A brief aside to talk with our friend David

I’ve just been reading a passage from David Hume’s A treatise of Human Nature*, about how we can come to some level of certainty in our investigations. It makes some good points (which I agree with and have thus far in my investigation, not disagreed with), and at other points falls catastrophically on its face. Let’s go!

[Edit: I have removed the first argument I made about this passage from Hume as I possibly have misunderstood a term he uses – demonstrable sciences – and applied to it meaning which he did not. I have thus replaced the older argument with what I feel to be a much stronger one. Thank you Dan for pointing out my error – I would hate to have continued on in it!]

We are permitted to substitute words for other words which would still manage to convey the initial concept accurately. “Concepts” afford us that luxury. We will apply such a substitution here, in order to make the argument more obvious to the reader:

Hume says these two things in the passage:

By the term infallibility, one means complete correctness or, quite literally, truthfulness.

Furthermore, when Hume says truth is the effect of reason he is essentially saying that it resides in the mind alone – thus it does not reside outside the mind (we can with some certainty know he meant this as he was largely an Idealist).

So the conclusion that Hume’s argument arrives us at is:

I hope, for the sake of my argument, by “demonstrable sciences” he would include the disciplines of Physics and Logic. But he may truly have been referring strictly to mathematics, in which case, the
absurdity of the assertion is still evident.

What Hume is proposing is that, on the one hand, the demonstrable sciences are infallible – truthful. On the other, that truth is merely the residue of thought in the mind – that nothing is objectively true.

How this argument defeats itself, in the first, is that the concept of “infallibility” is utterly meaningless, as truth, apparently, is only in the mind. And so Hume then must not be permitted to use the word to his advantage.

Secondly, granting him use of the term, what is implied is that nothing Hume says at all can be trusted, because, well, truth is only in the mind, and thus, nothing of a standard that can be shared between minds, or asserted in any Universal way.

Thirdly, and more importantly, Hume is saying that in fact mathematics is not, of itself, true. So, 2+2 can equal 5 – it’s no sweat really. A triangle can be made of more than 3 sides – and why not – as the predicate/subject agreement of an a prioi statement can’t hold me! The shortest distance between two points may in fact not be a straight line – I can imagine wormholes and so, they’re truth.

This is sheer lunacy. In fact, it’s a lunacy that Kant was thankful Hume didn’t commit. He was thankful that Hume did not dismiss math as illusory. It would appear though, that it is the inevitability of his reasoning from this passage (and I’m sad for Kant that he missed it).

Now, I think it’s reasonable to propose, that if every human were annihilated, there would, perhaps
in some remote corner of the Universe, hidden away on any icy moon, be a few triangles huddling together to keep warm. Truly, if there be in the Universe nothing more than two, even infinitesimally small points (no matter how far apart they be) that can be connected by a line, Hume is shown to be in error.

Another consequence is this: Hume says we cannot trust our faculties – our subjective sensory experience – and so must apply reason to our discoveries, in order that we might make up for our facultative weakness, and move closer to probable truth (and as he says of our investigations, certainty is only ever a matter of increasing probability), since some of the principals of our reason are in fact based on mathematic, and there for infallible, principals.

Pardon me?

Let’s evaluate the implications, based on what we’ve established so far:

1. our faculties are mind
2. reason is in the mind
3. truth is of the mind

What he is advocating is that we apply our minds to our minds. Since our faculties are faulty, we apply reason, logic, that is infallible principals, to the fallible observations. But, since truth is only in the mind (thus, not real, thus, not truth), what we are in essence doing is applying fallibility to fallibility. Thus what we arrive at, for all our labors, is absolutely nothing but whimsy. We are left with utter meaninglessness.

Now, let’s give David the benefit of the doubt. Maybe he was having a rough day. Maybe he was behind on his sleep. Maybe he had a bad piece of cheese and was suffering from a bout of indigestion, and was thus out-of-sorts when he wrote this piece. I suppose, however, since he was
an Idealist, there’s no such thing as indigestion at all, it’s only in the mind (and so too would every disease be Psychosomatic and self-inflicted).

Since triangles exist; since there are points with space between them; since 2+2 does in fact amount to four (and they’re quite happy about the new living arrangement I might add) it is evident that we cannot appeal to Hume in this matter.

This is too bad, as I agree with what his general point is: that we apply reason to observation, in recursive and ongoing way, to refine our knowledge. He says:

“Since therefore all knowledge resolves itself into probability, and becomes at last of the
same nature with that evidence, which we employ in common life, we must now examine this latter species of reasoning, and see on what foundation it stands.

In every judgment, which we can form concerning probability, as well as concerning knowledge, we ought always to correct the first judgment, derived from the nature of the
object, by another judgment, derived from the nature of the understanding.”

We continually evaluate and interrogate our first judgment, until we have, at last (which never comes because he says it must take place in infinitum), been exacting enough to render a “probability,” more
probable. Thus, we can only really arrive at “maximal probability.”

In this series of my thoughts of philosophy in science, that is where I am headed: let us understand that our “scientific conclusions” are only “maximal probabilities” given the knowledge we have up to this point accumulated, but are not definitive and are open to revision – though I cannot in good conscience stop there.

Support for my point, from Hume’s own mouth:

“we ought always to correct the first judgment, derived from the nature of the object, by another judgment, derived from the nature of the understanding.”

So, we are encouraged to bring further judgments to bear on the first, to maximize our possibility of correctness – that’s all I’m advocating, but at a paradigmatic level. It does not serve us to simply limit self-correction to our understanding of objects and not our very methods of evaluation. We are permitted to subjugate an entire methodology to refining judgments, so that we might better establish its role and its correctness.

* thanks again to Dan for recommending this article, and for his refining questions.

tags: David Hume, philosophy, science