When can we be absolutely certain that something is true?

Propeller of a Junkers JU-52
Are there any statements that are absolutely and certainly true? Yes! Analytic statements are true by their own nature. In this post I’ll outline some of them.

One of my most favorite responses to questions from students is: “It depends on how you see it.” To many of my students this response can be quite frustrating at times. “Why can he not give us a clear, clean, yes/no answer to a simple question? Why does he always want to explore the ‘grey zone’? I want to have some certainty!”, they say.

Well, today I’d like to do exactly that. I’d like to give you a few examples of statements that are absolutely, 100% true. These statements do not require a complicated debate on whether they are true or not. The examples that I’m going to give you are going to be absolutely true with 100% certainty. This may come as a surprise to some of you, who were taught that you are supposed to critically examine and question nearly everything.

There are indeed categories of statements that are true by definition. Philosophers like to call them analytic statements. We know that they are true and they do not require empirical verification (verification by sense perception). Well, here we go:

  • “TOK is Theory of Knowledge”: This is a statement of identity. They are true by definition. Can you give me a counter example? Some of you may now say that “TOK” could also stand for something else. True, but this still does not make the sentence “TOK is Theory of Knowledge” wrong! Another example could be “Mike is Michael.”
  • “All white swans are swans”, “A mouse is an animal”, “All TOK students are students.” These statements assert that one class (eg. mouse) is included in a larger class (eg. animal). Statements of inclusion are also always true. Now, again someone may object here. What about a computer mouse? A computer mouse is not an animal, so the statement “A mouse is an animal” must be wrong! No. In this case we have simply given two objects (the little animal and the computer hardware) the same name, but they are still different objects and therefore belong to different categories or classes. We still mean different things, even though we call them the same way.
  • “One meter has 100cm”, “A bachelor is an unmarried man”, “A square has four sides”: These are definitions and they are true by definition. The point is, that certain things are true because we defined them to be true. If some international commission were to decide that there are only 99 cm in one meter, then this would be the new truth and the new basis for future measurements.
  • “If you are alive, then your heart beats”: Statements that make an implicit meaning explicit are also 100% true. Here are two more examples: “Every husband is married” and “If Armstrong was on the moon, then his little finger was also on the moon.”

Dogmatism and skepticism are both, in a sense, absolute philosophies; one is certain of knowing, the other of not knowing. What philosophy should dissipate is certainty, whether of knowledge or ignorance. – Bertrand Russell

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5 Responses to When can we be absolutely certain that something is true?

  1. Eric

    As a TOK teacher, I love this site, and really appreciate the work that has gone into it.

    I would like to add to this discussion something that C.S. Lewis wrote in “The Problem of Pain” that I think is related, and answers an above objection. The books is out of copyright, so it is legitimate to post here. The full text can be viewed at:

    There is a small skip from our current discussion of “truth” to the concept of “absolutely impossible,” but I think the connection to the conversation, and why the current conversation reminded me of this passage will become obvious to the readers of this blog.

    “Omnipotence means ‘power to do all, or everything’.1 And we are told in Scripture that ‘with God all things are possible’. It is common enough, in argument with an unbeliever, to be told that God, if He existed and were good, would do this or that; and then, if we point out that the proposed action is impossible, to be met with the retort ‘But I thought God was supposed to be able to do anything’. This raises the whole question of impossibility.

    In ordinary usage the word impossible generally implies a suppressed clause beginning with the word unless. Thus it is impossible for me to see the street from where I sit writing at this moment; that is, it is impossible to see the street unless I go up to the top floor where I shall be high enough to overlook the intervening building. If I had broken my leg I should say ‘But it is impossible to go up to the top floor’ – meaning, however, that it is impossible unless some friends turn up who will carry me. Now let us advance to a different plane of impossibility, by saying ‘It is, at any rate, impossible to see the street so long as I remain where I am and the intervening building remains where it is.’ Someone might add ‘unless the nature of space, or of vision, were different from what it is’. I do not know what the best philosophers and scientists would say to this, but I should have to reply ‘I don’t know whether space and vision could possibly have been of such a nature as you suggest.’ Now it is clear that the words could possibly here refer to some absolute kind of possibility or impossibility which is different from the relative possibilities and impossibilities we have been considering. I cannot say whether seeing round corners is, in this new sense, possible or not, because I do not know whether it is self-contradictory or not. But I know very well that if it is self-contradictory it is absolutely impossible. The absolutely impossible may also be called the intrinsically impossible because it carries it’s impossibility within it’self, instead of borrowing it from other impossibilities which in their turn depend upon others. It has no unless clause attached to it. It is impossible under all conditions and in all worlds and for all agents.

