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The phrases in their context!

Extract from A TREATISE OF HUMAN NATURE:

Beasts certainly never perceive any real connexion among objects.
It is therefore by experience they infer one from another.
They can never by any arguments form a general conclusion, that those objects, of which they have had no experience, resemble those of which they have.
It is therefore by means of custom alone, that experience operates upon them.
All this was sufficiently evident with respect to man.
But with respect to beasts there cannot be the least suspicion of mistake; which must be ownd to be a strong confirmation, or rather an invincible proof of my system.
Nothing shews more the force of habit in reconciling us to any phaenomenoun, than this, that men are not astonished at the operations of their own reason, at the same time, that they admire the instinct of animals, and find a difficulty in explaining it, merely because it cannot be reducd tothe very same principles.
To consider the matter aright, reason is nothing but a wonderful and unintelligible instinct in our souls, which carries us along a certain train of ideas, and endows them with particular qualities, according to their particular situations and relations.
This instinct, it is true, arises from past observation and experience; but can any one give the ultimate reason, why past experience and observation produces such an effect, any more than why nature alone shoud produce it? Nature may certainly produce whatever can arise from habit: Nay, habit is nothing but one of the principles of nature, and derives all its force from that origin.
PART IV. OF THE SCEPTICAL AND OTHER SYSTEMS OF PHILOSOPHY.
SECT. I. OF SCEPTICISM WITH REGARD TO REASON.
In all demonstrative sciences the rules are certain and infallible; but when we apply them, our fallible said 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 deceived us, compared with those, wherein its testimony was just and true.
Our reason must be considered 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.
There is no Algebraist nor Mathematician so expert in his science, as to place entire confidence in any truth immediately upon his discovery of it, or regard it as any thing, but a were probability.
Every time he runs over his proofs, his confidence encreases; but still more by the approbation of his friends; and is raised to its utmost perfection by the universal assent and applauses of the, learned world.
Now it is evident, that this gradual encrease of assurance is nothing but the addition of new probabilities, and is derived from the constant union of causes and effects, according to past experience and observation.
In accompts of any length or importance, Merchants seldom trust to the, infallible certainty of numbers for their security; but by the artificial structure of the accompts, produce a probability beyond what is derived from the skill and experience of the accomptant.
For that is plainly of itself some degree of probability; though uncertain and variable, according to the degrees of his experience and length of the accompt.
Now as none will maintain, that our assurance in a long numeration exceeds probability, I may safely affirm, that there scarce is any proposition concerning numbers, of which we can have a fuller security.