Burgersdyk divides the logicians of his day into the Aristotelians, the Ramists and the Semi-Ramists, who endeavoured, like Goclenius of Marburg, to mediate between the contending parties.
Like the Arabian logicians, and some of the scholastics, who held that ideas existed in a threefold form - ante res, in rebus and post res - he laid down the principle that the archetypal ideas existed metaphysically in the ultimate unity or intelligence, physically in the world of things, and logically in signs, symbols or notions.
The list given by the schoolmen and generally adopted by modern logicians is based on the original fivefold classification given by Aristotle (Topics, a iv.
The love of unity has often made logicians attempt to resolve these three processes into one.
For this reason it has been elevated by some logicians above all other inferences, and for this very same reason attacked by others as no inference at all.
But in the course of the development of the science, logicians have endeavoured to correct those defects, and have diverged into two schools.
From studying this succession of empirical logicians, we cannot doubt that sense, memory and experience are the real origin of inference, analogical, inductive and deductive.
Conceptual logicians were, indeed, from the first aware that sense supplies the data, and that judgment and therefore inference contains belief that things are or are not.
But at length many of them became formal logicians, who held that logic is the investigation of formal thinking, or consistent conception, judgment and reasoning; that it shows how we infer formal truths of consistency without material truth of signifying things; that, as the science of the form or process, it must entirely abstract from the matter, or objects, of thought; and that it does not tell us how we infer from experience.
St Thomas made a great advance by making logic throughout a rationalis scientia; and logicians are now agreed that reasoning consists of judgments, discourse of propositions.
Formal logicians say that, if they had to consider the matter, they must either consider all things, which would be impossible, or select some, which would be arbitrary.
Secondly, it does not content itself with the mere formulae of thinking, but pushes forward to theories of method, knowledge and science; and it is a hopeful sign to find this epistemological spirit, to which England was accustomed by Mill, animating German logicians such as Lotze, Daring, Schuppe, Sigwart and Wundt.
Neither Mill, however, nor any of the later logicians whose theories we have quoted, has been able quite to detach judgment from conception; they all suppose that an idea, or ideas, is a condition of all judgment.
This view, which has influenced not only German but also English logicians, such as Venn, Bradley and Bosanquet, destroys the fabric of inference, and reduces scientific laws to mere hypotheses.
We do not mean existing here and now, nor yet out of time and place, but at any time and place (semper et ubique) - past, present and future being treated as simply existing, by what logicians used to call suppositio naturalis.
But recent logicians, although they perceive the difference, nevertheless tend to make the proposition thej measure of the judgment.
Worse still, logicians seem unable to keep the judgment apart from the proposition.
Not that men should or can carry this logical postulate out in ordinary life; but it is necessary in the logical analysis of judgments, and yet logicians neglect it.
But as by the admission of both logicians these reconstructions of Darapti are illogical, it follows that their respective reductions of categorical universals to existentials and hypotheticals are false, because they do not explain an actual inference.
Aristotle, indeed, was as well aware as German logicians of the force of convertible premises; but he was also aware that they require no special syllogisms, and made it a point that; in a syllogism from a definition, the definition is the middle, and the definitum the major in a convertible major premise of Barbara in the first figure, e.g.: The interposition of an opaque body is (essentially) deprivation of light.
- Alexander the Commentator defined synthesis as a progress from principles to consequences, analysis as a regress from consequences to principles; and Latin logicians preserved the same distinction between the progressus a principiis ad principiata, and the regressus a principiatis ad principia.
It is no accident that it was the psychology of apperception and the voluntaryist theory or practice of Herbart, whose logical theory was so closely allied to that of the formal logicians proper, that contributed most spring from a common stock, though to us unknown - namely sense and understanding."
The first way is that of the purely formal logicians, of whom Twesten 2 and in England H.
It does not follow, however, that the laws asserted by the formal logicians are invalid or unimportant.
Those formal logicians ° of the Kantian school, then, may be summarily dismissed, though their undertaking was a necessary one, who failed to raise the epistemological issue at all, or who, raising it, acquiesced in a naïve dualism agnostic of the real world as Kant's essential lesson.
It is logic or a rationale of thought by thought, with a full development among other matters of all that the most separatist of logicians regards as thought forms. It offers a solution of what has throughout appeared as the logical problem.
With a brilliant subtlety Bradley analyses the various types of judgment in his own way, with results that must be taken into account by all subsequent logicians of this type.
The transmutation of Mill's induction of inductions into a postulate is an advance of which the psychological school of logicians have not been slow to make use.
It has been chiefly indebted to writers, who were not, or were not primarily, logicians, to Avenarius, for example, for the law of the economy of thought, to Wundt, whose system, and therewith his logic,' is a pendant to his psychology, for the volitional character of judgment, to Herbert Spencer and others.
The System der Logik (1828) of Bachmann (a Kantian logician of distinction) contains a historical survey (pp. 569-644), as does the Denklehre (1822) of van Calker (allied in thought to Fries), pp. 12 sqq.; Eberstein's Geschichte der Logik and Metaphysik bei den Deutschen von Leibniz bis auf gegenwartige Zeit (latest edition, 1 799) is still of importance in regard to logicians of the school of Wolff and the origines of Kant's logical thought.
Liard, Les Logiciens Anglais Contemporains (5th ed., 1907), deals only with the 19th-century inductive and formal-symbolic logicians down to Jevons, to whom the book was originally dedicated.
The recognition of the importance of hypotheses has led to various attempts at drawing up exact rules for their formation, but logicians are generally agreed that only very elementary principles can be laid down.
(1) Aristotle himself and subsequent logicians restrict the term to arguments in which there are but two premises.
(2) In point of fact, all logicians further confine the syllogism to arguments in which the terms are related as subject and predicate (or attribute in the widest sense).
The problem raised is a real one, and has been discussed by all logicians, from the time of Mill especially.
Mill, has been disputed on the ground that adjectives are applied both to concrete and to abstract terms. Hence some logicians make a separate class for adjectives, as being the names neither of things nor of qualities, and describe them as Attributive terms.
Throughout his logical writings De Morgan was led by the idea that the followers of the two great branches of exact science, logic and mathematics, had made blunders, - the logicians in neglecting mathematics, and the mathematicians in neglecting logic. He endeavoured to reconcile them, and in the attempt showed how many errors an acute mathematician could detect in logical writings, and how large a field there was for discovery.
But the darkest period was succeeded by the dawn of a reformation; travelling logicians were willing to maintain these against all the world; whilst here and there ascetics strove to raise themselves above the gods, and hermits earnestly sought for some satisfactory solution of the mysteries of life.
Lastly, the very form of induction that has been used by logicians in the collection of their instances is a weak and useless thing.
The reason of this is not far to seek, and has been pointed out by logicians of the most diametrically opposed schools.
Men bred in the cloister and the lecture-room of the logicians, trained in scholastic disputations, versed in allegorical interpretations of the plainest words and most apparent facts, could not find the key which might unlock those stores of wisdom and of beauty.