A priori reasoning

“ Since, therefore, in the cases which lay the strongest claims to be examples of knowledge a priori, the mind proceeds from the idea of a thing to the reality of the thing itself, we can not be surprised by finding that illicit assumptions a priori consist in doing the same thing erroneously ”

“ A conclusion, therefore, however correctly deduced, in point of form, from admitted laws of nature, will have no other than an hypothetical certainty. At every step we must assure ourselves that no other law of nature has superseded, or intermingled its operation with, those which are the premises of the reasoning; and how can this be done by merely looking at the words? We must not only be constantly thinking of the phenomena themselves, but we must be constantly studying them ”

“ In his view, unless a thing was not merely conceivable, but even explainable, it could not exist in nature. All natural phenomena, according to him, must be susceptible of being accounted for a priori. ”

“ Principles of Evidence and Theories of Method are not to be constructed a priori. The laws of our rational faculty, like those of every other natural agency, are only learned by seeing the agent at work. ”

“ In respect of Mind and its works, just as in the case of Nature, we must guard against being so far misled by a well-meant endeavour after rational knowledge, as to try to exhibit the necessity of phenomena which are marked by a decided contingency, or, as the phrase is, to construe them a priori. ”

“ Our assent to the conclusion being grounded on the truth of the premisses, we never could arrive at any knowledge by reasoning, unless something could be known antecedently to all reasoning.
Examples of truths known to us by immediate consciousness, are our own bodily sensations and mental feelings. I know directly, and of my own knowledge, that I was vexed yesterday, or that I am hungry to-day. Examples of truths which we know only by way of inference, are occurrences which took place while we were absent, the events recorded in history, or the theorems of mathematics. ”

“ Thus logical knowledge is not derivable from experience alone, and the empiricist’s philosophy can therefore not be accepted in its entirety, in spite of its excellence in many matters which lie outside logic. ”

“ The nearest approach which human theories can make to perfection is to diminish this residue, this caput mortuum of observation, as it may be considered, as much as practicable, and, if possible, to reduce it to nothing, either by showing that something has been neglected in our estimation of known causes, or by reasoning upon it as a new fact, and on the principle of the inductive philosophy ascending from the effect to its cause or causes. ”

“ The valid, then, even the eternally valid, enters our human consciousness through the narrow portals of the instant’s experience. Reasoning is an empirical process, whatever else it also is. One who observes the nature of a realm of abstractly possible experience, does so by reading off the structure of a presented experience. Necessity comes home to us men through the medium of a given fact. This is the general result of modern exact Logic. This is the outcome of the recent study of the bases of mathematical science. ”

“ Every phenomenon or so-called 'fact' has an infinity of aspects or properties, as we have seen, amongst which the fool, or man with little sagacity, will inevitably go astray. But no matter for this point now. The first thing is to have seen that every possible case of reasoning involves the extraction of a particular partial aspect of the phenomena thought about, and that whilst Empirical Thought simply associates phenomena in their entirety, Reasoned Thought couples them by the conscious use of this extract. ”

“ The forms under which the critical method is applied—such as the distinctions between a priori and a posteriori elements in cognition, between matter and form, between phenomena and noumena, between sense, understanding, and reason—ought not to disguise from us the true nature of the question which underlies all of them. ”

“ For one thing, we have found that every step towards Truth is a step away from vague possibilities, and towards determinateness of idea and of experience. Our very ideas themselves, even when expressed as hypotheses, or as universal definitions, or as a priori mathematical constructions, or as judgments of hypothetical or of universal type, are from the outset destructive of vague possibilities, and involve Determination by Negation. ”

“ This brings us to a second charateristic of philosophical propositions, namely, that they must be a priori. A philosophical proposition must be such as can be neither proved nor disproved by empirical evidence. Too often we find in philosophical books arguments based upon the course of history, or the convolutions of the brain, or the eyes of shell-fish. Special and accidental facts of this kind are irrelevant to philosophy, which must make only such assertions as would be equally true however the actual world were constituted. ”

“ For the propositions of which necessary truth is composed are so linked together that, given one, the rest can always follow. But necessary truth, which is arrived at 'a priori,' that is, by the mind's own working, is quite as real as contingent truth, which is arrived at 'a posteriori,' or by the teachings of experience, in other words, through our own senses or those of others. ”

“ If, he says in the fourth paragraph of the Note, ‘If we examine those arguments which, in any of the sciences above mentioned, are supposed to be the mere effects of reasoning and reflection, they will be found to terminate at last in some general principle or conclusion for which we can assign no reason but observation and experience.’ If an argument be not a process of reasoning, neither word is intelligible. ”

“ It is usual to point out that Psychology tries to explain the subjective processes of conception, judgment and reasoning, and to give their natural history; but that Logic is wholly concerned with the results of such processes, with concepts, judgments and reasonings, and merely with the validity of the results, that is, with their truth or consistency; whilst Psychology has nothing to do with their validity, but only with their causes. ”

“ Thus our intuitive knowledge, which is the source of all our other knowledge of truths, is of two sorts: pure empirical knowledge, which tells us of the existence and some of the properties of particular things with which we are acquainted, and pure a priori knowledge, which gives us connections between universals, and enables us to draw inferences from the particular facts given in empirical knowledge. Our derivative knowledge always depends upon some pure a priori knowledge and usually also depends upon some pure empirical knowledge. ”

