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[1.0] Philosophy, Empiricism, & Billiard Balls

v1.1.1 / chapter 1 of 6 / 01 dec 23 / greg goebel

* David Hume believed there were two broad categories of philosophy: one which was entertaining and inspirational, the other which was analytical. Although he thought "easy" inspirational philosophy was fine in its place, he was focused on "abstruse" analytical philosophy. He clearly understood that abstruse philosophy could easily fall into obscurantism; it was his goal to cut through the "intangling brambles" of dubious philosophy to obtain something of value.

His tool was "skeptical empiricism" -- too often mischaracterized as an unlimited skepticism, which Hume emphatically rejected, instead being the assertion that all we could know about the Universe was what we observed of it. From that basis, Hume constructed a theory of mind, built around a carefully-crafted definition of "causality", resting on the question of: What happens in the collision of billiard balls?

HUME ON KNOWLEDGE


[1.1] THE ROOTS OF EMPIRICISM
[1.2] THE TWO SPECIES OF PHILOSOPHY
[1.3] HUME'S THEORY OF MIND & CAUSALITY

[1.1] THE ROOTS OF EMPIRICISM

* David Hume was misunderstood in his lifetime, and remains misunderstood. That's not because his work is too high-flown; no, though subtle, it's pragmatic and straightforward.

The pragmatism was a necessary consequence of his adoption of the Newtonian approach to understanding the world. In the century before Hume, Isaac Newton took an "empirical" view of the Universe. Under empiricism, we observe the physical world around us and, from our observations, come to a comprehension of it. Empiricism dovetails with skepticism: anything that exists in the physical Universe that we can't observe in any tangible sense, we don't know anything tangible about. Put informally, empiricism says: What you see is what you get.

Empiricism was nothing new; it was articulated 2,000 years before Hume by the Greek scholar Epicurus, who believed our senses were the only true sources of information about the world around us. Epicurus rejected Plato's "idealism" -- the attempt to obtain knowledge of the world through reasoning instead of observation -- and the skepticism of Pyrrho, who believed the senses were an unreliable guide to the world.

Epicurus accepted that our senses could mislead us, but asserted that we had nothing else to tell us about the world. Anything could be possible, but we could only know about what actually was through observation. He believed that morality was ultimately based on our feelings, not on reasoning; although he didn't reject the gods, he saw no reason to believe in an afterlife, and a fixation on it could undermine our ability to deal with the here and now. Epicurus accordingly judged that we ought to enjoy the better things in life -- a notion lingering in the modern term "epicure" -- but believed in moderation, not unrestrained hedonism.

Empiricism was later examined by the English philosopher John Locke, a rough contemporary of Newton -- and Locke's early investigation suggested that the principle of "what you see is what you get" is, if appealing, more simple-minded than it sounds. If we can only rely on perceptions, does that mean we can only place trust in what we see in the here and now, not what we remember? What about our memories -- can they be trusted? And how about the observations by others of things that we haven't seen ourselves? Even when we see things in the here and now, are we actually perceiving them correctly? Aren't the things we see filtered through our preconceptions and subject to our misconceptions?

The Irish scholar Bishop George Berkeley -- incidentally, the city of Berkeley in California is named after him, though he actually pronounced his name "Barkeley" -- took Locke's ideas on empiricism one step further, asking: can we even assume a physical world actually exists independent of human observers, or do we conclude the only reality is in our mind?

It's a good bet that people asked such a question would reply that, yes, we can assume an external world -- but they would not be able to give any reason why. After all, if we insist that we can only trust our senses, then if we are serious in our skepticism, we then have to ask how we can prove our senses are trustworthy. What if the external world just an illusion? Does a tree exist when we don't see it?

Berkeley argued that, if we truly accept the empirical principle, we can't assume any such thing, to conclude that the only reason we perceive a consistent external world was because of God. If the external world only amounts to elements in our own consciousness, then a comprehensive external Universe, superior to and consistent in space, time, and from one person to another, could only exist from the absolutely pervasive and constant consciousness of the Deity. As was put in a set of well-known limericks by the 20th-century Catholic theologian Ronald Knox:


   There was a young man who said:  God
   Must think is exceedingly odd:
   If he finds that this tree
   Continues to be
   When there's no one about in the quad.

