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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?

  • Cogito is not even an "axiom", it is an inference, and many consider it invalid. Perhaps, the "I think" part could be an axiom, or at least "thinking is occuring". As for "all concepts must be conceived by someone", this is explicitly denied by objective idealists, and philosophical realists, more generally, believe in existence of concepts, and truths, that no one ever thought. – Conifold May 31 '17 at 0:28
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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

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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

  • Good points. Perhaps I should say instead, "all concepts originated from some person or persons"? – Frpzzd May 29 '17 at 23:26
  • I would agree with that, and I think you'd be hard pressed to find anyone who would disagree about concepts coming from people (maybe someone could argue animals do also though, like a dog could have a concept of fear). I think this follows directly from the fact that concepts are mental in nature, so it doesn't make sense to talk of concepts existing without people in the same way people talk about physical objects existing without people. So it's part of the concept of 'concept.' There are many uncontroversial statements in general though - e.g. "Pancakes are food" – Franz May 30 '17 at 0:16
  • They are not hard to find at all, starting with Plato to, more recently, Cantor and Godel. To them concepts exist ideally independently of any people, and would have existed without them. – Conifold May 31 '17 at 0:16
  • Even outside a philosophical context, this is not realistic. Did a person or persons originate the concept of food? Presumably when they did so, they were already eating. Most ideas coalesce, they do not spring into being fully formed and distinct from all earlier forms. We are just tricked by our traditions of ownership into imagining otherwise, and then into pretending that what we imagine is actually happening. – jobermark May 31 '17 at 19:05
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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)

  • Welcome to the Philosophy.SE. Do you have any references you can provide for how you derived this answer? I am not familiar with "the realm of ideas". – PV22 May 30 '17 at 18:03

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