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The rationalist descartian position states that everything can be doubted except doubt itself. With the phrase "cogito ergo sum" it claims to establish the existence of one ones existence, if i did not get it wrong, through exerting doubt which is supposedly undoubtable.

So this (that you exist therefore you doubt, and vice versa) are in their consideration the only two fundamental axioms existing. Now i have some questions, i couldn't up with an answer for:

  1. if these two assumptions or truth are 'just' a set of axioms, does that imply that a different set of fundamental axioms can not be excluded?

  2. if so, could we potentially establish these or similar two truths also with another set of axioms? could we try to construct a theory not necessarily based on the need of an entity such as existence (so basically a thought school based on non-existence) or is that self-contradicting?

  3. cogito ergo sum is a circular implication, does that mean that it excludes provability?

  4. being a circular pair of axioms can it still be possible to use these as premisses for more complex syllogism deriving more complex knowledge from these two fundamentals by using methods like descartian circle, or is that a not completely "kosher" method in logic?

  5. If we couldn't derive komplex knowledge like language from these two axioms, how could they provide the tools (language, logic...) to analyze themselves and therefore be proven as true facts? Or is there always a degree of uncertainty involved because the axioms cannot prove themselves but need a "homunculus", something outside the system, to prove them?

  6. If methods to produce more complex knowledge from these two axioms fails and being a cirular pair of axioms can we safely apply Wittgensteins expression "sinnlos"? Though they may or may not have some degree of true-ness to them, they might not have any "Bedeutung" attached to them, therefore making no statement about anything substantial.

  7. I finally have one last question, which isn't really related to this directly: If -as i read in other posts- logic is not provable by logic itself, therefore downgrading logic from a tool of absolute verity to a "mere" model to acquire close-to-truth information, wouldn't that make any logically proven theorem, or in general every axiom system a theory rather that a fact? wouldn't that make axioms themselves a matter of debate?

sorry for my bad english, and if any of these questions are too naive...but i would appreciate any clarification

closed as too broad by Joseph Weissman Jul 12 '13 at 5:10

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • Related question: philosophy.stackexchange.com/questions/70/… – jeroenk Jun 4 '13 at 10:01
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    Maybe this could be decomposed into several questions? --Also, that related question is close enough it might be worth referencing and responding to. Welcome to Philosophy, by the way! We are here if you need help as you revise/develop this a bit further. – Joseph Weissman Jul 12 '13 at 5:10
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Logic enable to check validity, not verity. You take a set of axioms (basic independant not contradictory propositions) and a set of rules to combine axioms : logic is the game that explore where you can go from this axioms with this set of rules. Also you may take an "arbitrary" proposition and ask yourself, "can I go there from my given axions and rules?". According to Gödel's incompleteness theorems, there are propositions for which the answer is "may be I could reach it with my given sets, but there's no general short cut and while I may find a way, I may just as well never leave this logical incertitude".

Whether axioms are true is somwhere between arbitrary decision and trust in your perceptions.

From a logical point of view, an absolute solipsism is as sound as realism.

From a logical point of view, "I think so I am", or any equivalent formulation – even those which may possibly grammaticaly hide the subject of the action like "thinking implies being" or "cogito ergo sum" –, is just a tautology : "I is I", "I ⇒ I".

If you decide that tautologies are sources of truth, and that you believe that "I" (you are existing), then you decide that your own existence is true.

Of course, logical analyze is far from your only source of data which feed your "decision process", even in ontological process. If you are hungry, chances are good that you won't cogitate for long on the ontological status of hunger before you decide to make actions that you think required to make you satiated.

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