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The phrases in their context!

Extract from A TREATISE OF HUMAN NATURE:

But this decision, though it should be favourable to our preceding judgment, being founded only on probability, must weaken still further our first evidence, and must itself be weakened by a fourth doubt of the same kind, and so on in infinitum: till at last there remain nothing of the original probability, however great we may suppose it to have been, and however small the diminution by every new uncertainty.
No finite object can subsist under a decrease repeated IN INFINITUM; and even the vastest quantity, which can enter into human imagination, must in this manner be reduced to nothing.
Let our first belief be never so strong, it must infallibly perish by passing through so many new examinations, of which each diminishes somewhat of its force and vigour.
When I reflect on the natural fallibility of my judgment, I have less confidence in my opinions, than when I only consider the objects concerning which I reason; and when I proceed still farther, to turn the scrutiny against every successive estimation I make of my faculties, all the rules of logic require a continual diminution, and at last a total extinction of belief and evidence.
Should it here be asked me, whether I sincerely assent to this argument, which I seem to take such pains to inculcate, and whether I be really one of those sceptics, who hold that all is uncertain, and that our judgment is not in any thing possest of any measures of truth and falshood; I should reply, that this question is entirely superfluous, and that neither I, nor any other person was ever sincerely and constantly of that opinion.
Nature, by an absolute and uncontroulable necessity has determined us to judge as well as to breathe and feel; nor can we any more forbear viewing certain objects in a stronger and fuller light, upon account of their customary connexion with a present impression, than we can hinder ourselves from thinking as long, as we are awake, or seeing the surrounding bodies, when we turn our eyes towards them in broad sunshine.
Whoever has taken the pains to refute the cavils of this total scepticism, has really disputed without an antagonist, and endeavoured by arguments to establish a faculty, which nature has antecedently implanted in the mind, and rendered unavoidable.
My intention then in displaying so carefully the arguments of that fantastic sect, is only to make the reader sensible of the truth of my hypothesis, that all our reasonings concerning causes and effects are derived from nothing but custom; and that belief is more properly an act of the, sensitive, than of the cogitative part of our natures.
I have here proved, that the very same principles, which make us form a decision upon any subject, and correct that decision by the consideration of our genius and capacity, and of the situation of our mind, when we examined that subject; I say, I have proved, that these same principles, when carryed farther, and applied to every new reflex judgment, must, by continually diminishing the original evidence, at last reduce it to nothing, and utterly subvert all belief and opinion.
If belief, therefore, were a simple act of the thought, without any peculiar manner of conception, or the addition of a force and vivacity, it must infallibly destroy itself, and in every case terminate in a total suspense of judgment.
But as experience will sufficiently convince any one, who thinks it worth while to try, that though he can find no error in the foregoing arguments, yet he still continues to believe, and think, and reason as usual, he may safely conclude, that his reasoning and belief is some sensation or peculiar manner of conception, which it is impossible for mere ideas and reflections to destroy.
But here, perhaps, it may be demanded, how it happens, even upon my hypothesis, that these arguments above-explained produce not a total suspense of judgment, and after what manner the mind ever retains a degree of assurance in any subject? For as these new probabilities, which by their repetition perpetually diminish the original evidence, are founded on the very same principles, whether of thought or sensation, as the primary judgment, it may seem unavoidable, that in either case they must equally subvert it, and by the opposition, either of contrary thoughts or sensations, reduce the mind to a total uncertainty.
I suppose, there is some question proposed to me, and that after revolving over the impressions of my memory and senses, and carrying my thoughts from them to such objects, as are commonly conjoined with them, I feel a stronger and more forcible conception on the one side, than on the other.
This strong conception forms my first decision.
I suppose, that afterwards I examine my judgment itself, and observing from experience, that it is sometimes just and sometimes erroneous, I consider it as regulated by contrary principles or causes, of which some lead to truth, and some to error; and in ballancing these contrary causes, I diminish by a new probability the assurance of my first decision.
This new probability is liable to the same diminution as the foregoing, and so on, IN INFINITUM.
It is therefore demanded, how it happens, that even after all we retain a degree of belief, which is sufficient for our purpose, either in philosophy or common life.
I answer, that after the first and second decision; as the action of the mind becomes forced and unnatural, and the ideas faint and obscure; though the principles of judgment, and the ballancing of opposite causes be the same as at the very beginning; yet their influence on the imagination, and the vigour they add to, or diminish from the thought, is by no means equal.
Where the mind reaches not its objects with easiness and facility, the same principles have not the same effect as in a more natural conception of the ideas; nor does the imagination feel a sensation, which holds any proportion with that which arises from its common judgments and opinions.
The attention is on the stretch: The posture of the mind is uneasy; and the spirits being diverted from their natural course, are not governed in their movements by the same laws, at least not to the same degree, as when they flow in their usual channel.
If we desire similar instances, it will not be very difficult to find them.