I was browsing Hume and had an insight that advanced my understanding of Treatise 1.4.1, "Of scepticism with regard to reason," considerably. The section, as one might expect, contains an argument about the fallibility of reasoning; in particular: demonstrative reasoning turns out to have exactly the same evidence or certainty as probabilistic reasoning, and probabilistic reasoning turns out, if it were taken (falsely, as Hume thinks) to be grounded on pure reason, to annihilate itself. This is not, I think, generally understood properly, and, reading the section again last night, I lighted upon what should at least be a partial key to the section. The key, like so many keys to philosophical passages, is right out in the open, in the first paragraph:
In all demonstrative sciences, the rules are certain and infallible; but when we apply them, our fallible and uncertain faculties are very apt to depart from them, and fall into error. We must, therefore, in every reasoning form a new judgment, as a check or controul on our first judgment or belief; and must enlarge our view to comprehend a kind of history of all the instances, wherein our understanding has deceiv'd us, compar'd with those, wherein its testimony was just and true. Our reason must be consider'd as a kind of cause, of which truth is the natural effect; but such-a-one as by the irruption of other causes, and by the inconstancy of our mental powers, may frequently be prevented. By this means all knowledge degenerates
into probability; and this probability is greater or less, according to our experience of the veracity or deceitfulness of our understanding, and according to the simplicity or intricacy of the question.
Did you see it? Here's the same paragraph again, with the key elements highlighted:
In all demonstrative sciences, the rules are certain and infallible; but when we apply them, our fallible and uncertain faculties are very apt to depart from them, and fall into error. We must, therefore, in every reasoning form a new judgment, as a check or controul on our first judgment or belief; and must enlarge our view to comprehend a kind of history of all the instances, wherein our understanding has deceiv'd us, compar'd with those, wherein its testimony was just and true. Our reason must be consider'd as a kind of cause, of which truth is the natural effect; but such-a-one as by the irruption of other causes, and by the inconstancy of our mental powers, may frequently be prevented. By this means all knowledge degenerates into probability; and this probability is greater or less, according to our experience of the veracity or deceitfulness of our understanding, and according to the simplicity or intricacy of the question.
In other words, Hume's approach to reason in 1.4.1 is to analyze it according to the causal analysis of 1.3. This causal analysis contains the following elements:
1) There is no connection discoverable a priori between cause and effect.
2) Our idea of causation is that of constant conjunction combined with that of necessary connection.
3) Our idea of necessary connection derives not from anything we find in the objects themselves, but entirely from the determination of the mind to pass from one object to another in inference.
4) By experiencing causal sequences of this sort we begin to develop rules or maxims to assist us in sorting them out.
5) Hume gives eight general rules - the most general maxims of causation - for judging of cause and effect in 1.3.15.
In 1.4.1, Hume is applying this analysis to reasoning. As he says, "Our reason must be consider'd as a kind of cause, of which truth is the natural effect." But we know that reasoning is an imperfect or incomplete cause of true conclusions, since we are often wrong. This is, as Hume rightly says, true even in demonstrative sciences. A sign of this is, as Hume rightly notes, that we check our work. To develop a causal analysis of the relation between reason and truth, then, we need to develop "a history of instances" (I suspect it's not an accident that this phrase sounds like the Baconian account of induction) in which we get the truth and in which we get error. This is, in fact (as Hume also rightly notes), the sort of thing we do in checking our reasoning in the first place. What Hume then notes is that there is no intrinsic stop to checking. I can reason, check my reasoning, check the reasoning involved in checking my reasoning, check the reasoning involved in checking the checking of my reasoning, ad infinitum. If (as Hume thinks the rationalist account of reason requires) the certainty of one's reasoning depends on its being right, the fact that there's no stop to checking shows that there is a compounding uncertainty: we can be wrong in our reasoning; we can be wrong about whether we are correct in our reasoning; we can be wrong about whether we are correct in our judgment of whether we are correct in our reasoning; and so on, infinitely. To take a very simplified case, if there is an 80% chance that there's an 80% chance that there's an 80% chance that there's an 80% chance that there's an 80% chance that there's an 80% chance, etc., etc., that there's an 80% chance we are right, how certain can we really be that we are right (note that the same applies to our certainty about our being wrong; contrary to what is sometimes thought, this only strengthens Hume's argument)? This, Hume argues, means that the rationalist account of reason, the one that tries to justify reasoning in terms of pure reason itself, annihilates reason. In place of this Hume proposes his own account of reason, which is that ultimately reason is grounded on custom and instinct. In his famous words, "Nature, by an absolute and uncontroulable necessity has determin'd us to judge as well as to breathe and feel," and "belief is more properly an act of the sensitive than of the cogitative part of our natures."
His argument is often thought to be wrong; but it is not wrong for the reasons often claimed, nor is the source of its wrongness what is usually identified as the source, nor (for that matter) is it as wrong as it is often thought to be. If we try to characterize reasoning's being a source of truth, Hume is absolutely right that there is no easy analysis; he is entirely right that if we are forced into this infinite regress (for that is what it is) we've mired ourselves in skepticism; he is completely right that there are accounts of justification, warrant, checking, certainty, reasoning, or whatever you want to call them, that force us into this infinite regress; he is entirely right that reasoning must be based on something more peremptory than reasoning itself. His project of trying to find a causal analysis of reasoning's relation to true conclusions is an entirely reasonable and useful one. In my view, his critique is quite right. The flaw is his attempt to make this into an argument for his own (already flawed) account of belief, and thus is found chiefly in his own causal analysis of reasoning. Hume's critique could just as easily be marshalled in favor of an Aristotelian or a Platonic view of reason as it could for his own; presumably he would think these ruled out by his general principle (that ideas are derived from impressions of which they are copies), but this is not, I think, right, even if we held the general principle to be correct (which we needn't).
This understanding of 1.4.1 as a causal analysis of reasoning has ramifications for other aspects of Hume, e.g., for what he is doing in the rest of Part IV (particular in 1.4.2 and 1.4.7), as well as for (possibly) his account of reason's relation to the will and others.
