Term (logic)

“ It will simplify matters to bear in mind that the intension of a term is the same thing as its meaning. To take an example, the term 'man' applies to certain things, namely, all the members of the human race that have been, are, or ever will be: this is its quantity in extension. But the term 'man' has also a certain meaning, and implies certain attributes—rationality, animality, and a definite bodily shape: the sum of these attributes constitutes its quantity in intension. ”

“ These various operations might be brought within the compass of the science, and the additional advantage be obtained of a very simple definition, if, by an extension of the term, sanctioned by high authorities, we were to define logic as the science which treats of the operations of the human understanding in the pursuit of truth. ”

“ You will find these seven words——Proposition, Attribute, Term, Subject, Predicate, Particular, Universal——charmingly useful, if any friend should happen to ask if you have ever studied Logic. Mind you bring all seven words into your answer, and your friend will go away deeply impressed——'a sadder and a wiser man'. ”

“ Logic takes cognizance of our intellectual operations only as they conduce to our own knowledge, and to our command over that knowledge for our own uses. If there were but one rational being in the universe, that being might be a perfect logician; and the science and art of logic would be the same for that one person as for the whole human race. ”

“ 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. ”

“ 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 ”

“ 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. ”

“ 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. ”

“ It has been disputed whether Logic is a science or an art; and, in fact, it may be considered in both ways. As a statement of general truths, of their relations to one another, and especially to the first principles, it is a science; but it is an art when, regarding truth as an end desired, it points out some of the means of attaining it—namely, to proceed by a regular method, to test every judgment by the principles of Logic, and to distrust whatever cannot be made consistent with them. Logic does not, in the first place, teach us to reason. ”

“ If, as was said at an earlier point, the different stages of the logical idea are to be treated as a series of definitions of the Absolute, the definition which now results for us is that the Absolute is the Notion. That necessitates a higher estimate of the notion, however, than is found in formal conceptualist Logic, where the notion is a mere form of our subjective thought, with no original content of its own. ”

“ 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. ”

“ 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. ”

“ In some problems, for example, the analysis of space and time, the nature of perception, or the theory of judgment, the discovery of the logical form of the facts involved is the hardest part of the work and the part whose performance has been most lacking hitherto. It is chiefly for want of the right logical hypothesis that such problems have hitherto been treated in such an unsatisfactory manner, and have given rise to those contradictions or antinomies in which the enemies of reason among philosophers have at all times delighted. ”

“ 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 function of logic in philosophy, as I shall try to show at a later stage, is all-important; but I do not think its function is that which it has in the classical tradition. In that tradition, logic becomes constructive through negation. Where a number of alternatives seem, at first sight, to be equally possible, logic is made to condemn all of them except one, and that one is then pronounced to be realised in the actual world. Thus the world is constructed by means of logic, with little or no appeal to concrete experience. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ The metaphysical inquiry into the nature and composition of what have been called Abstract Ideas, or, in other words, of the notions which answer in the mind to classes and to general names, belongs not to Logic, but to a different science, and our purpose does not require that we should enter upon it here. ”

“ Can the analytic logician prevent all osmosis between his logic and his psychology?22 If not, and if the psychological act is subjective, woe then to his logic. Had the new logic begun with a bold challenge of the psychical character of the act of knowing, the prospect of a logic free from epistemology would have been much brighter. ”

“ The ideas which, on the particular occasion, they happen to represent, are banished from the mind during every intermediate part of the process, between the beginning, when the premises are translated from things into signs, and the end, when the conclusion is translated back from signs into things. Nothing, then, being in the reasoner's mind but the symbols, what can seem more inadmissible than to contend that the reasoning process has to do with any thing more? ”

“ The philosophy of reasoning, to be complete, ought to comprise the theory of bad as well as of good reasoning. ”

“ Logic itself rests upon assumptions to which nothing in the world of reality corresponds. For example, the correspondence of certain things to one another and the identity of those things at different periods of time are assumptions pure [31] and simple, but the science of logic originated in the positive belief that they were not assumptions at all but established facts. ”

“ The definition is a sort of notice to ourselves and others, what assumptions we think ourselves entitled to make. 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. ”

“ 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. ”

“ Other researchers perceived logic as a product of our experience, in particular thinking, as this applies to our self-constitution in the natural world and the world we ourselves created. As a corpus of rules and criteria, logic applies to language, but there is a logic of human actions, a logic of art, a logic of morals, etc., described by rules for preserving consistency, maintaining integrity, facilitating causal inference and other relevant cognitive operations, such as articulating a hypothesis or drawing conclusions. ”

“ It is enough if the analysis as far as it goes is correct, and if it goes far enough for the practical purposes of logic considered as an art. The separation of a complicated phenomenon into its component parts, is not like a connected and interdependent chain of proof. ”

“ Logic is a portion of the Art of Thinking: Language is evidently, and by the admission of all philosophers, one of the principal instruments or helps of thought; and any imperfection in the instrument, or in the mode of employing it, is confessedly liable, still more than in almost any other art, to confuse and impede the process, and destroy all ground of confidence in the result. ”

“ Nor are consciousness and linguistic analysis all the instruments of the logician. Logic has to consider the things we know, the minds by which we know them from sense, memory and experience to inference, and the sciences which systematize and extend our knowledge of things; and having considered these facts, the logician must make such a science of inference as will explain the power and the poverty of human knowledge. ”

“ For the proposition, that the course of nature is uniform, possesses rather the brevity suitable to popular, than the precision requisite in philosophical language: its terms require to be explained, and a stricter than their ordinary signification given to them, before the truth of the assertion can be admitted. ”

“ 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. ”

“ 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. ”

“ Hence arose conceptual logic; according to which conception is a simple apprehension of an idea without belief in being or not being, e.g. the idea of man or of running; judgment is a combination of conceptions, adding being or not being, e.g. man is running or not running; and reasoning is a combination of judgments: conversely, there is a mental analysis of reasoning into judgments, and judgment into conceptions, beneath the linguistic analysis of rational discourse into propositions, and propositions into terms. ”