... Propositions Section 2 The Law of the Excluded Middle Section 3 Logical Equivalence Section 4 Well-Formed Formulas or WFFs Sectio... ...sophic Logic Section 1 Definition of Neutrosphic Logic Section 2 Logical Connectives in Neutrosophic Logic Section 3 Algebraic Propertie... ... 1 Classical Logic Section 1 Propositions In classical logic, a logical variable is restricted to the values of true(T) and false(F). The ... ...ry in the result column, there are 2 n different Boolean functions for n logical variables. Given the truth values in the column above the 5, ... ...on 1.1.4: In the expression p → q, p is known as the antecedent and q the consequence. The implication is often described as the if-then connective. ... ...on ( p /\ q ) \/ ( ¬ p /\ ¬q ). The ↔ connective can also be considered logical equality. Exclusive or (^) can be considered logical inequality ... ...is no middle between the two “extreme” values of true and false. One consequence of this law is the concept of a vacuous proof. What this means ... ...It is interpreted as a statement that if the antecedent is true, then the consequence is also true. The statement is then false if the antecedent is... ...also true. The statement is then false if the antecedent is true, but the consequence is false. With this notion, if it is not possible to prove the...

...art of a National Science Foundation grant proposal for Interdisciplinary Logical Sciences. 1.2. Neutrosophy, a New Branch of Philosophy A) Etymo... ...etting all possible states from <P> to <Non-P> until <Anti-P>. And, as a consequence, for any two propositions <M> and <N>, there exist two referen... ...And, later, others will reinstall it back... Consequently, philosophy is logically necessary and logically impossible. Agostoni Steuco of Gubbio w... ...es to interpret each notion or theory by tracing its respective practical consequences". We mean to know reality through thought, and thought throug... ...y propositions (theorems, lemmas, etc.) (p 1 ), (p 2 ), ..., (p m ), by logical combinations of its axioms. Developing [C], we find all proposit... ...we find all propositions of [P] (p 1 ), (p 2 ), ..., (p m ), resulted by logical combinations of (a 1 ), (a 2 ), ..., (a n ), moreover other propos... ...), moreover other propositions (r 1 ), (r 2 ), ..., (r t ), resulted by logical combinations of (b) with any of (a 1 ), (a 2 ), ..., (a n ). Si... ...eterminacy, not only <good> or only <bad> - with rare exceptions, if its consequence is G% happiness (pleasure). In this case the action is G%-usef... ...by its conformity to given binding rules (deontology), and equally by its consequences. The same sentence is true in a reference system, and fa...

... is null and void. Any actions which are intended to terminate it and to annul its consequences should be legally and morally permissible. The sam... ...atements cannot be derived with certainty from any negative statement. This formal-logical trait reflects a deep psychological reality with unsettl... ...t. This formal-logical trait reflects a deep psychological reality with unsettling consequences. A positive statement about one's affiliation ("I ... ...nd self-aggrandizement, and the reification and embodiment of said subversion. The logical outcome is to call for the overthrow of all political sy... ...ute them. They dedicate all their attention to the immediate and ignore the future consequences of their actions. In other words, their attention a... ...g and, therefore, regards himself as omnipotent, omniscient and protected from the consequences of his own acts (immune) – the personality disorder... ...: a series of potentialities with attached probabilities, the potentials being the logically and physically possible products. What can we learn a... ...stitute a theory and produce falsifiable predictions. A metaphor is also subject to logical and aesthetic rules and to the rigors of the scientific ... ...its inclusion in the definer) is the very definition of a tautology, the gravest of logical fallacies. On the other hand: if such an external sour...

