I

Peter Strawson uses Wittgenstein’s therapeutic method to answer Hume by showing, in exact terms, how the question of the justification of induction ‘has its source in a confusion.’ He begins by distinguishing the ‘validity’ of a deductive conclusion, from the ‘reasonableness’ of an inductive proposition.

Strawson admits that by deductive standards, inductive propositions are always invalid, as it is the very nature of induction that its conclusions are never contained in their premises; however, he points out that the justification of a particular inductive proposition makes no appeal to the validity of the inductive method as a whole, but only to its own reasonableness, that is, to the reasonableness of the particular proposition.

For Strawson, it is a meaningless question, whether induction itself is justified by inductive standards (as in: ‘is the law legal?’), and it is irrelevant whether induction, as a method, is justified in terms of deductive validity. Some inductive propositions are reasonable, while others are not, therefore the justification of induction itself, which Strawson interprets as being equivalent to an assertion that: ‘...all conclusions arrived at inductively [are] justified,’ although false, is irrelevant to the reasonableness of any given inference.

Strawson nevertheless attempts a validation of induction by positing a ‘supremely general proposition,’ which, taken together with a set of empirical evidence, in order to draw conclusions about events outside of experience, transforms the inductive process into a special form of deduction, in which the conclusions are contained within the combined premises. However, he concludes that such general propositions are, inevitably, too vague to be meaningful, and describes induction as merely assuming the existence of such a supreme proposition (along the general lines of: ‘nature is uniform’), without being obliged to define one.

He concludes that there is no criterion, by which the expectations of events outside of experience, arrived at through inductive reasoning, can be said to be justified, beyond one’s experience of the accuracy of one’s inductive inferences in the past. Although our experience of accurate inferences is undoubtedly our rationale for continuing to use the inductive method of reasoning, Strawson does not, hereby, dissolve Hume’s skeptical argument, but leads us, rather, to a kind of stale mate.

His answer to Hume, if he chose to answer him, rather than to undermine the validity of the question, must be: ‘The conclusions of inductive reasoning are not valid by deductive standards. There is no necessary connection between past events and future expectations, and the accuracy of inductive inferences amounts to little more than a happy coincidence; however, the accuracy of the method is sufficient to justify its continued use.’

In my view, Strawson evades the question, rather than dissolving it. If Hume’s contention is that inductive inferences, drawn from empirical evidence, have no valid rational foundation, then Strawson’s conclusion, that they are often reasonable, but never valid, supports it. Strawson offers a pragmatic answer to an epistemological question. He defends the use of deduction, while Hume questions its metaphysical basis. Hume is obviously not suggesting that we abandon inductive reasoning, because it lacks a rational justification, but simply that we understand it more precisely.

Although Strawson bases his defense of induction on the reasonableness of some of its conclusions. He cannot determine a criterion to establish reasonableness. ‘There is no privileged number of favourable instances which we take as decisive in establishing a generalization...If we could frame a rule which would tell us precisely when we had conclusive evidence for a generalization, then it would yield just the proposition required as the supreme premise.’

Induction does contain a supreme premise concerning the uniformity of nature. It is evident from the fact that we are willing to make far more generalized inferences about the behavior of the material world, than about human behavior. We recognize the fact that, as opposed to the operation of human free will, nature operates on some principle of approximate predictability, and we use this recognition to formulate beliefs about those elements we cannot see. The proposition is, however, only vaguely defined.

It is reasonable to have a degree of belief in a proposition that is proportional to the strength of the evidence; however, this concept of ‘reasonableness’ is not concretely definable. Human beings are capable of formulating expectations about the future, some of which are accurate and some of which are inaccurate. Extending away from our accurate expectations about events outside of empirical experience is a continuum of reasonableness. Virtually all of our accurate expectations and some of our incorrect expectations are reasonable, while some of our accurate and some of our inaccurate expectations are unreasonable.