“ Having noticed, in order to exclude from the province of Reasoning or Inference properly so called, the cases in which the progression from one truth to another is only apparent, the logical consequent being a mere repetition of the logical antecedent; we now pass to those which are cases of inference in the proper acceptation of the term, those in which we set out from known truths, to arrive at others really distinct from them. ”

“ It is therefore necessary, in analysing a belief, to look for some other logical form than a two-term relation. Failure to realise this necessity has, in my opinion, vitiated almost everything that has hitherto been written on the theory of knowledge, making the problem of error insoluble and the difference between belief and perception inexplicable.
Modern logic, as I hope is now evident, has the effect of enlarging our abstract imagination, and providing an infinite number of possible hypotheses to be applied in the analysis of any complex fact. ”

“ But Reasoning, even in the widest sense of which the word is susceptible, does not seem to comprehend all that is included, either in the best, or even in the most current, conception of the scope and province of our science. The employment of the word Logic to denote the theory of argumentation, is derived from the Aristotelian, or, as they are commonly termed, the scholastic logicians. ”

“ This mode of expression, exhibiting as the type of all reasoning from experience "The men A, B, C, etc., are so and so, therefore any man is so and so," would much better manifest the true idea--that inductive reasoning is always, at bottom, inference from particulars to particulars, and that the whole function of general propositions in reasoning, is to vouch for the legitimacy of such inferences. ”

“ Whether these general principles are given a priori, as the intuitionists hold, or whether they are the abstract expression of an experience invariably and unconditionally repeated, at all events they must be such that from them all our scientific theories may be deduced; they must appear in all our researches as the criterion of the truth of the results, and they must underlie all our anticipations of truth as the guiding principles. ”

“ If we had sufficiently capacious memories, and a sufficient power of maintaining order among a huge mass of details, the reasoning could go on without any general propositions; they are mere formulæ for inferring particulars from particulars. The principle of general reasoning is (as before explained) , that if, from observation of certain known particulars, what was seen to be true of them can be inferred to be true of any others, it may be inferred of all others which are of a certain description. ”

“ If the intuition must conform to the nature of the objects, I do not see how we can know anything of them a priori. If, on the other hand, the object conforms to the nature of our faculty of intuition, I can then easily conceive the possibility of such an a priori knowledge. ”

“ We infer the unknown from the known. Though our logic be without flaw and we violate no mathematical principle, yet are our conclusions not absolute. They rest of necessity upon assumptions, and these are subject to modification indefinitely as our knowledge becomes more complete. ”

“ ON THE NOTION OF CAUSE, WITH APPLICATIONS TO THE FREE-WILL PROBLEM The nature of philosophic analysis, as illustrated in our previous lectures, can now be stated in general terms. We start from a body of common knowledge, which constitutes our data. On examination, the data are found to be complex, rather vague, and largely interdependent logically. By analysis we reduce them to propositions which are as nearly as possible simple and precise, and we arrange them in deductive chains, in which a certain number of initial propositions form a logical guarantee for all the rest. ”

“ What is called formal logic is animated with the hope of extracting these formulations directly from an analysis of the procedure of thought. The most general logical principles which have appeared in the historical development of formal logic are definition, self-evidence, inference, and observation. ”

“ And in truth it never does exist, except as the result of experience. Consenting, for the sake of the argument, to discuss the question on a supposition of which we have recognized the radical incorrectness, namely, that the meaning of a proposition relates to the ideas of the things spoken of, and not to the things themselves; I must yet observe, that the idea of man, as a universal idea, the common property of all rational creatures, can not involve any thing but what is strictly implied in the name. ”

“ In reasoning upwards, from observations confessedly imperfect to general laws, we must take care always to regard our conclusions as conditional, so far as they may be affected by such unavoidable imperfections; and when at length we shall have arrived at our highest point, and attained to axioms which admit of general and deductive reasoning, the question, whether they are vitiated by the errors of observation or not, will still remain to be decided, and must become the object of subsequent verification. ”

“ It is no disparagement, therefore, to the science of Human Nature, that those of its general propositions which descend sufficiently into detail to serve as a foundation for predicting phenomena in the concrete, are for the most part only approximately true. ”

“ But how little does the psychologist know about the association of ideas, compared with what the logician has discovered about the processes of inference! The fact is that our primary consciousness of all mental operations is hardly equal to our secondary consciousness of the processes of the one operation of inference from premises to conclusions permeating long trains and pervading whole sciences. This elaborate consciousness of inferential process is the justification of logic as a distinct science, and is the first step in its method. ”

“ But when the conclusion is a proposition concerning a Thing, the postulate involved in the definition which stands as the apparent premiss, is the existence of a Thing conformable to the definition, and not merely of an idea conformable to it. This assumption of real existence we always convey the impression that we intend to make, when we profess to define any name which is already known to be a name of really existing objects. ”

“ Now, the elements of the proposition before us are these: As "the properties of matter might have been such as to render a totally different set of laws axiomatic" (therefore) "these laws [now in force] must be considered as resting.... not on intuitive perception:" that is, the intuitions in which these laws are recognized must not be held authoritative. Here the cognition posited as premiss is, that the properties of the matter might have been other than they are; and the conclusion is that our intuitions relative to existing properties are uncertain. ”