    ‘All agents’ here includes God Himself. His Omnipotence means power to do all that is intrinsically possible, not to do the intrinsically impossible. You may attribute miracles to Him, but not nonsense. This is no limit to His power. If you choose to say ‘God can give a creature free will and at the same time withhold free will from it’, you have not succeeded in saying anything about God: meaningless combinations of words do not suddenly acquire meaning simply because we prefix to them the two other words ‘God can’. It remains true that all things are possible with God: the intrinsic impossibilities are not things but nonentities. It is no more possible for God than for the weakest of His creatures to carry out both of two mutually exclusive alternatives; not because His power meets an obstacle, but because nonsense remains nonsense even when we talk it about God.

    It should, however, be remembered that human reasoners often make mistakes, either by arguing from false data or by inadvertence in the argument it’self. We may thus come to think things possible which are really impossible, and vice versa.2 We ought, therefore, to use great caution in defining those intrinsic impossibilities which even Omnipotence cannot perform. What follows is to be regarded less as an assertion of what they are than a sample of what they might be like.”

  2. quan

    i think what you are saying here is that “we can be absolutely certain that something is true when the subject goes accord with certain condition”.

    TOK is theory of knowledge – human convention defined it so, so under the condition of following the definition it is true. I don’t argue whether this is false in anyway but this truthfulness depends on the condition of convention.

    all the other examples are also human convention.

    although I would like to focus on 2 interesting examples you give.

    if you are alive, your heart beats – those opposing stem cell research label an embryo alive, even though there’s no heart to beat.

    if amstrong was on the moon, then his finger was certainly on the moon – this is true under the condition that his finger did not get chopped off prior to departure.

    so certainly true is not that different to certainly false or simply true or simply false since they are all in such a way due to “conditions”.

  3. Bandana

    I really appreciate the effort you make in putting entire conversations between you and your students. This leads to clear revelation of the context as well as the concept and therefore clearer understanding. Your dedication shows.

  4. admin

    Thank you very much (a bit late, I know) for the compliments. Yes, making this site was a bit of a challenge, and it’s always nice to hear that the contents of the site meet the interests of the readers. I have to admit that I’m not an expert on postmodernism, one of the things that I do know, is that followers have a rather relativistic view of the world. I think I’ll write a post about relativism.

  5. Claire

    Mr Kim-
    i just wanted to thank you for putting together such a thoughtful and thought-provoking website! I read almost all of your articles and thoroughly enjoyed them. I am not a TOK student, I actually attended a high school with the IB programme and tried to get in, but didn’t get accepted. (My scores were 95 on the english section, and somewhere dismally low, like in the 40’s, on the math) I can’t believe there wasn’t a TOK class for the general students, and i feel totally cheated since i didn’t even know about it! but anyway, i am now a sophomore in college, and i’m writing a final 15 page paper for honors anthropology. The subject is postmodernism, as it relates mostly to anthropology but also to art, architecture, literature, etc. One of the main premises of postmodern thought, as you may be aware, is that there is no such thing as objective information, and that facts aren’t really facts at all. This was a difficult concept to wrap my head around before i could begin writing, and i found the study of knowledge theory extremely relative and helpful. I can tell you put a lot of effort into this site, and that you are a passionate and insightful teacher. So thank you, and props on the great work!
    Also, if you have any ideas about postmodernism in anthropology or as it relates to TOK, i would love to hear from you!

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