   Dear Sir:  Your astonishment's odd:
   I am always about in the quad.
   And that's why the tree
   Will continue to be
   Since observed by, yours faithfully, God. 

Berkeley did add some significant qualifications to his ideas to make them sound less outrageous -- but even in his time, his version of idealism was properly regarded as silly, James Boswell famously describing Dr. Samuel Johnson's reaction to it:

BEGIN_QUOTE:

After we came out of the church, we stood talking for some time together of Bishop Berkeley's ingenious sophistry to prove the nonexistence of matter, and that every thing in the universe is merely ideal. I observed, that though we are satisfied his doctrine is not true, it is impossible to refute it. I never shall forget the alacrity with which Johnson answered, striking his foot with mighty force against a large stone, till he rebounded from it: "I refute it THUS!"

END_QUOTE

Bishop Berkeley had indeed uncovered difficulties in Locke's thinking, and Berkeley also worried, with good reason, that empiricism would undermine the case for religion -- and so, in a clumsy Zen fashion, he decided to use it to justify the case for God instead. However, in following up the defects in Locke's ideas to their ridiculous conclusions, Berkeley created an argument far too useless to convince either believers or nonbelievers of anything, except to be exasperated with Berkeley.

BACK_TO_TOP

[1.2] THE TWO SPECIES OF PHILOSOPHY

* David Hume outlined his reconsideration of Locke and Berkeley in his youthful book, A TREATISE OF HUMAN NATURE. Hume wanted to know if the empirical science of Newton could be applied to human nature, in essence the human mind:

BEGIN_QUOTE:

There is no question of importance, whose decision is not comprised in the science of man; and there is none, which can be decided with any certainty, before we become acquainted with that science. In pretending, therefore, to explain the principles of human nature, we in effect propose a compleat system of the sciences, built on a foundation almost entirely new, and the only one upon which they can stand with any security.

END_QUOTE

Hume elaborated on his ideas about human nature at length, presenting ideas to challenge the conventional wisdom. Alas, the TREATISE was not well-received, and in fact was not all that well-written, not in a league with elegant mature writings. Taking his failure to heart, Hume came back to his "skeptical-empirical" philosophy in the much-improved ENQUIRY INTO HUMAN UNDERSTANDING -- the 1ST ENQUIRY.

Section I of the 1ST ENQUIRY, titled "Of The Different Species Of Philosophy", raises the curtain on what is to follow, starting out by identifying two sorts of philosophy:

BEGIN_QUOTE:

The one considers man chiefly as born for action; and as influenced in his measures by taste and sentiment; pursuing one object, and avoiding another, according to the value which these objects seem to possess, and according to the light in which they present themselves. As virtue, of all objects, is allowed to be the most valuable, this species of philosophers paint her in the most amiable colours; borrowing all helps from poetry and eloquence, and treating their subject in an easy and obvious manner, and such as is best fitted to please the imagination, and engage the affections.

... The other species of philosophers consider man in the light of a reasonable rather than an active being, and endeavour to form his understanding more than cultivate his manners. They regard human nature as a subject of speculation; and with a narrow scrutiny examine it, in order to find those principles, which regulate our understanding, excite our sentiments, and make us approve or blame any particular object, action, or behaviour.

They think it a reproach to all literature, that philosophy should not yet have fixed, beyond controversy, the foundation of morals, reasoning, and criticism; and should for ever talk of truth and falsehood, vice and virtue, beauty and deformity, without being able to determine the source of these distinctions.

END_QUOTE

Hume noted that engaging "easy" philosophy is inevitably more popular than rigorous "abstruse" philosophy:

BEGIN_QUOTE:

It is certain that the easy and obvious philosophy will always, with the generality of mankind, have the preference above the accurate and abstruse; and by many will be recommended, not only as more agreeable, but more useful than the other. It enters more into common life; moulds the heart and affections; and, by touching those principles which actuate men, reforms their conduct, and brings them nearer to that model of perfection which it describes.

On the contrary, the abstruse philosophy, being founded on a turn of mind, which cannot enter into business and action, vanishes when the philosopher leaves the shade, and comes into open day; nor can its principles easily retain any influence over our conduct and behaviour. The feelings of our heart, the agitation of our passions, the vehemence of our affections, dissipate all its conclusions, and reduce the profound philosopher to a mere plebeian.

