Sloppy Language About What’s True: Part III

Today, a technical interregnum, a necessary pause for proof of that claim that each of us must come equipped with knowledge that cannot be learned. Stuff that is only known to be true only through introspection, via what we call intuition or, sometimes, faith; philosophers usually settle on the technical term a priori (or on phrases more technical still).

David StoveHere is one (of many) proofs given by David Stove in his The Rationality of Induction1 He made this argument in the support of a priori knowledge in his larger work showing induction is reasonable2. All you need know about Bolzano (named below), is that he disputed the idea that we all of us come with built-in knowledge. The formula numbers are as they appeared in the book.

Reading this passage, as with reading any proof, requires some sophistication. This cannot be avoided. But if you are comfortable with the idea of built-in knowledge, then you can skip this and start after the quote. Careful readers will recognize that Stove’s simple argument is also a proof that empiricism—the belief that all knowledge comes from observation—is false.

First, as to our knowledge of validity. Bolzano says that the validity of barbara, or rather, that the barbara schema always preserves truth, is a hypothesis reasonably believed by us, just because of the extensive experience we have had of never finding a counter-example to it. That is, our grounds for believing (149), or rather, for believing

     (166) For all x, all F, all G, either ‘x is F and all F are G is false’, or ‘x is G‘ is true,

consist just of observations we have made, such as

     (151) Abe is black and Abe is a person now in this room and all persons now in this room are black.

That is putting it starkly; still it is, in essence, what Bolzano believes. We learn deductive logic by inductive inference.

But now, this is tacitly to concede, to certain propositions of non-deductive logic, precisely the intuitive status which Bolzano expressly denies to any proposition of deductive logic. Our putative logic learner is supposed to be devoid of all intuitive logical knowledge. Yet Bolzano is evidently crediting him with knowing, straight off, at least this much: that

     (167): (151) confirms (149).

Of course, he need not be supposed to know that he knows (167); still, he is evidently being supposed to know it. But to know (167) is to have some logical knowledge, even is only non-deductive logical knowledge.

And Bolzano must suppose that (167) is known by our logic learner intuitively. Otherwise he would have to have learnt it, as he is supposed to be learning (166), by experience. And how would he accomplish this?

It must at any rate be from some observation-statements. I do not know what kind of observation-statements Bolzano would regard as confirming (167): let us just call these observation-statements

     (167) O1.

But even if our logic learner has found by experience that O1 he will be no further advanced. To learn (167), he needs to know, not only that O1, but that

     (169): (168) confirms (167).

But this is a proposition of logic too. If he does not know (169) intuitively, as by hypothesis he does not, then he will have to learn it, too, from experience. No doubt from some observations

     (170) O2.

But that is not enough. He will also need to know that

     (171): (170) confirms (169);

and so on.

Obviously, he is never going to make it. Experience is not enough.

Especially careful readers—especially those convinced by this proof, as I am—will recognize that in order to interpret this proof, to assimilate it and follow it, requires precisely the kind of built-in knowledge of which the proof speaks. We must have a priori knowledge.

We are finally ready to tackle the notion that some propositions are “just true.” Propositions of this sort are usually the kinds of truths spoken of above, but there are also moral or ethical truths, too (of these, another day). The claim that there exist “universal truths”—propositions which say are just plain true—is consistent with claim that all truth is conditional, because whatever a priori knowledge we have is conditional on our intuition, or is taken “on faith.” To speak of these truths (in a technical sense) we must first affix the condition, “Given my faith or intuition, this proposition is just true.”

This seems to open the way to relativism because, as direct experience tells us, different people will claim a certain proposition true or false just because their intuitions or faith direct them oppositely. Many times, of course, these differences are mistakes in reasoning, or there are other pieces of evidence that are assumed (as in French speaking chickens) that the speaker is not aware of or does not acknowledge. Skip these cases and focus on just those claims where nothing is assumed except intuition or faith.