The extreme of a reasonable expectation is that I shall continue to be seated in my chair, until I, or some external force, removes me from it; the extreme of an unreasonable expectation is that Helen of Troy will materialize in my lap before I finish this paper. However, between its extremes, the spectrum of expectations is an unbroken continuum. My expectation that my computer will not crash as I go for water is still on the reasonable side, but approaching a grey area between reasonable and unreasonable. An expectation that I will get an A in Philosophy would be unreasonable, but approaching the center.

The proposition that accepting into belief (some, if not all of) the conclusions of inductive reasoning is rationally justified requires a criterion, by which reasonable expectations are distinguishable from unreasonable expectations. Such a criterion would amount to a distinct line, dividing into two halves the continuous spectrum of expectations. This line is undefined, and expectations which lie close to the center of the spectrum can jump back and forth constantly between reasonableness and unreasonableness. Those expectations which are very reasonable are slightly unreasonable, and vice versa, and those which are moderately reasonable are moderately unreasonable. Only when our expectations are far removed from the grey area in the center, does it become clear on which side they lie.

Furthermore, there are three separate spectrums of expectations, by which an individual engages in inductive reasoning. There is an objective measure of reasonableness of expectation, which is defined by mathematical probabilities and physical possibilities; there is a phenomenological measure of reasonableness of expectation, based on each individual’s awareness of relevant data; and there is a subjective measure of reasonableness of expectation, based on actual beliefs (explicit and implicit), on which level all my expectations are reasonable.

There is a finite probability, for instance, that, by picking six numbers out of forty every Friday, I will win the lottery, one day. This mathematically determined probability defines the expectation of the event as being on the extremely unreasonable side; there is the degree of expectation the individual ‘should’ entertain, based upon his knowledge and understanding of probability, for example, if he misunderstood the odds as being a little worse than one in three, he should have a fairly high expectation of winning; and there is his actual expectation after he has combined his understanding with his desire, which allows him, in times of stress, to seek comfort in the perception of the reasonableness of his expectation of winning and to justify a fifty-two dollar a year expense, even where such an expectation has no probablistic or rational justification. Conversely, people living on the San Andreas fault who have thorough knowledge of the extreme statistical probability of a major earthquake, apparently perceive the expectation of impending disaster as being unreasonable.

Because it works far more often than it fails us, the ability to modify our behavior according to inductive reasoning is an active agent in natural selection. Strawson suggests that its effectiveness offers proof of its basis in objective being; however, its effectiveness does not imply a necessary connection between our perception of the extreme reasonableness of an inference and its accuracy. Induction is guessing no matter how well we do it.

II

Malcolm’s argument against the use of analogy, as a solution to the problem of the existence of other minds, is based on Wittgenstein’s position that our only criteria for understanding the psychological states of others are behavioral. It also reflects Hume’s objections to inductive reasoning. However, while Hume showed that there is no necessary connection between the experience of a number of occurrences of an event and expectation of the outcome of the next occurrence, Malcolm points out that, regarding the problem of other minds, we attempt to make a number of generalized inferences, on the basis of a single example. This would amount to an extreme case of the fallacy of induction, as Hume defines it.

Malcolm points to the difference between the phenomenon, ‘my pain,’ and the phenomenon, ‘his pain.’ The latter phenomenon can only be perceived by virtue of external manifestations, including language, which, as with Wittgenstein, is only a complex pain behavior. My experience of ‘my pain’ consists of three components: stimulus, sensation, and response, while my experience of ‘his pain’ consists only of stimulus and response. I must fill in the missing piece of ‘his pain’ by analogy from ‘my pain.’

