The first paragraph of Hume’s “Of Scepticism with Regard to Reason”

 

"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 judgement, 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."

                Hume's first sentence in this paragraph makes the fairly reasonable claim that, due to our fallible faculties, even in the demonstrable sciences we are liable to fall into error.

                His second sentence starts by claiming that "We must, therefore, in every reasoning form a new judgement as a check or control on our first judgement or belief;"

                This "must" and "therefore" suggests that the claim attached to them is logically required by what is claimed in the first sentence. But this does not appear to be true. We do not have to take notice of our fallibility, and if we do take notice of it, logically we still do not have to do anything about it.

                Does this statement mean a) “we must form a new judgement, which will be a check or control on our previous judgement”, or that b)“ if we want a check or control on our judgement we will need a new judgement”?

                It is tempting to try and make sense of the first part of this second sentence by changing its order and supposing that 'IF we want a check or control on some reasoning we must[i] form a new judgement on it.' Here it is no longer a requirement resulting from Hume's first sentence. But Hume’s eventual paradox results from claiming every judgement requires a new judgement. If we only need a new judgement as a check or control on any judgement we might not need a new judgement if we didn’t want a check or control.  This brings up the question 'What purpose this check or control is supposed to fulfil?' In short, why should we need it? This question is especially puzzling given the second half of Hume's second sentence; there are other, and more useful, ways of checking or controlling our reasoning than viewing a history of our past reasoning and comparing the proportion of correct to incorrect instances it has produced. Hume himself mentions three such strategies; artificial accounting, going over your reasoning again, asking someone to check it, but only seems to see them as showing everyone agrees even our demonstrative reasoning’s are only probably true[ii].

       The purposes of our normal, but not apparently Hume’s, checks are to increase the likelihood of discovering any errors and so increase the possibility of truth. But the only thing Hume's type of new judgement seemingly effects is to make us aware how careful we need to be if we want to avoid making a mistake. After this effect it has lost its point because it itself is apparently not a check designed to increase the probability of truth.—also does "a new judgement" perhaps mean 'a different judgement'; Otherwise, again, why not just repeat your reasoning as a check?

                Hume next claims that our reason must be looked upon as a sort of cause of which truth is the (uncertain) effect, and then appears to return to the point of his first sentence of this paragraph saying that "by this means all knowledge degenerates into probability".

                I think that this last sentence could almost be placed directly after the first, and would then make some sense of the paragraph.[iii]

                The start of the paragraph would then read 'Our faculties are uncertain, even in the demonstrative sciences we can fall into error. By this means all knowledge degenerates into probability'.[iv] Since all knowledge is only probable, Hume thinks we must judge of it as he has said we must judge probabilities in three chapters dealing with the probability of chance, of causes, and un-philosophical probability. This is through ways in which the imagination makes a possibility more or less lively in comparison with its competitor possibilities. For instance, instances of the same possibility will increase that possibilities liveliness in the imagination; instances of contrary possibilities will destroy the liveliness of each in the imagination[v]. The possibility with a remainder of liveliness will be judged (or, believed as) probable, through the degree of its liveliness.

                This probability will consequently not be of a mathematical sort,[vi] but claims to be how either a mathematical or experienced superiority of one possibility can produce superior belief.[vii] In the present case, it will require a review of our past judgements as true or false, just as we must review the results of an uncertain causal situation to judge the probability of any possible outcome in a present case. So we will be looking on our judgement as a sort of cause. Consequently the probability resulting from our normal ways of checking our judgements will itself result from this sort of judgement even upon any mathematical results of those checks.

So; If the only form of control of judgements must involve a judgement of their probability, and if the belief in that probability (in spite of any surface mathematical relationships we think unmediatedly produce the belief) must be reached through Hume’s mechanisms making the various possibilities more or less lively than one another in the imagination, then the only form of control must be through these Humean mechanisms.

                But supposing the above is true, it would just seem to show that the only form of check on our judgements isn’t a very good way of checking our judgements, and checks on reasoning would almost subvert themselves at once, without needing Hume’s infinite train of judgements on judgements. Even worse, any attempt to understand Hume's argument in terms of what he says about his science of Human nature will mean that it is reason as it is described by his own science which subverts itself. So Hume could not be validly claiming that reason as independently understood when left to itself subverts itself, in order to then claim independently understood reasoning must be replaced by reasoning as understood by his science of human nature. But Hume still could claim that a different part of human nature solves the paradox that would otherwise be created by this part.