted by other aspects such as gender.

The highest most powerful coding (software) is limited by its processor and by the housing of the processor, the computer tower which allows it to function optimally, such as having a fan to cool it out, unrelated to the coding but necessary nonetheless. The best coding in the slowest computer or processor is hindered tremendously.

And right now I am reading your posting and I assume therefore, you are. But I’m not thinking of you, as in your body, nor your brain the organ, I am thinking that you the person, the intelligence exists and I am interacting with you the mind (and spirit/life).

If I read any material that contains autobiographical markings I can infer that at the very least, that mind existed. A biolographical marking I can infer another mind influenced the mind that write the biography, therefore at least two minds/persons.

In much the same way God has left written text, and from the text we can infer that this mind/person at the very least existed. Further based on what God prophecied and also came to fulfillment, God was able to know or predict at least, future events sometimes centuries in advance.

There is the issue of God’s disembodiment but I would refer you to my response in a separate question as to the fact that God overcame this issue.

Is God's disembodiment problematic?

Answer 13

First of all you need to decide a reference frame. For example we can see light only between 400nm- 800nm wavelength. Light below this wavelength or above can't be seen by us that doesn't mean it doesn't exist. Now let's take a different views. If something exists, then it should exist for everyone else and in the same form. Now you see blue color as blue color but a dog might see it differently. What seems one metre length to me is different for a fish. A square for me is an ellipse for a fish. Now if you're able to see anything that also doesn't mean that it exists. If you see a star in the sky, there are chances that star must have died years ago and now you're seeing it's light only and not the star. With that logic you just see the light only and not the actual object, all the time. Same thing is with sound and other feelings. It's your mind which is processing responses and giving direction or making you feel specific things.

Now if you see what is the only common thing in all the examples. it's the observer who is there all the time, which is you. Only thing which you can't disprove that it exist is you, yourself. Rest of things are just a perception made by you.

Answer 14

Several responses to my question are technical and are only of interest to logicians, not the general public. I admit that in the serious analysis of important questions, strict definitions and rigorous application of agreed rules are important for accuracy. However, you can't convince Colin Hunt that God exists using the equations of quantum mechanics. Colin Hunt learned that God exists from his mother, when he was two years old and nothing will convince him that the god of Israel was invented thousands of years ago by a tribe in order to explain what causes the weather and to justify possession of land stolen from their closely related neighbors. There are many Proofs of God that to Colin Hunt are merely happy confirmations of his already firm belief. The First Cause argument is very convincing to Colin Hunt and he doesn't want to check it, nor does he want anybody else to check it. Many philosophers have checked it and rejected it. Sophisticated theologians have invented an improved proof based on the discovery that the "universe" had a "beginning", but even more sophisticated critics point out that all it does, is suggest that the cause of the supposed beginning is a mystery. When a proof ends with "and we call that God", we are left with the thought that any logical variable would do just as well. You could end the proof with "and we call that Brian".

Answer 15

These Insights are not new, those who are meditative enough are able to perceive them. The ancient texts spoke about them;

So deep, so pure, so still It has been this way forever You may ask, “Whose child is it?”- but I cannot say This child was here before the Great Ancestor - Dao De Ching

That which is nonexistent can never come into being, that which is can never cease to be - Bhagavad Gita

In the unreal there is no duration and in the real there is no cessation. Indeed the conclusion between the two has been analyzed by knowers of truth - Bhagavad Gita

😃🙏

Answer 16

Using the science of ontology, you can come up with accurate predictions of the existence of possible ontological entities. Mendeleev successfully predicted the existence of chemical elements with his table of periodic elements. Even though at that time the scientist didn't knew about the existence of all chemicals, Mendeleev discovered the map of chemical families which identified the existence of yet to be discovered chemicals.

Ontology is the map of possibilities. Ontologies reflect the structure of existence. Ontologists can discover the maps of existence. For example, some portion of existence is know - enough to start making the ontology. All you need to discover is proper structure of and relationships between the entities.

I don't see why theology couldn't be analyzed ontologically and see what's there [in the unknown...].