Although they can be written in a completely symbolic form using, for example, propositional calculus, theorems are often expressed in a natural language such as English.

Although Elizabeth Anscombe never employed the term " the direction of fit ", Searle has strongly argued that the following passage from her work Intention was, by far, " the best illustration " of the distinction between the tasks of " the words ( more strictly their propositional content ) to match the world … that of getting the world to match the words ":

Although the logical consequence relation is only semidecidable, much progress has been made in automated theorem proving in first-order logic.

Although the main focus of his work was on medicine, anatomy, and physiology, Galen also wrote about logic and philosophy.

Although Dewey is known best for his publications concerning education, he also wrote about many other topics, including experience, nature, art, logic, inquiry, democracy, and ethics.

Although it was based on the proof methods of logic, Planner, developed at MIT, was the first language to emerge within this proceduralist paradigm 1969.

Although early Cretan coins occasionally exhibit multicursal patterns, the unicursal seven-course " Classical " design became associated with the Labyrinth on coins as early as 430 BC, and became widely used to represent the Labyrinth – even though both logic and literary descriptions make it clear that the Minotaur was trapped in a complex branching maze.

Although Descartes did not pursue the subject, he preceded Leibniz in envisioning a more general science of algebra or " universal mathematics ," as a precursor to symbolic logic, that could encompass logical principles and methods symbolically, and mechanize general reasoning.

Although such relays once were the backbone of automation in such industries as automobile assembly, the programmable logic controller ( PLC ) mostly displaced the machine tool relay from sequential control applications.

Although he is commonly known for Occam's razor, the methodological principle that bears his name, William of Ockham also produced significant works on logic, physics, and theology.

Although Dirac did not at first fully appreciate what his own equation was telling him, his resolute faith in the logic of mathematics as a means to physical reasoning, his explanation of spin as a consequence of the union of quantum mechanics and relativity, and the eventual discovery of the positron, represents one of the great triumphs of theoretical physics, fully on a par with the work of Newton, Maxwell, and Einstein before him.

Although the Ancient Greeks had no separate word for logic as distinct from language and reason, Aristotle's newly coined word " syllogism " ( syllogismos ) identified logic clearly for the first time as a distinct field of study.

Although the development of mathematical logic had made applications to algebra possible, they came about slowly ; results published by Anatoly Maltsev in the 1940s went unnoticed because of the war.

" Although the psychological or epistemological specifics given by Mill through which we build our logical apparatus may not be completely warranted, his explanation still nonetheless manages to demonstrate that there is no way around Kant's a priori logic.

Although they contained no microprocessors but were built around transistor-transistor logic ( TTL ), Hewlett-Packard calculators as far back as 1968 had various levels of programmability such that could be called microcomputers.

Although genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases, fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, so that their experience can be used in the design of the controller.

Although CMOS logic can be implemented with discrete devices for demonstrations, commercial CMOS products are integrated circuits composed of up to millions of transistors of both types on a rectangular piece of silicon of between 10 and 400mm < sup > 2 </ sup >.

Although antifuse OTP has been available for decades, it wasn ’ t available in standard CMOS until 2001 when Kilopass Technology Inc. patented 1T, 2T, and 3. 5T antifuse bit cell technologies using a standard CMOS process, enabling integration of PROM into logic CMOS chips.

Although they were not ready to commit to funding such a large project, the British government showed interest due to the logic of locating the capital on high ground safe from tidal waves.

Although ternary most often refers to a system in which the three digits,, and are all whole numbers, the adjective also lends its name to the balanced ternary system, used in comparison logic and ternary computers.

Although a similar observation was made by Aristotle and was known to Greek and Medieval logicians ( in the 14th century, William of Ockham wrote down the words that would result by reading the laws out ), De Morgan is given credit for stating the laws formally and incorporating them in to the language of logic.

Although consistency can be proved by means of model theory, it is often done in a purely syntactical way, without any need to reference some model of the logic.

Although extensively remodelled, that house still exists today -- including the study over the garage where George would " escape " from Gracie's illogical logic.

