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Law of noncontradiction pdf Continue Theorem For the Fargo episode, see the No-Controversy Act. This article uses forms of logical notation. For a brief description of the characters used in this notation, see the List of Logic Symbols. In logic, the Non-Compliance Act (LNC) (also known as the Controversial Law, the Principle of Inconsistent (PNC) or the Principle of Contradictions) states that conflicting sentences cannot be true in the same sense at the same time, for example, two sentences A is B and A not B are mutually exclusive. Formally, this is expressed as tautology (p ∧ p). One of the reasons for such a law is the principle of explosion, which states that everything stems from contradiction. The law is used in reductio ad absurdum evidence. To express the fact that the law is uncourized and to avoid ambiguity, the law is sometimes amended, in accordance with the fact that contradictory proposals cannot be true at the same time and in the same sense. It is one of the so-called three laws of thought, along with its addition, the law excluded by the medium, and the law of identity. The law of non-contract is logically equivalent to the law of the excluded average under the laws of De Morgan. However, no system of logic is built on these laws alone, and none of these laws enforce withdrawal rules such as modus ponens or De Morgan's laws. The law is not controversial and the law of the excluded means create a dichotomy in the logical space in which the two parts are mutually exclusive and jointly exhaustive. The law is not a contradiction merely an expression of the mutually exclusive aspects of this dichotomy, and the law of the excluded means is an expression of its jointly exhaustive aspect. Interpretation This section requires additional citations to verify. Please help improve this article by adding quotes to reliable sources. Non-sources of materials can be challenged and removed. (July 2016) (Learn how and when to delete this template message) One of the difficulties in applying the law is not contrary to the ambiguity in the sentences. For example, if you don't explicitly specify as part of A and B, A may be B at one time, not at another. A and B may in some cases sound mutually exclusive linguistically, even if A may be partially B and partly not B at the same time. However, it is impossible to betray the same thing at the same time, and in the same sense, the absence and presence of the same fixed quality. Heraclitz according to Plato and Aristotle, Heraclitt is said to have denied the law no contradictions. This is likely if, as Plato pointed out, the law does not tolerate the change of things in the world. If the philosophy of becoming is impossible without change, then (potential) of what should become must already exist in a real object. In We Step and Don't Step In The same rivers; we are, and we are not, and the object of Heraclitus and Plato simultaneously must be in some sense what it is now, and have the potential of (dynamic) of what it can become. Unfortunately, so little is left of Heraclitus's aphorisms that not much about his philosophy can be said with certainty. He seems to believe that the struggle of opposites is universal both inside and on the other side, so both opposing and quality must exist at the same time, albeit in some cases in different ways. The road up and down is the same implies either the road leads in both directions, or there can be no road at all. This is a logical addition to the law on non-contradiction. According to Herazlit, change and constant conflict of opposites is a universal logo of nature. Protagoras Personal subjective perception or judgment can be said to be true only at the same time in the same respect, in which case, the law of non-contradictions should be applicable to personal judgments. Protagoras's most famous saying: Man is a measure of everything: things that are, what they are, and things that are not, that they are not. However, Protagoras was referring to things that are used or somehow connected to people. This is of great importance in the meaning of his aphorism. Properties, social entities, ideas, feelings, judgments, etc. arise in the human mind. However, Protagoras never imagined that a person should be a measure of stars or a movement of stars. Parmenides Parmenides used an ontological version of the law on non-contradiction to prove that there is, and to deny emptiness, change and movement. He also refuted the opposite assumptions. In his poem about nature, he said, the only ways of investigation there are for thinking: one that is and that cannot be the way of persuasion (for it is present on the truth) is another that is not true, and that it is right that it is not, that I point you to a path completely incomprehensible to you can not know that it can not be achieved you point to it ... For the same for thinking and for what nature is or something in Parmenides is a highly controversial issue. Some have taken it for what exists, some to be what is or may be the subject of scientific research. Socrates in Plato's early dialogues, Socrates uses the elenctic method to explore nature or define ethical concepts such as justice or virtue. The refutation of elenctic depends on the dichotomy of the thesis, which can be divided into exactly two mutually exclusive parts, only one of which may be true. Socrates then continues to demonstrate the opposite of the conventional part, using the law not against contradictions. According to Gregory Vlastos, the method has the following steps: Socrates argues the thesis, for example, Courage is the endurance of the soul, which Socrates considers false and targets for refutation. Socrates ensures the consent of his interlocutor for further premises, for example, Courage is fine and Ignorant endurance - it is not good. Socrates then argues, and the interlocutor agrees that these further preconditions imply the opposite of the original thesis, in this case it leads to: Courage is not the endurance of the soul. Socrates then claims that he has shown that his interlocutor's thesis is false and that his denial is true. The version of Plato's synthesis of Plato's Non- Resistance Act states that the same thing clearly cannot be acted upon or acted in the same part or in relation to the same thing at the same time, on the contrary (Republic (436b)). In this Plato carefully phrase three axiomatic limitations on action or reaction: 1) in the same part, 2) in the same respect, 3) at the same time. The effect is to momentarily create a frozen, timeless state, somewhat similar to the shapes frozen in action on the Parthenon frieze. Thus, he achieves two main goals of his philosophy. First, it logically separates the platonic world from the formally cognizable world of momentarily fixed physical objects. Second, it provides the conditions for the use of a dialectic method when searching for definitions, such as in Sophiste. Thus, Plato's law of non-contradiction is an empirically obtained necessary starting point for everything else that he has to say. Aristotle, on the other hand, changes the order of Plato's derivatives. Instead of starting with experience, Aristotle begins a priori with the law of non-resistance as a fundamental axiom of the analytical philosophical system. This axiom requires a fixed, realistic model. Now he begins with a much stronger logical basis than the non-reporting of Plato's actions in response to the contradictory demands of the three parts of the soul. Aristotle's contribution the traditional source of law is not a contradiction of Aristotle's metaphysics, where he gives three different versions. Ontological: It is impossible that the same thing does not belong and not belong to the same thing at the same time and in the same respect. (1005b19-20) psychological: No one can believe that the same thing can (at the same time) be and not be. (1005b23-24) Logically (a.k.a. medieval Lex Contradictoriarum) : The most specific of all the basic principles is that contradictory proposals are not correct at the same time. (1011b13-14) Aristotle is trying some evidence of this law. At first, he claims that each expression has one meaning (otherwise we could not communicate with each other). This precludes the possibility that being a man is not meant to be a man. But man means two-legged animal it is a human being, it is necessary (by virtue of the value of man) that he must be a two-legged animal, and therefore it is impossible at the same time for him not to be a two-legged animal. Thus, it is impossible to say, really at the same time, that the same is and is not human (Metaphysics 1006b 35). Another argument is that anyone who believes something can't believe in its contradiction (1008b). Why doesn't he just get up first and walk into the well or, if he finds one, through a rock? In fact, he seems to be quite careful of rocks and wells. Avicenna Avicenna's comment on metaphysics illustrates the general view that the law is not controversial and they are like them are among the things that do not require our development. Avicenna's words for stubborn are quite joking: He should be subjected to fire, as fire and not fire are one of them.
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