Malcolm shows that the word ‘pain’ in each of these two phrases means something completely distinct, (the phenom as a third person entity) which in itself invalidates the application of analogy between them. However, he also claims that, while we have the ‘evidence of our senses’ for the two external components of ‘his pain,’ we have not the ‘evidence of our senses’ for the connecting step. Malcolm presumes, therefore, that my observation of the behavior of, or verbal conversation with a third party, does not amount to ‘evidence of my senses.’ This presupposition begs the question, as in: are the wave patterns on the surface of a river ‘evidence’ (of our senses) of the topology of the river bed? Malcolm says the relationship of pain to pain behavior is contingent. However, does not the idea of faking pain behavior necessarily imply a mind, with the understanding necessary to fake?

It would be more precise to say that I have no sensory apparatus that is sensitive to any element of another being’s experience of his own pain, or his own thoughts, beyond the other being’s outward behavior. My sensory apparatus, as a material structure, has evolved to interpret contact only with specific elements of the material world, and just as my own mind is not an element of the material world, neither should I expect any other mind to be so.

The fact that something exists where it cannot be perceived by human senses does not support the conclusion that it does not exist, any more than an analogy supports the conclusion that it does. Although my experience of ‘my pain’ may be an invalid basis for an analogical understanding of the meaning or nature of ‘his pain,’ it is sufficient to show me that there are elements of my own experience, which are not accessible to the direct sensory processing of others, but can only be understood by them, on the basis my behavioral responses (authentic and feigned), including language. This recognition strengthens the possibility, if not the belief, that, although undefinable, other minds probably exist. It confirms that, if other minds do exist, it is not a contradiction of rational and physical possibility that they are largely ‘invisible’ to my senses. It then becomes necessary to separate the question of the existence of other minds from the question of the nature of other minds.

Malcolm acknowledges that the most compelling evidence for the existence of other minds (and their similarity to our own), is language. He argues that intelligible sounds are contingent to an understanding of their meaning. However, he only addresses language in the model of a monologue. He says that we do not attribute to such objects as talking trees and computers, unable to manifest any external behavior appropriate to the sounds they emit, the property of understanding of their words.

However, conversation, and more complex uses of language, such as poetry, are not as easily separated from understanding, as are the simple sentences of a talking tree. While it is true that the ability of a tree to define the word ‘vixen’ does not necessarily imply the tree’s understanding of the word ‘vixen,’ it does require some level of understanding of the question: ‘what do you mean by vixen?’ The appropriateness of its answer implies that it understands the concept and parameters of a question, can distinguish between a question and a statement, and knows specifically what it has been asked.

Furthermore, while saying ‘ouch’ may be reduced to a form of verbal reflex reaction to pain, laughing at most jokes requires some level of understanding of their meaning. We may hesitate to attribute to Malcolm’s ‘calculating boy’ the property of understanding the numbers he manipulates, but if we are to use what we would or would not attribute as a measure of the meaningfulness of our propositions, we must admit that everyone would attribute to him some form of mind.

IV

The principle of the ethics of belief, as Clifford defines it, does not apply only to religion, even if a defense of agnosticism is his actual intention. In fact, religious faith is a special case, in that it explicitly demands the suspension of skeptical doubt. One may be a skeptic, or religious, but by definition, one cannot be both. If we restrict the question to ship owners, it is primarily a pragmatic one. No one would argue that, while it would be best for a ship owner to be absolutely certain of every detail of his ship’s readiness for sea, as well as all the relevant weather conditions in advance, such knowledge is impossible, and that, if there are going to be thriving economies based on sea travel in the world, at some point, every merchant has to make a decision (a leap of faith) to be satisfied with the information he has, and give the order to sail.

Clifford defines belief as the link between sensation and action. He foreshadows Wittgenstein, in that behavior is his only criterion for belief. Because he defines belief only in terms of human actions, an ethical component is inevitable. He points to the contribution of the mistaken beliefs of the present generation to the ills of future generations, and demands that we acknowledge our responsibility to our descendents. However, it is the ethics of our actions, with which Clifford is concerned, and he only assumes the application of the ethical nature of specific human actions to the beliefs which produce them.

