- Are there any other things we can be certain of?
- Are there any 'hooks' that can be hooked into 'I think therefore I am', that one could be 100% certain are truthful as 'I think therefore I am' itself?
We can be pretty certain of tautologies, which are axioms of logic based on the principle of non-contradiction. After all, 'cogito ergo sum' already presupposes that something must exist in order to think, and presupposes a notion of 'ergo', both of which are (to Descartes at least) at least as certain as the full phrase itself.
Necessary truths, which are defined either as being true in all possible worlds, or by their falsification leading to contradictions (both of those definitions are essentially the same) are also certain truths, because no matter how we may imagine a universe to look, it cannot sustain contradictions. Therefore, the classic example 'all bachelors are unmarried', is a necessary truth, because the definition of a bachelor is someone unmarried. For this statement to be false, a man would have to be both married and unmarried - an impossibility. Hence, this statement cannot be false and therefore must be true. (I think. See here and here)
In addition, like logical proofs, the results of mathematical proofs are similarly trustworthy, so to speak. If a rectangle is defined as a four sided polygon whose sides interact at right angles, and we prove that a polygon has these properties, it must necessarily be a square. The same idea (I think) applies to numbers.
Some may argue these points, but some argue on Descartes' argument as well. It seems like these are some things that we can be at least as sure of as we may be of 'cogito ergo sum'.
I'd say 'I think, therefore I am' isn't something we are 100% certain of. Or rather, what it entails is nebulous.
The fact that I am a thinking 'being' at this instance says nothing about 1 second ago. I "remember" it, but personal recollection is hardly a solid source of evidence. I could refer to external sources for validation of myself, but there is nothing about being a thinking being that confirms that my understanding of reality actually correlates to what reality is.
'Cogito ergo sum' is just the acceptance that we have to start somewhere if we want to attempt getting an 'objective' understanding of reality. It's an agreed upon baseline, that exists mainly because to not accept it as fact means we can't really know anything.
Often the things we can be pretty certain of are ontological commitments.
Exploiting ontological commitments
A typical example is a Henkin style completeness proof for first order predicate logic. We are talking about formulas and deductions that we "can" write down, so we can be pretty certain that we can write down things. We use this certainty to construct a syntactical model of the axioms. (The consistency of the axioms enters by the "non-collapse" of the constructed model.)
I don't know whether the earliest (Gödel/Tarski style) completeness proofs also relied on the same sort of ontological commitment. The last section below indicates why it is highly likely that some sort of ontological commitment is required for any completeness proof, as long as no explicit notion of "existence" relative to which we talk about "completeness" is specified.
What ontological commitments are really there?
One point of contention is how much ontological commitment is really there. Just because I can write down some things doesn't mean that I can write down an arbitrarily huge amount of things. Or maybe I can write them down, but I thereby might destroy things I wrote down earlier.
What ontological commitments are really needed?
For a completeness proof, we must show that for each unprovable formula, there exists a structure were the unprovable formula is false and all axioms are true. This structure must "exist" in a suitable sense, because what else could be meant by "completeness"? If only the structures that can be represented in a computer with 4GB memory would be said to "exist", then first order predicate logic would not be "complete" relative to this notion of "existence".
I'd say that we can't have certain knowledge regarding the real world, and that certain knowledge is restricted to logic and mathematics. This includes statements such as "cogito ergo sum", see the answers to "Could `cogito ergo sum' possibly be false?". As soon as we consider statements about reality (rather than some artificial system constructed from rules and axioms) we have to put up with the idea that we can only have uncertain knowledge, with different levels of support/corroboration from the evidence/observations. IMHO the search of certain knowledge regarding reality is misguided.
Dubito ergo Cogito, ergo Sum
I doubt, therefore I think, therefore I am.
Ergo ... ergo or therefore ... therefore are the signs and significations of reason. Can one doubt 'doubt' by doubting 'reason'?
Al-Ghazali thought so (Deliverance from Error, page 22):
Then sense-data spoke up: "what assurance have you that your reliance on rational data is not like your reliance on sense-data? Indeed, you used to have confidence in me. Then the reason-judge came along and have me the lie. But were it not for the reason-judge, you would still accept me as true. So there may be, beyond the perception of reason, another judge. And if the latter revealed itself, it would give the lie to the judgments of reason, just as the reason-judge revealed itself and gave the lie to the judgments of sense. The mere fact of the nonappearance of that further perception does not prove the impossibility of its existence."
So perhaps one has to learn to judge and not merely reason.
Al-Ghazālī, A. H. (2006). Al-Ghazālī’s Path to Sufism: his Deliverance from Error [al-Munqidh min al-Dalal], R.J. McCarthy translator.
Another aspect of "ego cogito ergo sum" ignored by the current answers is that it is a statement about the subject itself. But it is more than that, it is also a sort of instruction for anybody to convince himself that he exists, so it is more than just a subjective analytical statement, but also the predicted outcome of an experiment anybody could try to verify for himself.
You might have trouble to imagine anybody who would not be convinced of his own existence after performing this experiment. But assume somebody with a severe psychiatrical condition. For him, maybe the assertion "I am mad" would work better:
mad man: "I think I finally understood. I am mad!"
partner: "But you are crazy, why do you think that?"
mad man: "See, now you also tell me that I am insane!"
But Descartes was a philosopher, not a mad man. So it seems more appropriate to compare his instructions with teachings of other great philosophers like Socrate. He also made statements about himself, like: "As for me, all I know is that I know nothing, for when I don't know what justice is, I'll hardly know whether it is a kind of virtue or not, or whether a person who has it is happy or unhappy." We may assume that Socrate himself knew whether this assertion was true or false. The more interesting question is whether his discussion partners could know whether this statement was true or false. In fact, I believe they could not know this. All they could know was that Socrate was criticizing people who believed that they knew things which felt squarely outside their domain of expertise.