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How can I know nothing is red and green all over, when I’ve never checked every red thing?

A friend gave me this puzzle and I can't stop thinking about it.

A surface cannot be completely red and completely green at the same time, in the same place. I am sure of this. But I have not checked every red thing in the world. I did not do an experiment. I just see that it must be so, by thinking. How is that possible? Is it really knowledge, or just something about how we use the words "red" and "green"?

The reason it bothers me: last month I read al-Ghazālī's Deliverance from Error, where he describes a period when he doubted even things like "ten is more than three". He imagined that reason might be judged by some higher faculty, the way reason judges the senses when it tells us the sun is bigger than it looks. If someone as serious as al-Ghazālī could doubt that, what makes "red and green can't overlap" safe?

Please explain simply what "a priori" knowledge is and what the main positions are. I know the word but not much more.

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4 answers

Accepted answer

  1. Henrike Vogel

    ✓ Accepted answer Fellow

    "A priori" means known independently of experience, not before it. You need experience to have the concepts red and green at all. The question is whether, once you have them, your knowledge that they exclude each other depends on further observation. It seems not; that is what makes it a priori.

    The main accounts of what such knowledge is:

    • Rationalism: reason directly grasps some necessary truths, as a kind of intellectual seeing.
    • Conceptual analysis: you are unpacking what your concepts already contain, as with "bachelors are unmarried".
    • Conventionalism: such truths record the rules of our language, not facts about the world.
    • Kant: some a priori truths are synthetic, saying something substantive, yet necessary because they reflect the structure our experience must have. His example is 7 + 5 = 12.
    • Empiricism (Mill, and in a different way Quine): there is no real a priori; such truths are just extremely well-confirmed generalisations, revisable in principle.

    Your example is famous precisely because it is awkward for the conceptual-analysis view. Nothing in the definition of "red" says "not green". You cannot look it up the way you can look up "unmarried" in "bachelor". So either the exclusion is a fact about colours that reason grasps (the rationalist or Kantian answer), or our concepts contain more than their definitions show.

    1. Fajar Nugroho

      Fellow

      Thank you, Henrike. This is clear. But it makes my al-Ghazālī worry bigger. If a priori knowledge is "reason seeing", what protects it from the worry that reason itself might be wrong, like the senses?

      Helpful · 2
      1. Bilal Rashid

        Fellow

        Fajar, al-Ghazālī's own answer is worth knowing, because he does not claim to have proved his way out. He says the doubt lasted about two months and was cured not by an argument but by a light that God cast into his breast, after which the necessary truths of reason were accepted again as trustworthy. You can read that as theology, or as the honest admission that the first principles of reasoning cannot be demonstrated without using them. Philosophers in many traditions have reached the second conclusion by other routes.

        Helpful · 3

Other answers

  1. Tomasz Szewczak

    Fellow

    A nice historical footnote: this exact example broke part of Wittgenstein's early philosophy. In the Tractatus all necessity was supposed to be logical necessity, and the simplest propositions were supposed to be independent of each other. But "this point is red" and "this point is green" are not independent: one excludes the other, and not by logic. By 1929 he admitted the colour-exclusion problem could not be handled in the old framework. So you are in very good company being bothered by it.

    Helpful · 1