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In Descartes's Meditations, in order to establish a firm foundation upon which he could build a framework to determine philosophical and material truths, he begins by removing all of his then-current beliefs and examining what could be admitted as indubitable. In effect, he begins by doubting everything, including, understandably, his own existence. This, indeed, is enabled by the "decision" to, as a rule, doubt any proposition which may brought to consideration (at least initially).

The question is, isn't such a doubt contradictory? For if it was possible then one would have accept that nothing is true, and we would have to deny the ensuing cogito argument by default. And, by a similar argument we must also reject the notion of reason itself. As a result, one would be stuck in sort of circular state. Certainly, this is something the modern logicians would find disagreement with.

Also, if this is the case, how can Descartes's premises and argument be made rigorous? Perhaps his project is similar to developing any logical system, in that there must be certain truths in the system not provable by propositions inherent to the system. In this case, one such truth maybe that reason is something which we have to assume is true and works. Though, based on a subtle observation, this may circular as well.

In asking this, I am intending to invoke a philosophical discussion and analysis of Descartes's cogito argument from a modern, rigorous perspective as a logical argument.

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The question is, isn't such a doubt contradictory? For if it was possible then one would have accept that nothing is true, and we would have to deny the ensuing cogito argument by default.

Not quite.

The hyperbolic doubt that Descartes proposes is contradictory, and that's what makes the cogito work, i.e., why we have to accept the cogito.

We can doubt all kinds of things, but we cannot doubt our own existence, because such a doubt is self-defeating: if we doubt we exist, we must still exist to be able to doubt. Therefore, the fact that we exist is indubitable.

Also, if this is the case, how can Descartes's premises and argument be made rigorous? Perhaps his project is similar to developing any logical system, in that there must be certain truths in the system not provable by propositions inherent to the system. In this case, one such truth maybe that reason is something which we have to assume is true and works. Though, based on a subtle observation, this may circular as well.

That's true, but as you point out, it is true of all explanations. This is known as Agrippa's Trilemma, and is unescapable. All explanatory systems are ultimately either grounded on axioms not proven within the system, or circular, or relying on an infinite regress. There's no fourth option. All we can do is recognize this, and move on.

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In effect, he begins by doubting everything, including, understandably, his own existence. This, indeed, is enabled by the "decision" to, as a rule, doubt any proposition which may brought to consideration (at least initially).

Interesting .. while the method of doubt enables Descartes to suspend belief in sensory and proposition based facts, I think the strength of his conclusion regarding the cogito rests on an important destinction: the 1st person 'qualiatic' experience of existing as a doubting, affirming, remembering etc agent is neither propositional nor sensorial in essence - it's experiential. The experience of being-there in the world is not reducible to either sensory data or propositional (analytic truths, memories etc) facts, and this together with its undeniable omnipresence places it outside the parameters of that which can be called into doubt.

isn't such a doubt contradictory?

if the above line of reasoning is accepted i think the answer must be no, there is no contradiction inherent to this line of reasoning .. It creates space for criticism, such as Nietzsche's view in Beyond Good and Evil that the cogito is an effect of the grammatical structure of language (subjects taking aspects of experience as objects), seeing the phrase 'the person thinks' in the same way as 'the lightning flashes' - i.e. the former phrase implies the existence an agent who thinks, but does the second phrase imply the existence of an agent that flashes? Nietzsche argues that just as the lightning is identical to the flash (there is no lightning behind the flash, the lightning is the flash); so too there is no thinker behind the thinking, just pure thinking

Also, if this is the case, how can Descartes's premises and argument be made rigorous?

my answer would be no .. in the above example of Nietzsche's observation, criticism is not leveled specifically at the rigor of logical relations between the propositions which comprise the argument for the cogito, rather they target the nature of the means of its expression (language) in general. In relation to improving on the logic that

doubting (dreaming, affirming etc) implies the existence of a doubter

i am doubting

∴ i exist

my answer must be no, acceptance of the first premise entails the logical truth of the conclusion .. if the first premise is accepted, it does not need to be more rigorous. To revise the first premise into a more suitable form will be a departure from directly addressing his original argument, and will not amount to an improvement of logical rigor.

I am however frequently wrong :) an this is my first response here. But thanks for the question it's always good to go back to these things..

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