...ery measurement because such communication would have to be superluminal. The only logical conclusion is that all the information relevant to the d... ... the issue of infinity and finiteness. The number of points in a line served as the logical floodgate which led to the development of Set Theory by ... ...eld and the representations of the world in the language field (that is to say, the consequences of repression). All three are, therefore, Activatio... ...ster or a network when they materialize. They can, however, relate to each other a- logically (negation or contradiction) and still constitute a pa... ...ied by another structure at the exact, infinitesimal, moment of realization. The consequence: only one of two exogenous events, which share the s... ...l-inclusive and all- pervasive. Nothing is outside its orbit and everything that is logically and physically possible is within its purview. If some... ... outcomes of appropriately designed experiments. Their explanatory powers are of no consequence. Positivists ascribe meaning only to statements that... ... confidence in a scientific theory or not. Is the theory aesthetic (parsimonious), logical, does it provide a reasonable explanation and, thus, doe... ...ething which is known to the believer to be true) versus implicit one (in the known consequences of something whose truth cannot be known). Truly, w...

...ts with those to physical property. (I outline that process and its negative consequences in the next chapter.) They will argue, and again I agree, th... ...1.qxd 8/28/08 11:04 AM Page 19 milk, you cannot. Excludable property is, logically enough, property from which others can easily be excluded or ke... ...might, during sixty years, to Boswell’s eldest son. What would have been the consequence? An unadulterated copy of the finest biographical work in the ... ...om the same evidence” or from extending those arguments and developing their consequences. In a line that Hesse rightly highlights, he declares that a... ... of authors’ rights it turned out, in Hesse’s words, to reflect “an epistemo- logically impure and unstable legal synthesis that combined an instrument... ...century.” Poor Jefferson. How lucky we are to have Mr. Helprin to remedy the consequences of his lack of vision. Or perhaps not. Think of the way that... ...imply because they may be used to infringe copyrights. That, however, is the logical implication of their claim. The re- quest for an injunction below... ...ss to the property. The rules that forbid circumvention of these systems are logically, if not elegantly, referred to as the anticircumvention provisi... ... ing the operation of computers, a metaphor that enables us to imitate their logical processes. In the words of Wikipedia, “despite their simplicity—[...

...s to read “our daily paradoxes” Smarandache has not certainly referred to the logical, mathematical or linguistic meaning of the word/notion “parado... ...y creation plan. A sulking and introverted nature as that of Ion Barbu could, logically, straighten and aspire only towards a somehow utopian world;... ...erican playwright, without having claims to destroying myths, has unexpected consequences, as the result is almost a tragicomedy, in what the antiq... ... postmodernity- reality and term also large, having a historic and social, in consequence, first of all, a temporal motivation. This finding couldn’t... ...ncipation, of autonomy. Moreover, it is suggested the idea of a chronological consequence. G. Bajenaru in his study “The paradoxist post-modernism (... ...tions or emphasized through paradoxist means, replace the ample, rational and logical poems of the postmodernism. Only an attentive eye, a subtle mi... ...geous disputes for the latter. Thus, the new (post)industrial world supposes, logically, the performance (not only at an intentional level) as well a... ...eption, fore the romantic revolution”(p.8). The next reader’s question appears logically: what else will follow after the loop’s closing? If we admit...

...m the surname Empiricus would have been more appropriate, if it was given in consequence of prominence in the Empirical School. Sextus is known to th... ...ity to consist in subjective experience, but he does not follow this to its logical conclusion, and doubt the existence of anything outside of mind.... ...er of argument, by which the Sceptics arrived at the condition of doubt, in consequence of the equality of probabilities, and he calls the Tropes, th... ...stly be found in other authors of antiquity given in a similar way. [5] The logical result of the reasoning used to explain the first Trope, is that... ...not with equal understanding of the results to be deduced from it. [3] The consequence of the incompatibility of the mental representations produce... ...ted to Agrippa is a marked one, and shows the entrance into the school of a logical power before unknown in it. The latter are not a reduction of th... ...heories of Pyrrhonism, while the five are rather rules of thought leading to logical proof, and are dialectic in their character. We find this distin... ...points to an objective relativity, but with Agrippa to a general subjective logical principle. The originality of the Tropes of Agrippa does not lie... ...al assertion, Σεκεῖνλ νὐθ εἶλαη, [4] and proceeds to introduce the logical consequence of the denial of aetiology. The summing up of the Tropes of ...