Although we continue to pay our conversational devotions to `` free private enterprise '', `` individual initiative '', `` the democratic way '', `` government of the people '', `` competition of the marketplace '', etc., we live rather comfortably in a society in which economic competition is diminishing in large areas, bureaucracy is corroding representative government, technology is weakening the citizen's confidence in his own power to make decisions, and the threat of war is driving him economically and physically into the ground ''.

Although this kind of wholesale objection came at first from some men who were not technically Puritans, still, once the Puritans gained power, they climaxed the affair by passing the infamous ordinance of 1642 which decreed that all `` public stage-plays shall cease and be forborne ''.

Although the false glamour surrounding bourbon or other whisky commercials is possibly no more fatuous than the pseudo-sophistication with which TV soft-drinks are downed or toothpaste applied, there is a sad difference between enticing a viewer into sipping Oopsie-Cola and gulling him into downing bourbon.

Although the United States and the U.S.S.R. have been arguing whether there shall be four, five or six top assistants, the most important element in the situation is not the number of deputies but the manner in which these deputies are to do their work.

`` Although it is not the best of which he is capable '', said Shelley as he closed the book, `` it is still poetry of a high order ''.

Although the Af calculation is obvious by analogy with that for gravitational field and osmotic pressure, it is interesting to confirm it by a method which can be generalized to include related effects.

Although there is no question but that the process of washing fabrics involves a number of phenomena which are related together in an extremely complicated way and that these phenomena and their interrelations are not well understood at the present, this section attempts to present briefly an up-to-date picture of the physical chemistry of washing either fabrics or hard surfaces.

-- Although there was some variation in results which must be attributed either to trace impurities or to variation in wall effects, the photochemical exchange in the gas phase was sufficiently reproducible so that it seemed meaningful to compare the reaction rates in different series of reaction tubes for the purpose of obtaining information on the effect of chlorine concentration and of carbon tetrachloride concentration on the reaction rate.

Although the standard deviation values on which spread of the lines is based are relatively larger for those centers which begin to ossify early ( Table 1 ), there are considerable differences in this value between centers having the closely timed Onsets.

Although biopsies have shown structural changes in some of the reported cases of steroid-induced weakness, this case provides the only example known to us in which necropsy afforded the opportunity for extensive study of multiple muscle groups.

Although no drugs act exclusively on the hypothalamus or a part of it, there is sufficient specificity to distinguish drugs which shift the hypothalamic balance to the sympathetic side from those which produce a parasympathetic dominance.

Although it is in some ways comparable to a voluntary sale of assets for cash, to which section 203 quite clearly applies, the courts and Treasury have held that acquiring corporations in several types of non-taxable reorganizations may sue for refund of taxes paid by transferors.

Although she weighed only 108 pounds when she visited him, Carroll permitted her to go on a 10-day fast in which she took nothing but water.

Although it was at the Battle of The Little Horn, about which more words have been written than any other battle in American history, that the 7th Cavalry first made its mark in history, the regiment was ten years old by then.

Although the particular form of conceptualization which popular imagination had made in response to the experience of spirit was undoubtedly defective, the raw experience itself which led to such excesses remains with us as vividly as ever.

Although the theological forms of the past continue to exist in a way they do not in a more secularized situation, the striking thing is the rapidity with which they are being reduced to a marginal existence.

Although the primary mathematical properties of the middle number at the center of the Lo Shu, and the interrelation of all the other numbers to it, might seem enough to account for the deep fascination which the Lo Shu held for the Old Chinese philosophers, this was actually only a beginning of wonders.

Although I have emphasized the barriers which an aroused nationalism has raised against relations between Christians and non-Christians in Asia, the fact is that this development has also widened the gulf between certain Afro-Asian religions themselves.

Although a complete picture cannot be given, we can indicate some aspects of life into which the Christian faith entered as at least one creative factor.

Although I absolutely reject the Platonism of it, I have literally squealed with delight at the imperturbable perfection with which the position is laid down on page after page ''.

Although Albert Johnston was born in Kentucky, he lived much of his life in Texas, which he considered his home.

Although the name actually applies to a group of snakes, it is often used to refer only to one species in particular, the common or green anaconda, Eunectes murinus, which is one of the largest snakes in the world.