END_QUOTE

Worse for abstruse philosophy, any such philosopher could easily make blunders, with any small error derailing the entire line of reasoning. Easy philosophy, not attempting to put forward rigorous arguments, was not so vulnerable to error; any one error was likely to be nothing more than a blemish on the whole. In any case, neither sort of philosophy got that much respect, though the alternative was worse:

BEGIN_QUOTE:

The mere philosopher is a character, which is commonly but little acceptable in the world, as being supposed to contribute nothing either to the advantage or pleasure of society; while he lives remote from communication with mankind, and is wrapped up in principles and notions equally remote from their comprehension. On the other hand, the mere ignorant is still more despised; nor is any thing deemed a surer sign of an illiberal genius in an age and nation where the sciences flourish, than to be entirely destitute of all relish for those noble entertainments.

END_QUOTE

Hume suggested a balance:

BEGIN_QUOTE:

Abstruse thought and profound researches I prohibit, and will severely punish, by the pensive melancholy which they introduce, by the endless uncertainty in which they involve you, and by the cold reception which your pretended discoveries shall meet with, when communicated. >Be a philosopher; but, amidst all your philosophy, be still a man.<

END_QUOTE [ angle brackets added to original text for emphasis ]

Granting the limitations of abstruse philosophy, what could be said in its defense? One definition of philosophy is "asking questions about questions", or similarly "thinking about thinking" -- and not only do people do it, they can't keep from doing it, in all walks of life. There are philosophies of law, of politics, of science, of engineering. The world poses endless questions, and we are compelled to try to answer them. Besides, to a certain mindset, it's fun:

BEGIN_QUOTE:

Were there no advantage to be reaped from these studies, beyond the gratification of an innocent curiosity, yet ought not even this to be despised; as being one accession to those few safe and harmless pleasures, which are bestowed on human race.

END_QUOTE

Yes, of course it's true there is bad philosophy:

BEGIN_QUOTE:

Here indeed lies the justest and most plausible objection against a considerable part of metaphysics, that they are not properly a science; but arise either from the fruitless efforts of human vanity, which would penetrate into subjects utterly inaccessible to the understanding, or from the craft of popular superstitions, which, being unable to defend themselves on fair ground, raise these intangling brambles to cover and protect their weakness.

>Chaced from the open country, these robbers fly into the forest, and lie in wait to break in upon every unguarded avenue of the mind, and overwhelm it with religious fears and prejudices.< The stoutest antagonist, if he remit his watch a moment, is oppressed. And many, through cowardice and folly, open the gates to the enemies, and willingly receive them with reverence and submission, as their legal sovereigns.

END_QUOTE

Very well, then one of the main reasons to study philosophy is to learn to watch out for bad philosophy, and take it on:

BEGIN_QUOTE:

Is it not proper to draw an opposite conclusion, and perceive the necessity of carrying the war into the most secret recesses of the enemy? ... Accurate and just reasoning is the only catholic remedy, fitted for all persons and all dispositions; and is alone able to subvert that abstruse philosophy and metaphysical jargon, which, being mixed up with popular superstition, renders it in a manner impenetrable to careless reasoners, and gives it the air of science and wisdom.

END_QUOTE

As with the TREATISE, Hume's goal in the 1ST ENQUIRY was to probe human nature, the human mind -- though he didn't say so in the same bombastic terms, it seems having realized that the mind could not be studied in the same exacting detail as physics. Even so, he had no doubt of the value of that goal:

BEGIN_QUOTE:

It cannot be doubted, that the mind is endowed with several powers and faculties, that these powers are distinct from each other, that what is really distinct to the immediate perception may be distinguished by reflexion; and consequently, that there is a truth and falsehood in all propositions on this subject, and a truth and falsehood, which lie not beyond the compass of human understanding.

... And shall we esteem it worthy the labour of a philosopher to give us a true system of the planets, and adjust the position and order of those remote bodies; while we affect to overlook those, who, with so much success, delineate the parts of the mind, in which we are so intimately concerned?