...onship to each other of objects 10 therein – essential in essence to our logical comprehension of our physical location in relation to the world,... ...tioning on a physical level with our reality. Cause precedes effect in a “logical” fashion which enables us to predict and interact with our enviro... ... – out of time as we know it – and therefore experience at first hand the consequences of their own actions. Many people come away from this r... ...ave undergone N.D.E.s say that time is greatly compressed, as if it has no logical meaning. A description of time in this realm, wherever it is, is...

...s, and overthrow ing him out of his own mouth, or whether he is propounding consequences which would have been admitted by Zeno and Parmenides them ... ...ink that in visible objects you may easily show any num ber of inconsistent consequences.’ ‘Y es; and you should consider , not only the consequences... ...keness, motion, rest, genera tion, corruption, being and not being. And the consequences must include consequences to the things supposed and to othe... ...on on the negative as well as the positive hypothesis, with reference to the consequences which flow from the denial as well as from the assertion of ... ... is the object of these para doxes, some have answered that they are a mere logical puzzle, while others have seen in them an Hegelian propaedeutic o... ...en in two senses: Either one is one, Or , one has being, from which opposite consequences are deduced, 1.a. If one is one, it is nothing. 1.b. If one ... ...rocess is real, or in any way an assistance to thought, or , like some other logical forms, a mere figure of speech transferred from the sphere of mat...

... as we learn from the Memorabilia of Xenophon, first drew attention to the consequences of actions. Man- kind were said by him to act rightly when the... ...acknowledge that a large class of actions are made right or wrong by their consequences only; we say further that mankind are not too mindful, but tha... ... that mankind are not too mindful, but that they are far too regardless of consequences, and that they need to have the doctrine of utility habitually... ..., and the necessary foundation of that part of morals which relates to the consequences of actions, we still have to consider whether this or some oth... ...out entering on this wide field, even a superficial consider- ation of the logical and metaphysical works which pass under the name of Aristotle, whet... ...r of the other two, and in addition to them. SOCRATES: But do you see the consequence? 72 Philebus PROTARCHUS: To be sure I do. The consequence is,...

...e. But he is not to be regarded as the original inventor of any of the great logical forms, with the exception of the syllogism. There is little worth... ...e Sophists having an evil name; that, whether deserved or not, was a natural consequence of their vocation. That they were foreigners, that they made ... ...‘abscissio infinti,’ by which the Soph ist is taken, is a real and valuable logical pro cess. Modern science feels that this, like other processes o... ...n be caught in this way. But these divisions and subdivisions were favourite logical exercises of the age in which he lived; and while indulging his d... ...ed; and while indulging his dialectical fancy , and making a contribution to logical method, he delights also to transfix the Eristic Sophist with wea... ...oxes of Zeno extended far be yond the Eleatic circle. And now an unforeseen consequence began to arise. If the Many were not, if all things were name... ...d try our hand upon some more obvious animal, who may be made the subject of logical experiment; shall we say an angler? ‘V ery good.’ In the first pl... .... Suppose that you take all these hypoth eses in turn, and see what are the consequences which follow from each of them. STRANGER: Very good, and fir... ... sert discourse to be a kind of being; for if we could not, the worst of all consequences would follow; we should have no philosophy . Moreover , the ...

...epublic, and were probably first invented by Plato. The 3 greatest of all logical truths, and the one of which writers on philosophy are most apt to ... ... confu sion of them in his own writings. But he does not bind up truth in logical formulae,—logic is still veiled in metaphys ics; and the science w... ...ts that justice and injustice shall be considered without regard to their consequences, Adeimantus remarks that they are re garded by mankind in ge... ...that they are re garded by mankind in general only for the sake of their consequences; and in a similar vein of reflection he urges at the beginnin... ...s not the first but the second thing, not the direct aim but the indirect consequence of the good government of a State. In the discussion about rel... ...o good to the just and harm to the unjust? I like that better. But see the consequence:—Many a man who is ignorant of human nature has friends who ar... ... not some which we welcome for their own sakes, and independently of their consequences, as, for example, harmless pleasures and enjoyments, which del...