That it would always be better to act according to more accurate beliefs than those we have, although true, implies a moral absolute, which is, in practice, unattainable. The ship owner’s crime is not in failing to examine his beliefs about the condition of his ship, as thoroughly as humanly possible, but in placing greater value on profit, than on his crew’s safety. He, therefore, does not serve as an apt analogy for those religious leaders who decline to examine their doctrines skeptically, not out of indifference to the danger to their congregants, but in the sincere belief that they are bringing them to salvation, while television evangelists, who preach unexamined doctrine in exchange for tremendous personal incomes, are morally contemptible, wholly apart from the nature of their personal beliefs, examined or otherwise.

If I were a rooster, and every day the farmer came to feed my hens and me, I might understandably believe that the farmer was my servant, who had been sent by God to feed us, and, even knowing of a hole in the fence, would not lead my hens on a daring midnight escape through the woods to freedom. I might instruct them to stay put and lay lots of eggs for the nice farmer to take back to God to raise in heaven. Even if I can be faulted for not examining the facts of the case further, it is the same fault that each of us shares who plans for tomorrow, without investigating whether the sun should be expected to rise as usual.

Clifford equates such mistaken beliefs about the nature of the world, as those entertained by the above rooster, as a pestilence, which threatens to spread to the rest of the town, and indeed it is likely that few of the members of the chicken community will die of old age. However, the pestilence cannot spread owing to the beliefs themselves, but only, as Clifford acknowledges, through words and actions, extending from those beliefs. Again it is the behavior, and not the belief which defines the ethical implications.

I would answer Clifford by saying: it is true that I have an ethical responsibility to know all the information relevant to my action in the world (except, perhaps, in the case of religion, which presupposes its own ethic, defined by God, which equates morality with faith, and immorality with doubt); however, in proceeding on inadequate evidence, all men have sinned and fallen short of the glory of God. Clifford seems to be advocating the life of Hamlet, or Dostoyevsky’s underground man, who occupies his time seeking more and more primary causes for his actions, rather than acting.

Finally, Clifford introduces the idea that religion belongs to a class of beliefs, which are dictated by the will to believe them, because, for example, they are comforting and pleasant. Clifford implies that the insistence on religious faith is ethically unsound, first, because it denies our responsibility for the consequences of our own ignorance and misunderstanding, and second, because it creates an atmosphere of mutual deception. If I am recognized as being more concerned with the pleasantness of my beliefs than with their accuracy, my friends, says Clifford, will cry ‘peace’ to me, when there is no peace. They might tell me to give all my possessions to the poor because the world is to end next Tuesday.

I agree with Clifford, regarding the ethical responsibility of examining and reexamining one’s beliefs about the world; however, as a philosopher, I also realize that action in the world is necessary, and that no human action takes place under ideal conditions.

As did Strawson and Malcolm, Clifford evokes the spirit of Hume, in that, if Hume is correct in defining induction as devoid of rational justification, then it is inevitable that we must run the risk of spreading the pestilence of our unjustified beliefs to the townsfolk, for even if we can pass up ‘sweet fruit,’ if we are to continue living in the world, we must come out for food some time, and we must often rely upon the imperfect truths of inductive reasoning to find it.

Furthermore, although Clifford demonstrates the nature of epistemic duties as a general principle, they do not necessarily apply by analogy to religion, as religion explicitly presupposes an exemption from these specific duties, without appeal to any justification outside of its own value system. The acceptance of religious beliefs without rational proof constitutes an implicit acknowledgement of this exemption. In order to apply his concept of epistemic duties to religious belief, Clifford must argue not on the general principle of epistemic duty, but against the specific claim of religion to exemption from that duty.

V

In order to arrive at an epistemological justification of religious faith, especially in refutation of the argument by Clifford, that any belief on insufficient empirical evidence is inherently immoral, William James divides human beliefs into special categories. He says that religious faith is a genuine option, a particular kind of belief that requires a choice that is living, forced, and momentous.