END_QUOTE

To claim that the effort to understand the mind was futile was a folly greater than that achieved by any earnest, but misdirected, philosopher. To protest that abstruse philosophy could be difficult was merely an appeal to ignorance:

BEGIN_QUOTE:

To throw up at once all pretensions of this kind may justly be deemed more rash, precipitate, and dogmatical, than even the boldest and most affirmative philosophy, that has ever attempted to impose its crude dictates and principles on mankind.

>What though these reasonings concerning human nature seem abstract, and of difficult comprehension? This affords no presumption of their falsehood. On the contrary, it seems impossible, that what has hitherto escaped so many wise and profound philosophers can be very obvious and easy.<

END_QUOTE

Yes, there was much confusing, sometimes pointlessly so, in abstruse philosophy. Hume promised that he would cut a path through the thicket in the rest of the 1ST ENQUIRY, that he would ...

BEGIN_QUOTE:

... attempt to throw some light upon subjects, from which uncertainty has hitherto deterred the wise, and obscurity the ignorant.

Happy, if we can unite the boundaries of the different species of philosophy, by reconciling profound enquiry with clearness, and truth with novelty! And still more happy, if, reasoning in this easy manner, we can undermine the foundations of an abstruse philosophy, which seems to have hitherto served only as a shelter to superstition, and a cover to absurdity and error!

END_QUOTE

That goal was ambitious to the point of arrogant, but Hume proved up to the task.

BACK_TO_TOP

[1.3] HUME'S THEORY OF MIND & CAUSALITY

* Having set the stage, Hume went on to outline his skeptical-empirical philosophy, taking ideas that he had introduced in his TREATISE, and refining them in Sections II through IX:

   II:    Of The Origin Of Ideas
   III:   Of The Association Of Ideas
   IV:    Sceptical Doubts Concerning The Operations Of Understanding
   V:     Sceptical Solution Of These Doubts
   VI:    Of Probability
   VII:   Of The Idea Of Necessary Connexion
   VIII:  Of Liberty & Necessity
   IX:    Of The Reason Of Animals

These eight section are a block, parts of the same argument -- except for Section VIII, "Of Liberty & Necessity", which is something of an aside, and which is discussed separately.

Hume begins with his notions of "impressions" and "ideas", which were apparently mostly derived from the work of John Locke. In his discussion of them, Hume was less being descriptive than definitional. There are a lot of ways to partition the components of our mental landscape; Hume just came up with a workable -- if hardly unarguable, not all that inspiring, and certainly not modern -- system of definitions to give him a place to work from. Indeed, clearly recognizing that they were cumbersome, Hume stripped his discussion from the TREATISE down to a minimum in the 1st ENQUIRY, writing:

BEGIN_QUOTE:

... we may divide all the perceptions of the mind into two classes or species, which are distinguished by their different degrees of force and vivacity. The less forcible and lively are commonly denominated Thoughts or Ideas. The other species want a name in our language, and in most others; I suppose, because it was not requisite for any, but philosophical purposes, to rank them under a general term or appellation.

Let us, therefore, use a little freedom, and call them Impressions employing that word in a sense somewhat different from the usual. By the term impression, then, I mean all our more lively perceptions, when we hear, or see, or feel, or love, or hate, or desire, or will. And impressions are distinguished from ideas, which are the less lively perceptions, of which we are conscious, when we reflect on any of those sensations or movements above mentioned.

END_QUOTE

If that's all Hume thought was necessary to tell the reader about the matter, a reader could take him at his word, and move on. In any case, no matter how we define our mental elements, one of the consequences is that we only know the objects we perceive in the outside world by their observed attributes, their properties -- and indeed, we can only conceptualize things we have observed, or imaginative variations on them:

BEGIN_QUOTE:

Nothing, at first view, may seem more unbounded than the thought of man, which not only escapes all human power and authority, but is not even restrained within the limits of nature and reality. To form monsters, and join incongruous shapes and appearances, costs the imagination no more trouble than to conceive the most natural and familiar objects.

And while the body is confined to one planet, along which it creeps with pain and difficulty; the thought can in an instant transport us into the most distant regions of the universe; or even beyond the universe, into the unbounded chaos, where nature is supposed to lie in total confusion. What never was seen, or heard of, may yet be conceived; nor is any thing beyond the power of thought, except what implies an absolute contradiction.

