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I know a similar question already exists on this site, but please bear with me.

Descartes's famous Dubito ergo Cogito ergo sum preassumes the existence of an "I".

Since there is an assumption involved the inference( if so), or the statement made under it is affected by the truth value of the assumption. (If the assumption is false, the statement may no longer stand).

In this fashion is it possible to make a statement without any assumptions whatsoever which is true, and thus is absolutely true? If there are no assumptions whatsoever involved then we know that the statement stands absolutely.

I know it might be hard to come up with something without any assumptions whatsoever, but if we could prove that there exists a statement which has minimum assumptions or least cardinality of the set of assumptions, we could arrive at a so called "maximum truth", unless of course a proof or logic exists which implies that no such statement could exist (eg. If i could remove an assumption ad infinitum)

  • How about just the existence of conscious experiences? Yes, I agree that it is somewhat problematic to infer that there is a "something-that-has-thoughts-and-other-conscious-experiences" (i.e. The "I" in Descartes' argument), but the existence of just those thoughts and conscious experiences themselves seems pretty certain. – Bram28 Jul 2 '18 at 16:21
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    If you make no assumptions at all you have no language by which to convey anything, and thus you cannot make a statement. You cannot even think about anything because without the assumption that your thoughts are an abstraction of something conceivable, then you cannot perform any kind of reasoning about anything. – MichaelK Jul 2 '18 at 16:28
  • @bram28 it would be a truth based on observation, requiring an observer( The I). Therefore we must pre suppose something.(correct me if i am wrong). Also i was looking for something in logic, but maybe this can be a place where i find the answer. – novice Jul 2 '18 at 16:30
  • @michaelk then minimal set of assumptions? Can we show that a sentence of some kind cannot be reduced further by removing assumptions, given a language. – novice Jul 2 '18 at 16:33
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    You may be interested in looking at proof theory. It is a mathematical effort to be able to phrase things like this. For example, you can use it to prove that, for any given statement in any language, it is possible to construct a language within which you can prove said statement without assumptions. In fact, it's trivial. You just bake the assumptions into the grammar of the language. Now if you want to say that the language is fixed, we find another problem. How do we fix it? We need a language to describe how we fixed it... – Cort Ammon Jul 4 '18 at 0:02
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It depends on what you mean by "know," what you mean by "something," and what you mean by "assumptions." Actually, it depends on a whole lot more than that, but those are the really fun words.

What makes this topic tricky is that the concept of "knowing" is so deeply buried in our language(English) that it's hard to even capture something that describes it acceptably.

The most general answer must be "maybe," but if we restrict ourselves to the most common senses of the words in philosophy, the answer is a resounding "no." In order to find a "maybe" answer we have to step away from the typical definitions.

For example, what is "something" you can know, anyways? Your words imply that being able to make a "statement" is part of the puzzle. So how about we start with a particularly obnoxious statement:

Oh freddled gruntbuggly,
Thy micturations are to me
As plurdled gabbleblotchits on a lurgid bee.

Is that something I can "know?" What does it mean, anyway? The most common answer is that any statement, stated in a language, must be interpreted in some way to arrive at some semantic truth -- something knowable. I must have an understanding of the language.

And the assumption that my interpretation of this statement is correct is an assumption. We can't just handwave it away and say "oh, assume our interpretation of the language is right." If we do that, then we immediately find that we can sneak assumptions into the grammar of the language to hide them from our counting. We didn't really decrease the assumptions, we just moved them.

Also, how do we count them? If I use the language of propositional logic for a moment, if I assume one statement, A∧B∧C, did I actually assume anything less than if I assumed three statements, A, B, and C? Even counting assumptions is a tricky beast. In computing, there's a concept called Kolmogorov complexity which studies how many bits of information it takes to convey something in a particular language. Even then, it's used mostly to prove the impossibility of stating certain things:

In particular, for almost all objects, it is not possible to compute even a lower bound for its Kolmogorov complexity (Chaitin 1964), let alone its exact value.

One fascinating path people have taken is to consider trying to create self-hoisting languages, which can prove their own consistency. This was a fascinating effort in the early and mid 1900's, but what we found was that it is generally not possible. Propositional logic is too weak to be able to admit the self-referential structures required for a language to talk about itself. First Order Logic has to deal with Godel's Incompleteness Theorem, which is notorious. Second Order Logic can indeed talk about itself, but it can't admit proofs of its own correctness. So of our "standard" languages, none of them admit statements without assumptions.

So can you know something without an assumption? Well... maybe. We can show that entire vast swaths of what we'd like to say knowledge "is" cannot operate without an assumption. However, none of the "typical" structures can prove that we're using the right definition of "know" or "assumption" or anything, really. So maybe the definition of "know something without assumptions" that you are using indeed admits such a thing. Or maybe it doesn't. We can't devise the language to prove one way or the other without making an assumption.

I'd like to close with two great resources. One is a beautiful speech by Jon Steele on How to Grow a Language. It's a massively long video, so the transcript may be more palatable. He constructs a language, from the ground up, using a very particular set of rules. I find what he was doing is much in the vein of what you are thinking about.

The second is one of my favorite quotes from Stranger in a Strange Land, by Heinlein. Mike Smith is the subject of this quote, and he was raised Mars, speaking Martian. Only upon coming to Earth did he have to learn English:

Short human words were never like a short Martian word — such as "grok" which forever meant exactly the same thing. Short human words were like trying to lift water with a knife.

And [God] had been a very short word.

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Knowledge that does not require assumptions is called by various names. Direct, unmediated, intuitive etc. I prefer 'knowledge by identity'. As Aristotle noted all other knowledge is either tautological or uncertain. Only what the sages call upper-case 'Knowledge' is free of assumptions. The rest is called 'relative knowledge'.

So in reply to the question 'Is it possible to know something without any assumptions?' I'd say that it is not possible to truly know something any other way. It seems to me this is a matter of logic.

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