In such cases that meet these three conditions, and which cannot be decided on intellectual grounds, James argues that we must be guided by our will to believe the best possible account. Religion is a living option in modern western culture which recognizes atheism and agnosticism as valid alternatives to religious faith. James addresses his argument to his White Anglo-Saxon Protestant community, in which Protestant religious faith and the agnostic position advocated by Clifford, are both living options. Furthermore, everyone in this community is forced to either accept the Protestant definition of spiritual truth or reject it. No one is free to abstain from this decision, because abstention is tantamount to rejection of the proposition.

If James argues that religion vs. agnosticism is a momentous option, the editor has omitted the argument, but what is included implies that, because an element of the religious proposition is that there is something eternal called the soul whose fate is at stake in my choice, as in the example of Pascal’s wager, the option is momentous. If a lunatic approached me, claiming to have the final say over the fate of my eternal soul, and commanded me to follow him, it would present me with a momentous option, but, according to James, it would be a dead option. For James’s audience, the choice between accepting or rejecting a definition of reality, based on the doctrine of the Protestant religion, is a genuine option, in that it is living, forced, and momentous.

While it is impossible to avoid the dilemma, James admits that it cannot be resolved rationally. He rejects Pascal’s wager in spirit, in that, as a cold calculation, it does not qualify as religious faith. However, he concludes by returning to Pascal’s principle of deciding between an eternal benefit and a finite benefit in order to introduce the idea that our passions and prejudices play a primary role, relative to pure reason, in determining our beliefs.

According to James, Clifford’s position regarding the religious hypothesis is that ‘to yield to our fear of its being error is wiser and better than to yield to our hope that it may be true.’ James, therefore, reduces the option to an arbitrary choice between hope and fear and allows his will, that the best account is the true account, to dictate his belief. Because he presumes that a skeptical attitude would cut him off from knowledge and understanding of the religious hypothesis that he hopes is true, and because we must always act with an imperfect understanding, he embraces an attitude of religious faith.

James succeeds only so far as he assumes the religious hypothesis to be true. Even the assertion that Pascal’s wager represents a momentous option assumes that there is actually something eternal and transcendental at stake. While James explores the consequences of rejecting true religious beliefs, he does not, unlike Pascal and Clifford, explore the possible consequences of accepting false religious beliefs. ‘Our errors are surely not such awfully solemn things’ he comments, quite offhandedly, presuming the insignificance of the Spanish Inquisition and the Beirut bombing in comparison to the great benefits of a state of Episcopalian grace. The indignation of Clifford as well as the rational arguments of Karl Marx are based on an understanding of the errors of religious belief as extremely solemn things.

The idea that the will to believe a proposition is evidence of its truth contradiction of the principle that the desire to believe a proposition renders it immediately suspect. The more comforting a belief, the more careful examination it demands. The successes of modern science, since its liberation from the dictatorship of religion in the European Middle Ages, is proof that skeptical examination of our beliefs can bring us closer to objective truth and reveal our previous errors to us, as well as their sources. James’s simple refusal of ‘obedience to the scientist’s command to imitate his kind of option’ is not a satisfactory justification for accepting the beliefs that comfort or flatter him most.

VI

Gettier’s argument that knowledge cannot be defined simply as justified true belief, is notably short.  The entire argument takes up two pages.  He begins by denying the validity of several recent epistemological positions regarding the definition of knowledge.  They all, according to Gettier, require that a subject believe a propositional statement to be true, that the proposition be true, and that the subject is justified in believing the proposition to be true.  It is Gettier’s position that these three conditions do not in themselves constitute knowledge.  He offers two cases in which these conditions are met and yet the subject can not be said to have ‘knowledge’ of the proposition in question.