The claim is that we must have some shared beliefs about what is true, and it is these beliefs which we speak of when we say “there are truths.” One is that “Other minds exist.” Or, more properly, “Given our intuitions or faith, other minds exist.” The only possible escape from believing this shared truth is solipsism, which is “Given my intuition, only I exist.” Deep, or metaphysical solipsists stop here. But other solipsists (there are varieties of the breed) might allow that “Given my intuition, it is true I exist; but I believe it is logically possible that others might exist.”

But to acknowledge “logical possibility” is to acknowledge at least the truth that logical propositions are true. So that if those other minds exist, they must have this knowledge, too because that is what a mind is. And then if one really is a metaphysical solipsist (good luck finding one) it is still true that “all” share beliefs about what is true—it just the case that “all” is one person. (How many solipsists will jump in and tell me, “Briggs, you don’t exist! Stop claiming you do!”)

In practice, of course, we all really do admit that truth (given our intuitions) that others minds exist. This, then, if just one of many truths that exist. The logical knowledge spoken of by Stove are others. Our task is now clear: since truths, via shared faith or intuition exist, we must identify what they are; we must also identify falsehoods, and that which is only probable. More on this later.


1p. 162-163. This book, especially the second half, is a treasure that all statisticians, probabilists, and logicians should read.

2Yes, some people think it isn’t. Bolazno was not one of these: he thought all (as in all) knowledge was known empirically.


  1. commieBob

    Any logic exercise has to start somewhere. If you aren’t allowed to have a priori knowledge, then you have to go back to the very beginning, wherever that is. What shall we all agree is true so that we can start reasoning from there?

    Logic should have error bars. It is only infallible when it is based on something that is exactly correct. Since nothing is absolutely accurate, logical conclusions will become less accurate as you extend the string of logical operations. Once you have too many layers of logic, your conclusions are probably wrong.

    So, we are between a rock and a hard place. Either we accept some truth based on our lived experience and start there, or we pile up logic from a much more distant starting place. In either case, we know that out conclusions will be flawed.

  2. Rich

    Don’t Aristotle’s Laws of Thought give us somewhere to start?

  3. DAV

    Bolazno has a point. What knowledge were you born with? Unless it’s innate, it had to be learned. Wouldn’t that make it empirical (also when derived from what was learned)?

  4. Luis Dias

    So, “plain truths” are intuitive truths…. and they are true because they are faith-based, so that makes them true…. and this is not a relativistic way of thinking because…. because there are other minds!! This must all be true, coz I have a deep faith in it.

    Mr Briggs, you confused yourself pretty badly in your last paragraphs. You started trying to say something, you entered into quite another thing and ended saying something entirely different.

    IOW, you didn’t solve the problem of faith-based knowledge when they are contradictory. What happens when two faith-based truths clash against one another, besides a medieval war? To acknowledge the existence of other minds is somewhat cute, but really we are dealing with a problem far beyond that one. How can you choose between these two faith-based absolute (and therefore entirely correct) truths?

    The only solution to your problem is to assume that they are not fundamental truths, that they may well be solvable by other means. This however entails the belief, which is nothing short of a religious belief, that there is a fundamental truth to be found at the core of “our” beliefs. But this is, (aha!) just another belief. That may run counter to different ones who may think that they already have the final answer.

    You can run from relativism, but you can’t hide forever, mr Briggs.

    There are also major major problems with everything you said earlier (mostly about strawmans), but let’s not spam your blog right now ;).

  5. What is a priori knowledge? For starters, let us ah-prior to the lowly amoeba. It has been demonstrated that the amoeba can sense light and certain chemicals. To some primitive degree, it can sense its environment.

    Similarly, David Stove, when he was a fetus, could sense light and certain chemicals, and on the day he was born could sense pain, evidenced by his howling on that auspicious occasion. Life hurt, and he knew it.

    Is that the a priori knowledge to which you refer? If so, I think you mean potential knowledge, or incipient knowledge. Because until the empirical event of sensation, only the potential was there.

