Formal logic

“ But such objections imply that nothing short of absolute truth has any value; that all our discussions and investigations in science or social affairs are without logical criteria; that Logic must be confined to symbols, and considered entirely as mental gymnastics. In this book prominence will be given to the character of Logic as a formal science, and it will also be shown that Induction itself may be treated formally ”

“ Pretending to deal with matters of pure reason, it constantly though surreptitiously proceeds on the methods of applied logic; its conclusions are as fallacious logically as they are experimentally. The laws of thought are formal, and are as binding in transcendental subjects as in those which concern phenomena. ”

“ Formal philosophy is called Logic. Material philosophy, however, which has to do with determinate objects and the laws to which they are subject, is again two-fold; for these laws are either laws of nature or of freedom. The science of the former is Physics, that of the latter, Ethics; ”

“ As an art logic may be called the navigation of the sea of thought.
§ 25. The laws of thought are all reducible to the three following axioms, which are known as The Three Fundamental Laws of Thought.
(1) The Law of Identity—
Whatever is, is;
or, in a more precise form,
Every A is A.
(2) The Law of Contradiction—
Nothing can both be and not be;
Nothing can be A and not A.
(3) The Law of Excluded Middle—
Everything must either be or not be;
Everything is either A or not A.
§ 26. ”

“ We must not, however, conclude that the generality of the principle is merely verbal; it will be found on inspection to be no vague or unmeaning assertion, but a most important and really fundamental truth. ”

“ 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. ”

“ The laws of mind as characterized in the preceding chapter, compose the universal or abstract portion of the philosophy of human nature; and all the truths of common experience, constituting a practical knowledge of mankind, must, to the extent to which they are truths, be results or consequences of these. Such familiar maxims, when collected a posteriori from observation of life, occupy among the truths of the science the place of what, in our analysis of Induction, have so often been spoken of under the title of Empirical Laws. ”

“ We shall fall into no error, then, if in treating of Induction, we limit our attention to the establishment of general propositions. The principles and rules of Induction as directed to this end, are the principles and rules of all Induction; and the logic of Science is the universal Logic, applicable to all inquiries in which man can engage. ”

“ Whether God and duty are realities, the existence of which is manifest to us a priori by the constitution of our rational faculty; or whether our ideas of them are acquired notions, the origin of which we are able to trace and explain; and the reality of the objects themselves a question not of consciousness or intuition, but of evidence and reasoning.
The province of logic must be restricted to that portion of our knowledge which consists of inferences from truths previously known; whether those antecedent data be general propositions, or particular observations and perceptions. ”

“ It is necessity, in the metaphysical sense, some here utterly obscure kind of ‘logical necessity’ which is the favourite toy of a number of art critics. To those who have some familiarity both with Logic and with Psychology the regular appearance of the term ‘logical’ in describing these relations is the clearest indication that nothing definite or adequately considered is being said. ”

“ Positive logic abstains, as we see, from speculating upon the leading principles of knowledge, principles of identity, of contradiction of causality, etc. These kinds of principles are not objects of examination or of discussion. ”

“ Of the science, therefore, which expounds the operations of the human understanding in the pursuit of truth, one essential part is the inquiry: What are the facts which are the objects of intuition or consciousness, and what are those which we merely infer? But this inquiry has never been considered a portion of logic. ”

“ The traditional Logic of the text-books, when it reasons from universals to their subalternate particulars, or derives particular conclusions from universal premises, does so by tacitly and, in general, by unjustifiably assuming the external existence of the objects reasoned about, while all the time still sundering external and internal. Reasoning itself is, to be sure, experience, but is, by hypothesis, experience of internal meanings, not of the external meanings which are taken, by this sort of thinking, to be the Reality. ”

“ The Conceptualist may urge that the Nominalist's forms of statement and argument exist for the sake of their meaning, namely, judgments [Pg 15] and reasonings; and that the Materialist's laws of Nature are only judgments founded upon our conceptions of Nature; that the truth of observations and experiments depends upon our powers of perception; that perception is inseparable from understanding, and that a system of Induction may be constructed upon the axiom of Causation, regarded as a principle of Reason, just as well as by considering it as a law of Nature, and upon much the same lines. ”

“ 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; making ourselves acquainted with the peculiarities of every case to which we attempt to apply our general principles. ”

“ Values, whether ethical or logical, without an examination and formulation of their ground, relations, origin, and interconnection, would be merely rules of thumb, popular phrases, or pastoral precepts. The actual methodology of the sciences or applied logic is logic as art. ”

“ Whether, therefore, we conform to the practice of those who have made the subject their particular study, or to that of popular writers and common discourse, the province of logic will include several operations of the intellect not usually considered to fall within the meaning of the terms Reasoning and Argumentation. ”