The question addressed by Gettier is derived from Plato who considers the necessary and sufficient conditions for "knowledge" at Theatetus 201 and Meno 98. Gettier identifies attempts made in recent years by Roderick Chisolm and A. J. Ayer to state such conditions as analogous to knowledge = "justified true belief" which he symbolizes:

(a) S knows that P is true.

(i) P is true.
(ii) S believes that P, and
(iii) S is justified in believing that P.

He then offers two examples in which these conditions hold, but P does not qualify as "knowledge." In both cases P has only a portion of the relevant evidence and manages "justifiably" to draw a true conclusion from it. In the first case, S concludes that the P: person with ten coins in his pocket will get the job, and in the second case, that, because one P is true, a set of either P/or a random P2 is also true. The first, I think, represents inductive inferences and the second deductive syllogisms. In the first case, Gettier proposes that if an incomplete knowledge of the conditions leads S to conclude that S2 will get the job, and he justifiably believes S2 has ten
coins, and S doesn't know that S will get the job and that S has ten coins, S will believe P. P would be "justified true belief," but based on the false inference that S2 gets job and clearly not knowledge. In the second case, P = if A then A or B. S is convinced of A, but A is false. S, however, randomly chances on a true B, so the proposition "either A or B" remains true. The deduction is justified, the P is true, S believes it, but P is not knowledge.

His first case involves a man who is correct and, according to Gettier, ‘justified’ in his belief about the outcome of a situation.  But because the subject’s beliefs are the result of valid reasoning concerning false information, Gettier would not allow those beliefs the status of ‘knowledge.’  His second example is based on similar principles, but regard a proposition of present fact rather than future outcome.

Although this argument has apparently been taken very seriously in the epistemological community, it appears to me to be based on simple inconsistencies in the use of terms, which reduce it to no more than a case of semantic confusion.

Gettier begins his argument proper with the statement that ‘it is possible for a person to be justified in believing a proposition that is in fact false.’  Clearly, this calls into question the term ‘justified.’ Although we often use it to express a minimum acceptable requirement, as in ‘excusable’ or ‘understandable,’ the word ‘just’ reflects an ideal value.  It is possible to understand ‘justification’ in an ideal sense as in perfect or absolute justification. However, Gettier has arbitrarily allowed himself to substitute the term ‘justification’ for Chisolm’s ‘adequate evidence,’ and for Ayer’s 'right to be sure.’

In a strict sense, it is contradictory ever to call a belief in what is untrue, ‘justified.’  Ayer might perhaps not allow that Smith has a right to be sure that Jones will get the job.  Neither need Chisolm allow a bygone count of Jones’ money the status of  ‘adequate evidence.’

If one reasons properly with false information, he may be justified in his reasoning, but he is not, in a strict sense, justified in accepting his premises, ergo his conclusions, as true.  In Gettier’s Case I, the false propositions are that: Jones will get the job and that Jones has ten coins in his pocket.  The proposition that Smith deduces is that the man who will get the job has ten coins in his pocket.  Smith can be said to be justified in believing that the first two propositions imply the third, but he is arguably unjustified in believing that the first two propositions are true, and therefore is not justified in believing the third to be true.

Gettier says that Smith accepts that the two pieces of false information are true as a result of ‘strong evidence.’  He has, therefore, again arbitrarily, equated ‘justification’ with ‘strong evidence.’  In order to refute the arguments of Chisolm and Ayer that he sites, he must show that Chisolm equates his idea of ‘adequate evidence,’ and that Ayer equates ‘the right to be sure’ with Gettier’s idea of ‘strong evidence,’ both of which I doubt he can do.

There is some leeway in the way the term ‘justified’ is used in English as in: [understandable or excusable] as opposed to [having an objectively sufficient (just) basis], and it is partially this leeway in which Gettier is operating and partially with the ambiguity as to whether justified reasoning of unjustified assumptions is tantamount to justified belief.  Ayer need simply reply that the fact that interviewers sometimes lie implies that Smith does not have ‘the right to be sure’ that Jones will get the job.  Gettier’s refutation of the validity of Ayer’s and Chisolm’s necessary and sufficient conditions for knowledge therefore fails.