    Knowledge is not a logical proposition. Nor is truth. Plenty of knowledgeable people are illogical. Consider the amoeba. Whether logic itself is true is another matter entirely.

    Now, you can deny the existence of other minds if you want to, but reality may come back to bite you. Does Luis really exist? I think not. But then Luis steals your car, and you really have to admit he’s out there.

  6. Alex Heyworth

    It’s remarkable how unpopular solipsism has become; I seem to be the only solipsist around.

  7. Luis Dias

    Alex, you made me chuckle in an embarrassing way at the office. Very well done ;).

  8. Sander van der Wal

    I am not convinced. In particular the reasoning “It is my intuition that I exist” doesn’t work for me. I know that I exist, but that is not because of intuition. My existence is an observation made by myself of myself. It is my intuition that other people are observers by themselves of themselves too.

    Then there is the problem what exact knowledge are people born with. Is there a list? What is on that list?

  9. Briggs


    Well, just the sort of knowledge which Stove proved you had.


    You’ll have to make a specific claim, old friend, otherwise I’ll be forced to show how relativism leads to the modern (not medieval) Gulag.

    Uncle Mike,

    And of course an amoeba’s reaction is purely chemical. There is no consciousness involved.

    Sander van der Wal,

    You made the observation that you exist, and from that observation you concluded that “Sander van der Wal exists.”

    Now, how did you know—this is the key—that observations of the type you made confirm the statement “Sander van der Wal exists”?

    You could have not learned this by experience. You had to come equipped with this kind of knowledge.

  10. Luis Dias

    Of course you have learned that by experience! It’s called childhood!!

    I won’t further the discussion right now, I’m in a hurry, but that error was just screaming at me.

  11. Briggs


    No, it won’t work. See Stove’s proof. You can’t bootstrap empiricism. Even babies have to know that observations verify certain propositions. And if they could learn it from their parents, then they’d already have to know that “parent’s teach” (you get the idea).

  12. Dear Uncle Matt,

    Of course amoebas are conscious. They sense their environments, and can differentiate between self and not self. Just as all animal life does. Birds do it, bees do it, even educated fleas do it.

    Consciousness IS chemical. It’s all chemistry. You are a bag of chemical reactions. We exist in a physical world, my friend.

    Do not despair, however, or lose your faith, because chemistry is a marvelous thing. Indeed, one might call it miraculous.

  13. Briggs

    Uncle Mike,

    My CCD camera also senses the environment but it is not conscious. The body is chemical, but consciousness is something that arises out of the workings of the body, but it is not the body. We are more than our chemicals. Whether that’s miraculous is a different question.

  14. The question is whether we are born with a priori knowledge. I offered the amoeba as proof. But let’s examine a more familiar non-human organism, the dog.

    My dog is extremely conscious, self-aware, aware of her surroundings, clever, capable of learning, too smart for her own good sometimes, a dreamer, and equipped with a full range of emotions, including love. She loves me and I love her. Without a doubt.

    Are those characteristics learned or inate? No doubt about it, they are inate. She was born with the potential for all those behaviors, mental and physical. As are all dogs.

    Now, my dog cannot create or even comtemplate logical syllogisms. Stove, Bolzano, et al are better at logic than Skinner (she is so cute you just want to skin her alive). But Skinner knows when she is hungry, and how to beg for food, and how to eat it. I suspect that the great metaphysicians, after a tough morning of meditation on the ethereal, also got a little peckish and went out for a nosh.

    How did they know to that? Deconstructing back to first principles, they were born hungry.

  15. Sander van der Wal

    I was self-aware before I knew that that meant “Sander van der Wal bestaat” (I am Dutch so the “does exist” bit became much later). I did not even know I was “Sander van der Wal ” at that time. I was “I”. You might call that (a kind of) knowledge.

    But given that that “I” was not self-evident earlier, it is still possible that that knowledge of “I” was created later, by some mechanism in the physical brain for instance. Which means that the physical brain must have a mechanism for creating (that kind of) knowledge, but doesn’t necessarily need to have knowledge built-in.

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