But though our thought seems to possess this unbounded liberty, we shall find, upon a nearer examination, that it is really confined within very narrow limits, and that all this creative power of the mind amounts to no more than the faculty of compounding, transposing, augmenting, or diminishing the materials afforded us by the senses and experience.

When we think of a golden mountain, we only join two consistent ideas, gold, and mountain, with which we were formerly acquainted. A virtuous horse we can conceive; because, from our own feeling, we can conceive virtue; and this we may unite to the figure and shape of a horse, which is an animal familiar to us.

END_QUOTE

We can imagine variations of things we know about, changed in size, or color, or form; or combinations of them. The particularly imaginative may be able to come up with things that seem entirely new, but they will always have roots in what is already known. The bottom line is that we cannot imagine, at least in any specific way, things beyond all our experience. In modern terms, this is why the view of the future in old science-fiction stories almost always seems quaint: the stories were based on the facts the authors had on hand at the time, and they could not know about things that hadn't been invented yet.

Hume knew nothing of science fiction, instead suggesting as a significant example that people had no way of visualizing the Deity, except as a glorified human:

BEGIN_QUOTE:

The idea of God, as meaning an infinitely intelligent, wise, and good Being, arises from reflecting on the operations of our own mind, and augmenting, without limit, those qualities of goodness and wisdom. We may prosecute this enquiry to what length we please; where we shall always find, that every idea which we examine is copied from a similar impression.

END_QUOTE

If we have no experience of anything at all, we have no substantial notion of it: "A blind man can form no notion of colours; a deaf man of sounds." If we are presented with arguments that we can't identify as linking to any experience, however indirect, then they are meaningless to us.

* That said, Hume moved on to associations between ideas:

BEGIN_QUOTE:

To me, there appear to be only three principles of connexion among ideas, namely, Resemblance, Contiguity in time or place, and Cause or Effect.

END_QUOTE

One thing may resemble another, or two might be often co-located, or two things may have a causal relationship with each other. Hume pointed out that our thinking about things falls into two categories:

BEGIN_QUOTE:

All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact.

Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain. That the square of the hypothenuse is equal to the square of the two sides is a proposition which expresses a relation between these figures. ... Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe.

Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise to-morrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood.

END_QUOTE

Relations of ideas -- theoretical thinking -- amounts to something of a game, where we postulate basic assumptions and rules, then logically determine their consequences. We can devise absolute proofs of those consequences, though the postulates are simply givens that may not be proveable in any way. Chess can be seen as a matter of relation: entirely logical in itself, being a game of skill with little luck involved, but based on more or less arbitrary rules.

However, when it comes to matters of fact about the real Universe, all we can know is what we observe of it: What we see is what we get. Anything might be, might not be; might happen, might not happen. We only say something exists or happens if it is observed to exist or happen -- reliably observed, that is, meaning any honest and competent skeptic can make the same observation and get the same answer. As Hume put it in his essay "On The Immortality Of The Soul", more on that later: "Abstract reasonings cannot decide any question of fact or existence."

While obviously we need to know the properties of the things in the world around us, Hume realized we are most focused on causal relationships -- cause and effect, causality. We want to do things, to accomplish things, and that means understanding causality. We want to get warm? We start a fire. We're thirsty? We drink. We're bored? We find amusements. We don't logically determine these causal relationships; we can only know of them from observational experience:

BEGIN_QUOTE:

I shall venture to affirm, as a general proposition, which admits of no exception, that the knowledge of this relation is not, in any instance, attained by reasonings a priori; but arises entirely from experience, when we find that any particular objects are constantly conjoined with each other.

Let an object be presented to a man of ever so strong natural reason and abilities; if that object be entirely new to him, he will not be able, by the most accurate examination of its sensible qualities, to discover any of its causes or effects.

Adam, though his rational faculties be supposed, at the very first, entirely perfect, could not have inferred from the fluidity and transparency of water that it would suffocate him, or from the light and warmth of fire that it would consume him.

END_QUOTE

What could be said of Adam could equally be said of a newborn infant. The infant is born with no knowledge of the world, instead learning the "rules" of reality though sometimes painful experimentation. That leads to the memorable example of Hume's billiard balls:

BEGIN_QUOTE:

A stone or piece of metal raised into the air, and left without any support, immediately falls: but to consider the matter a priori is there anything we discover in this situation which can beget the idea of a downward, rather than an upward, or any other motion, in the stone or metal?

