A second indubitable axiom

Question

The axiom "I think therefore I am" is the axiom of reality that René Descartes is famous for inventing. Does anybody know of any other such axioms that cannot be disputed (at least on an individual level)?

I was considering the statements "all concepts must be conceived by someone, and each concept was first conceived by someone" as a second axiom. Is this valid? Can anyone think of a way to doubt this statement? If we assumed this to be true as well, could we not also conclude that, since each concept has somebody who first conceived it, either I am the first person to invent all concepts that I am aware of, or that other individuals must exist that first conceived them?

Answer 1

You have actually anticipated Descartes himself in this question. After he established his own existence, as a mind, a thinking being, with the Cogito (I think therefore I am) he proceeded to ask about the sources of the concepts ("ideas" in his terms) in his mind.

But among these ideas, some appear to me to be innate, some adventitious, and others to be formed [or invented] by myself ... But again I may possibly persuade myself that all these ideas are of the nature of those which I term adventitious, or else that they are all innate, or all fictitious: for I have not yet clearly discovered their true origin.

Descartes was not easily convinced that he himself could not be - unconsciously, as in dreams - the source of all his ideas.

And as to the other reason, which is that these ideas must proceed from objects outside me, since they do not depend on my will, I do not find it any the more convincing. For just as these impulses of which I have spoken are found in me, notwithstanding that they do not always concur with my will, so perhaps there is in me some faculty fitted to produce these ideas without the assistance of any external things, even though it is not yet known by me; just as, apparently, they have hitherto always been found in me during sleep without the aid of any external objects.

What did convince Descartes that some of his ideas must indeed have a source external to himself, was the following causation principle:

For just as this mode of objective existence pertains to ideas by their proper nature, so does the mode of formal existence pertain tot he causes of those ideas ... And although it may be the case that one idea gives birth to another idea, that cannot continue to be so indefinitely; for in the end we must reach an idea whose cause shall be so to speak an archetype, in which the whole reality [or perfection] which is so to speak objectively [or by representation] in these ideas is contained formally [and really].

It was this causation principle (*) that was, then, what you called the second indubitable axiom. By invoking it, Descartes was, for the first time, able to convince himself that something existed outside of him. At least one being had to exist beyond himself, and this was God. It took a further series of arguments to convince Descartes that some other things, beside God, also existed outside of him.

(*) See also What were DesCartes's conceptions of objectivity & subjectivity?
(**) The quotes are from Descartes's Third Meditation

Answer 2

First thing I would say is that there are actually a lot of people who think Descartes is mistaken in his Cogito argument. See the criticisms at https://en.m.wikipedia.org/wiki/Cogito_ergo_sum

I don't think anyone would disagree about concepts being held by people. Although I can think of some odd situations where one might decide to say something like "google translate doesn't understand the concept of sarcasm, but does understand the concept of double negatives."

Also, I wouldn't say there is one person who was the first to invent the concept for something. To take "jazz" as an example, I don't think there was a first jazz musician who came up with its concept. It was a gradual thing

Answer 3

Too bad that others did not even try to reply the actual question, and focused only on saying how much they dislike the "cogito ergo sum" argument.

Indeed, it is an argument, not an axiom, but its conclusion "I exist" is what is indubitable, not exactly in the sense that you cannot question it, but that you know that you know it, with absolute certainty, without any chance that it can be wrong.

Unlike what Ram Tobolski said, the "causation principle" is not the second indubitable believe, I am still hoping to ever find an argument as magnificent as "cogito ergo sum" but for causation, but it seems that none has ever found it, and it is also not what you are looking for.

This is what I have understood. The "I exist" belief has an empirical component, the argument "cogito ergo sum" is logically valid, but I know that it is also logically solid —that means, that actually the conclusion is true— only if I know that the premises are true, and I know that the premise "cogito" is true, empirically, because I am thinking at the very moment I am questioning myself about all this, and I know it.

So the "second indubitable" belief, like "I exist", would be "I think", actually, and the others, independently of the order, would be actually any phenomenological experience I have, such as "I am seeing a coloured form", "I am feeling pain", etcetera. Why? Because even if the world does not exist and all that, the experience I am having is still happening, and I cannot deny that I am having some experience, with some qualities.

This is the basis for many other philosophical systems, such as the phenomenology of Husserl, and some theories of Bertrand Russell, and of the Vienna circle, about sustaining all knowledge on logic, while gathering the information these indubitable experiences give. However, they are not at all the only ones that have observed this, and you can find this in many many others.

Of course, the particularity of Descartes, and that most of these others philosophers neglect, except perhaps Husserl, is that he is not only accepting those phenomenological truths, but he is also questioning whatever is not as certain as that, specially the existence of the external world. The others take advantage of these true believes, but assume plenty of other things, therefore polluting the indubitability of their theories.

Answer 4

Yes but we must consider the fact hat we did not nor can we ever conceive of a concept on our own but rather that any concept is present within the realm of ideas (which is in turn part of the fabric of consciousness)