...of your observing it in yourself. Avoid fear, too, though fear is only the consequence of every sort of false- hood. Never be frightened at your own f... ...self,” interposed the elder. “No matter. You are a little late. It’s of no consequence….” “I’m extremely obliged to you, and expected no less from you... ... looked at him with curios- ity. “Is that really your conviction as to the consequences of the disappearance of the faith in immortality?” the elder a... ...ry of sixty thousand. That’ s very alluring to start with, for a man of no consequence and a beggar. And, take note, he won’ t be wronging Mitya, but ... ...then not he, Ivan. This letter at once assumed in his eyes the aspect of a logical proof. There could be no longer the slight- est doubt of Mitya’s gu... ...nd. Does all that exist of itself, or is it only an emanation of myself, a logical development of my ego which alone has existed for ever: but I make ... ...to me. I told him I don’t want to keep quiet, and he talked about the geo- logical cataclysm… idiocy! Come, release the monster… he’s been singing a h... ... that son, Dmitri, about the money, the envelope, and the signals? Is that logical? Is that clear? “When the day of the murder planned by Smerdyak... ...ate, so to speak, a romance, especially if God has endowed us with psycho- logical insight. Before I started on my way here, I was warned in Petersbur...

... regions of transcendental speculation back into the path of common sense. A logical or psy- chological phase takes the place of the doctrine of Ideas... ... ideal, in the de- lineation of which he is frequently interrupted by purely logical illustrations. The younger Socrates resembles his namesake in not... ...y the presence of Theodorus, the geometrician. There is political as well as logical insight in refusing to admit the division of mankind into Hellene... ...nd like rules might be extended to any art or science. But what would be the consequence? ‘The arts would utterly perish, and human life, which is bad... ... can tell?’ As in the Theaetetus, evil is supposed to continue,—here, as the consequence of a former state of the world, a sort of mephitic vapour exh... ...en it a single name. Whereas you would make a much better and more equal and logical classification of numbers, if you divided them into odd and even;... ...NG SOCRATES: Indeed I should. STRANGER: And there is a still more ridiculous consequence, that the king is found running about with the herd and in cl... ...hown in the previous argument. STRANGER: Thank you for reminding me; and the consequence is that any true form of government can only be supposed to b...

...idity the latter looks upon his revenge as justice pure and simple; while in consequence of his acute consciousness the mouse does not believe in the ... ...f it disgusts you to be reconciled to it; by the way of the most inevitable, logical combinations to reach the most revolting conclusions on the everl... ...t because they are stupid and limited. How explain that? I will tell you: in consequence of their limitation they take immediate and secondary causes ... ... be done if I have not even spite (I began with that just now, you know). In consequence again of those accursed laws of consciousness, anger in me is... ...ests they may at once become good and noble—are, in my opinion, so far, mere logical exercises! Y es, logical exercises. Why, to maintain this theory ... ...omes softer, and consequently less bloodthirsty and less fitted for warfare. Logically it does seem to follow from his arguments. But man has such a p... ...emptuously. “You thirst for life and try to settle the problems of life by a logical tangle. And how persistent, how insolent are your sallies, and at... ...ll. It is not worth while to pay attention to them for they really are of no consequence. Another circumstance, too, worried me in those days: that th... ... to me, tell me that, please?” I began, gasping for breath and regardless of logical connection in my words. I longed to have it all out at once, at o...

...ser heads than his own; he prefers to test ideas by the consistency of their consequences, and, if asked to give an account of them, goes back to some... ...ting the whole human race into heaven or hell for the greater convenience of logical division? Are we not at the same time describing them both in sup... ...mould human thought, Plato naturally cast his belief in immortal ity into a logical form. And when we consider how much the doctrine of ideas was als... ...ly verbal, and is but the expression of an instinctive confidence put into a logical form:—’The soul is immortal because it con tains a principle of ... ... in the Republic, a system of ideas, tested, not by experience, but by their consequences, and not explained by actual causes, but by a higher, that i... ...pro ceed from the less general to the more general, and are tested by their consequences; the puzzle about greater and less; the resort to the method... ...es, he said. And can all this be true, think you? he said; for these are the consequences which seem to follow from the assump tion that the soul is ... ...e in the best of the higher; but you would not confuse the principle and the consequences in your reasoning, like the Eristics—at least if you wanted ...