“ Any man of sense has only to open his eyes, or to observe himself within, to appreciate how all original knowledge is of the concrete, the definite, the individual. This, I say, is what the traditional method in logic seems to imply. ”

“ And so in all cases, the general propositions, whether called definitions, axioms, or laws of nature, which we lay down at the beginning of our reasonings, are merely abridged statements, in a kind of short-hand, of the particular facts, which, as occasion arises, we either think we may proceed on as proved, or intend to assume. In any one demonstration it is enough if we assume for a particular case suitably selected, what by the statement of the definition or principle we announce that we intend to assume in all cases which may arise. ”

“ I agree with the Humanists that, in all argument, the important thing to attend to is the meaning, and that the most serious difficulties of reasoning occur in dealing with the matter reasoned about; but I find [Pg vi] that a pure science of relation has a necessary place in the system of knowledge, and that the formulæ known as laws of contradiction, syllogism and causation are useful guides in the framing and testing of arguments and experiments concerning matters of fact. ”

“ 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. ”

“ 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. ”

“ If there be necessary and universal truths expressible in propositions of axiomatic simplicity and obviousness, and having for their subject-matter the elements of all our experience and all our knowledge, surely these are the truths which, if experience suggest to us any truths at all, it ought to suggest most readily, clearly, and unceasingly. ”

“ When we infer some fact from some other fact which does not really prove it, we either have admitted, or, if we maintained consistency, ought to admit, some groundless general proposition respecting the conjunction of the two phenomena. ”

“ The instances of new theories agreeing with and explaining old empiricisms, are innumerable. All the just remarks made by experienced persons on human character and conduct, are so many special laws, which the general laws of the human mind explain and resolve. ”

“ These fully developed thought-processes are marked off by the use of what is known as the general idea or notion such as man or virtue. Such general ideas when reduced to a precise form as by the logician are spoken of as concepts. And since the science of logic assumes thinking to take place by help of such conceptual products we may also speak of these full or explicit thought-processes as Conceptual Thought. ”

“ In that case, logic would be an imperative, not directed at the knowledge of truth, but at the adjusting and fixing of a world which must seem true to us. In short, the question is a debatable one: are the axioms of logic adequate to reality, or are they measures and means by which alone we can, create realities, or the concept " reality "? ”

“ The criterion of the truths of reason, or those which spring from conceptions, is found in an exact use of the rules of logic. As for ideas or notions, I call real all those the possibility of which is certain ”

“ Moreover, the act of generalizing or determining is really an act of judgment, so that the logician's account of conception presupposes judgment, while at the same time his account of judgment presupposes conception. But this is no evil; for logic does not essay to exhibit the actual genesis of thought but only an ideal for future thinking. ”

“ This throwing of the whole body of possible inferences from a given set of particulars, into one general expression, operates as a security for their being just inferences, in more ways than one. First, the general principle presents a larger object to the imagination than any of the singular propositions which it contains. ”

“ Without attempting in this place to justify my opinion, or even to define the kind of justification which it admits of, I merely declare my conviction, that the general principle to which all rules of practice ought to conform, and the test by which they should be tried, is that of conduciveness to the happiness of mankind, or rather, of all sentient beings ”

“ But to impose upon the facts in the first instance the yoke of a theory, while the grounds of the theory are reserved for discussion in a subsequent stage, is not a course which a logician can reasonably adopt. ”

“ Logic to be the Science, as well as the Art, of reasoning; meaning by the former term, the analysis of the mental process which takes place whenever we reason, and by the latter, the rules, grounded on that analysis, for conducting the process correctly. There can be no doubt as to the propriety of the emendation. A right understanding of the mental process itself, of the conditions it depends on, and the steps of which it consists, is the only basis on which a system of rules, fitted for the direction of the process, can possibly be founded. Art necessarily presupposes knowledge ”

“ These, which are states of the person's mind, are the real antecedent in the sequence, the real cause in the causation, asserted by the proposition. But these are also the real ground, or foundation, of the attribute Prudence; since wherever these states of mind exist we may predicate prudence, even before we know whether any conduct has followed. And in this manner every assertion respecting an attribute, may be transformed into an assertion exactly equivalent respecting the fact or phenomenon which is the ground of the attribute. ”

“ But the process by which truth is advanced is not confined to the philosopher; or perhaps we should rather say that some sort of crude philosophy is embedded even in the feeblest and earliest speculations of mankind. Our thoughts are guided by an implicit logic long before we have even a conception of logic in the abstract, or have the least thought of codifying and tabulating its formulæ. ”

“ 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. ”