VII

Hume’s ‘Sceptical solution to these doubts’ seems rather like a ‘reiteration of these doubts.’  He attempts in the section ‘The Problem of Induction’ to demonstrate that the principle of causality, which serves as the foundation of all of our inductive propositions and which is a continual element of our phenomenology, has no actual basis in reason or experience (that is, we do not sensorily experience any necessary connection between a causal event and its effect, nor is there any rational idea proceeding from the idea of the cause and necessitating the idea of the effect); and in the ostensible ‘solution’ he states that: ‘if we proceed not upon some fact, present to the memory or senses, our reasonings [are] merely hypothetical and however the particular links might be connected with each other, the whole chain of inferences [has] nothing to support it, nor [can] we ever, by its means arrive at the knowledge of any real existence.’  The perception of causality in the world around us is therefore no more than an assumption that things will act in a similar fashion to that in which they acted in previous similar situations.

Because causality is so thoroughly intertwined in our perception of the world, it seems strange at first the think that there is no identifiable support for it; however, Hume soon shows that such support is hard to find.  Nevertheless, I find serious flaws with many of his arguments.  He asserts, for instance,  that our expectations of effects of specific causes are determined by our experience of a series of similar situations.  He claims that a subject ‘who is brought on a sudden into this world,’ will not form an a priori inference that one billiard ball will communicate motion to another.  However, it is one of the characteristics of consciousness that subjects can not be brought on a sudden into this world and neither can anything else.  Everything in the observable universe (so far), including its observers, enters it gradually through an extensive process of causal events, and therefore we should expect the awareness of this fundamental principle to be native to any conscious being.
 Intelligent beings could not have evolved in a universe without the fundamental predictability of immediate relationships of causality, and the necessity of those relations are discoverable to reason through microscopic examination of the very cells of our bodies and the structures of our thalmi and cerebral corteces.  Not only are the conditions necessary for the physical processes that support life all dependent on the virtually uniform consistency of nature, but natural selection must necessarily promote more sophisticated perception of that consistency.

Because causality is inherent in our psychic structure, the claim that the principle of causality is only inferred by us through the experience of constant conjunctions is analogous to the proposition that our own existence is only inferred by us from the experience of our thoughts.  It is tautological in that knowledge is, strictly speaking, the experience of knowledge, and therefore everything is known to us only by experience.  Hume is simply pointing to the fact that our perception of abstract relationships and what Piaget calls formal operational thinking is different from our sensory perception of physical events and from the concrete operational thinking that accompanies it.

Our perception of  abstract relationships is only a rational construct, and should not be taken as one and the same as the relationships themselves, in the way that we take perception of physical events to be strictly determined by the objective events they reflect.  But the fact that we do not directly perceive relationships of causality, and therefore often misconstrue them, does not mean that such relationships are not actually at work in the world independent of our perception or definition, a fact that our reason demonstrates unambiguously.  The motion of the first billiard ball is not separate from the motion of the second; the interchange of energy is a continuum, and this continuum is the ultimate cause of the behavior of physical bodies.

A distinction must be made between understanding of causality and perception of causality.  I can induce the extreme mathematical probability that the earth will continue in its present orbit for the next eight hours, so that a relationship of causality is discoverable through reason, a priori (I can prove this in terms of the sunrise, not in terms of the totality of natural laws ceasing or continuing from one moment to the next, a distinction which Hume occasionally confuses), but this rational understanding is not the principle on which I conduct my daily affairs.  I do not sit down at breakfast and calculate the probabilities that I won’t be hit by a train when I step out of  the house.  I live according to a vast and continual system of expectations about the behavior of the world around me, based on a perception of causality, about which I never think at all, but which provides we with an evident (to me) basis for my abstract reasoning process.  I simply assume that the same predictability that makes it possible to walk down the street without fear of the ground opening up before me can be relied upon as a basis for abstract inductive propositions of causality.