... When I see, for instance, a Billiard-ball moving in a straight line towards another; even suppose motion in the second ball should by accident be suggested to me, as the result of their contact or impulse; may I not conceive, that a hundred different events might as well follow from that cause?

May not both these balls remain at absolute rest? May not the first ball return in a straight line, or leap off from the second in any line or direction? All these suppositions are consistent and conceivable. Why then should we give the preference to one, which is no more consistent or conceivable than the rest? All our reasonings a priori will never be able to show us any foundation for this preference.

END_QUOTE

We have no way of knowing how billiard balls work other than by reliably observing them. Having observed the actions of billiard balls, we can model their interactions with a theory of physics, and examine their behavior down to the atomic level. However, eventually we run out of observations, and then we can go no further; the causal chain inevitably comes to an end in the darkness of ignorance. We cannot see beneath appearances; asking why things are the way they are observed to be, after mining through all the observable details, is meaningless. The only answer is that if they weren't, they'd be some other way.

BEGIN_QUOTE:

These ultimate springs and principles are totally shut up from human curiosity and enquiry. Elasticity, gravity, cohesion of parts, communication of motion by impulse; these are probably the ultimate causes and principles which we shall ever discover in nature; and we may esteem ourselves sufficiently happy, if, by accurate enquiry and reasoning, we can trace up the particular phenomena to, or near to, these general principles. The most perfect philosophy of the natural kind only staves off our ignorance a little longer: as perhaps the most perfect philosophy of the moral or metaphysical kind serves only to discover larger portions of it.

END_QUOTE

Physics, with its reliance on mathematical reasonings, does seem to be, and is, exacting -- but tidy mathematics in science is misleading:

BEGIN_QUOTE:

Nor is geometry, when taken into the assistance of natural philosophy, ever able to remedy this defect, or lead us into the knowledge of ultimate causes, by all that accuracy of reasoning for which it is so justly celebrated. Every part of mixed mathematics proceeds upon the supposition that certain laws are established by nature in her operations; and abstract reasonings are employed, either to assist experience in the discovery of these laws, or to determine their influence in particular instances ...

END_QUOTE

Any mathematical analysis of events in the real Universe is no more valid than the assumptions on which it is based, with those assumptions obtained from reliable observation -- not by any mathematical proof, though mathematical proofs could provide leads for investigation. In addition, the results of that mathematical analysis are no more valid than they are observed to be in the real Universe; the analysis proves nothing in itself. The Universe works any way it actually works, and we just have to follow along as best we can. We observe what happens, and then put together theories that allow us to predict what happens in the future. If the theory isn't right, we don't get the results we predict.

This derivation of theories from observation is now called "induction", though Hume didn't use that term, instead calling it a form of "moral reasoning" -- a term he confusingly used in different ways. In any case, induction has a limitation, in that there's no guarantee that nature will go along with the model:

BEGIN_QUOTE:

The bread, which I formerly eat, nourished me; that is, a body of such sensible qualities was, at that time, endued with such secret powers: but does it follow, that other bread must also nourish me at another time, and that like sensible qualities must always be attended with like secret powers? The consequence seems nowise necessary.

END_QUOTE

In practice, we do assume that what we ate in the past will nourish us in the future, but there's no reasoning in it; it's a simple assumption of the regularity of the world, that things will operate in the future as they did in the past:

BEGIN_QUOTE:

Is there any more intelligible proposition than to affirm, that all the trees will flourish in December and January, and decay in May and June? Now whatever is intelligible, and can be distinctly conceived, implies no contradiction, and can never be proved false by any demonstrative argument or abstract reasoning priori.

... It is impossible ... that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance. Let the course of things be allowed hitherto ever so regular; that alone, without some new argument or inference, proves not that, for the future, it will continue so.

... It is certain that the most ignorant and stupid peasants -- nay infants, nay even brute beasts -- improve by experience, and learn the qualities of natural objects, by observing the effects which result from them. When a child has felt the sensation of pain from touching the flame of a candle, he will be careful not to put his hand near any candle; but will expect a similar effect from a cause which is similar in its sensible qualities and appearance.