Hume underemphasizes the subjective contribution to the definition of a given situation.  He assumes that the ‘first imagination of a particular effect, in all natural operations, is arbitrary where we consult not experience.’  However the particularity of a particular effect is defined by the observer.  If I raise a pen in the air and let go of it, how particular does my experience of pens have to be to expect it to fall down rather than up?  Do I have to have seen someone drop a pen before, or will experience of seeing a person drop any object suffice, or perhaps the experience of being held to the floor by gravity or perhaps reading Newton’s laws?  Would Hume allow my experience of gravitational force on my body as sufficiently similar to the particular effect of a falling pen to warrant causal inference?  How is it possible to ‘consult not experience?’  Perhaps the experience of rolling around in my mother’s womb taught me the principles which lead me to expect the pen to fall downward.

The definition of the situation itself relies upon a vast system of assumptions about causal relationships.  A dog sniffing around my feet as I am contemplating the raised pen in my hand, does not have my expectations about the outcome of the situation, because he does not define the situation in terms of the motion of a pen or as similar to other situations involving the effect of gravity on solid objects.  By focusing subjective attention upon the dropping of the pen, I define the situation as ‘similar’ to other physical events in my experience.  This definition presuppose a set of expectations about possible outcomes.  My definition of a given situation can only exist within a specific cognitive context.  Any coherent cognitive context must assume that predictability and universality of physical behavior is a property of the universe.
 
If knowledge is justified true belief, justification must be strictly defined.  I would define justification as depending first upon the truth of the proposition, and second upon knowledge of some explanation for the truth of the proposition (with reservations regarding what constitutes an explanation).  I am justified in believing a proposition is true when, first, it is true, second, I know why it must be true, and third, the why conforms to an objective, rather than imagined, cause/effect relationship.  This more precise definition of justification can be used to define knowledge simply as justified belief.

Using the term justification in its strictest sense, it is hard to find any specific beliefs that qualify as knowledge.  There is only belief, some of it, hopefully true, but most of it probably false or incomplete.  And there is the innate arrogance of human reason that does not preface every proposition with ‘I believe that....’

The flooding of the Nile serves as an illustration of the fundamental problem of human perception of causal relationships.  The ancient Egyptians attached to their gods, over the course of centuries, ever more complex metaphysical properties, whose effects were everywhere evident to the Egyptians.  They were certain (and even Ayer might say that had a right to be certain) that the annual flooding of the Nile, upon which their entire economy depended for millennia, was brought about by the benevolent intervention of the gods. We, on the other hand, explain the regularity of the event in terms of complex processes of the earth’s hydrosphere.  If inductive reasoning has a valid basis in objective reality, how could it have produced such widely divergent abstract systems?  Why (besides pure ethnocentrism) should we allow one system more authority than another?  If it is natural selection that has endowed higher animals with increasingly sophisticated faculties of induction, we are perhaps constrained to form abstract systems of causality based on whatever information is at hand, no matter how inadequate the information.  It may be an automatic process that we draw inferences even where we are not fully justified.  We should always, therefore, allow for the possibility of emendation of our working model of reality.

I would offer Hume the inductive proposition that the Milky Way galaxy will continue to spiral in a right-handed direction (if that is our perspective) through tomorrow.  I stipulate that this assumes that the universe will continue through tomorrow.  Here, I define the universe not in the archaic sense of ‘all that is,’ but in terms of modern physics as the four dimensional time/space continuum.  If this continuum continues into tomorrow, there are sufficient connections between its various parts, based upon necessary mathematical relationships (relations of ideas, to use Hume’s own terms), to render a reversal of the spin of the Milky Way between now and tomorrow, impossible.