If you assert, therefore, that the understanding of the child is led into this conclusion by any process of argument or ratiocination, I may justly require you to produce that argument; nor have you any pretence to refuse so equitable a demand.

END_QUOTE

It is often said that Hume defeated induction, but he simply pointed out that it wasn't really reasoning from first principles. True, induction is the basis for "mechanical" or "mechanistic" reasonings: we learn from early on that square pegs don't fit into round holes, but it's only by experience that we do so. Even for more elaborate mechanistic reasonings -- for an example in modern terms, constructing an elaborate model out of Lego blocks -- all the rules we have for the job were, directly or indirectly, acquired by experience.

All induction amounts to is learning by experience, and we are reliant on it, indeed it's more significant in our lives than formal reasoning. Hume suggested that arguments against induction were largely contrived, that it posed no real problems for the "Academic or Sceptical philosophy":

BEGIN_QUOTE:

The academics always talk of doubt and suspense of judgement, of danger in hasty determinations, of confining to very narrow bounds the enquiries of the understanding, and [most importantly] of renouncing all speculations which lie not within the limits of common life and practice.

END_QUOTE

That's honest skepticism, not the cheap sniping to which skeptics sometimes descend. Hume was puzzled at the hostility to skeptical philosophy, suggesting that its very neutrality was why it was so bitterly attacked:

BEGIN_QUOTE:

By flattering no irregular passion, it gains few partizans: By opposing so many vices and follies, it raises to itself abundance of enemies, who stigmatize it as libertine profane, and irreligious.

END_QUOTE

In fact, a measured skepticism, a mitigated skepticism, is simply ordinary good sense:

BEGIN_QUOTE:

Nor need we fear that this philosophy, while it endeavours to limit our enquiries to common life, should ever undermine the reasonings of common life, and carry its doubts so far as to destroy all action, as well as speculation. Nature will always maintain her rights, and prevail in the end over any abstract reasoning whatsoever.

END_QUOTE

It's the simple rule: What we see is what we get. We don't see cause; we only see consistent correlations:

BEGIN_QUOTE:

Suppose a person, though endowed with the strongest faculties of reason and reflection, to be brought on a sudden into this world; he would, indeed, immediately observe a continual succession of objects, and one event following another; but he would not be able to discover anything farther. He would not, at first, by any reasoning, be able to reach the idea of cause and effect; since the particular powers, by which all natural operations are performed, never appear to the senses; nor is it reasonable to conclude, merely because one event, in one instance, precedes another, that therefore the one is the cause, the other the effect.

END_QUOTE

In the modern phrase, "causation is not correlation." That's not quite right, however; all causation is correlation, but not all correlation is causation. If we have an absolutely consistent correlation, persisting in the face of efforts to weed out confounding influences, then we assume a causal relationship. However, it must be emphasized that we assume causes, we never really see them, we can't -- and our belief in a particular causal relationship breaks down, or at least weakens, once we find a reliable contradiction of the correlation. There's no logic involved, another principle is at work:

BEGIN_QUOTE:

This principle is Custom or Habit. For wherever the repetition of any particular act or operation produces a propensity to renew the same act or operation, without being impelled by any reasoning or process of the understanding, we always say, that this propensity is the effect of Custom. By employing that word, we pretend not to have given the ultimate reason of such a propensity. We only point out a principle of human nature, which is universally acknowledged, and which is well known by its effects.

... Custom, then, is the great guide of human life. It is that principle alone which renders our experience useful to us, and makes us expect, for the future, a similar train of events with those which have appeared in the past.

Without the influence of Custom, we should be entirely ignorant of every matter of fact beyond what is immediately present to the memory and senses. We should never know how to adjust means to ends, or to employ our natural powers in the production of any effect. There would be an end at once of all action, as well as of the chief part of speculation.

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In sum:

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... having found, in many instances, that any two kinds of objects -- flame and heat, snow and cold -- have always been conjoined together; if flame or snow be presented anew to the senses, the mind is carried by custom to expect heat or cold, and to believe that such a quality does exist, and will discover itself upon a nearer approach. ... All these operations are a species of natural instincts, which no reasoning or process of the thought and understanding is able either to produce or to prevent.

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