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Law of thought

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Law of thought The laws of thought are fundamental logical rules, with a long tradition in the history of philosophy, which collectively prescribe how a rational mind must think. To break any of the laws of t hought (for example, to contradict oneself) is to be irrational. Different person gave different ideas about this… According to Plato: Socrates, in a Platonic dialogue, described three principles derived from introspection. He asserted that these three axioms contradict each other. First , that nothing can become greater or less, either in number or magnitude, while remaining equal to itself … Secondly, that without addition or subtraction there is no increase or diminution of anything, but only equality … Thirdly, that what was not before cannot be afterwards, without becoming and having become.

According to Aristotle: The three classic laws of thought are attributed to Aristotle and were foundational in scholastic logic. They are: 1) law of identity 2) law of non-contradiction 3) law of excluded middle

1) law of identity: In logic, the law of identity states that an object is always the same as itself (A ≡ A). Any reflexive relation upholds the law of identity; when discussing equality, the fact that "A is A" is a tautology. In philosophy, the law is often attributed to Aristotle, although it I s also claimed that Aristotle never gave this law. However, Aristotle did write, "Now 'why a thing is itself' is a meaningless inquiry (for -- to give meaning to the question 'why' – the fac t or the existence of the thing must already be evident-e . g. that the moon is eclipsed- but the fact that a thing is itself is the single reason and the single cause to be given in answer to all such questions as why the man is man, or the musician musical', unless one were to answer 'because each thing is inseparable from itself, and its being one just meant this ' this, however, is common to all things and is a short and easy way with the question. The law of identity has deep impact on Aristotle's ethics as well. In order for a person to be morally praiseworthy or blameworthy for an action, he or she must be the same person before the act as during the act and after the act . Without the law of identity, Aristotle notes, there can be no responsibility for vice. 2) law of non-contradiction: In logic , the law of non-contradiction (also called the law of contradiction) states, in the words of Aristotle, that "one cannot faisalabad institute of textile & fashion design.

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say of something that it is and that it is not in the same respect and at the same time". According to Allan Bloom, "the earliest-known explicit statement of the principle of contradiction – the premise of philosophy and the foundation of rational discourse" – is given in Plato's Politeia (The Republic) where the character Socrates states, "It's plain that the same thing won't be willing at the same time to do or suffer opposites with respect to the same part and in relation to the same thing. According to Aristotle and Thomas Aquinas, this is a fundamental principle of thought, which can only be proved by showing the opponents of the principle to be themselves committed to it. Thus, Aristotle considers the case of someone who denies the principle in the strong way – holding that every proposition is both true and false – and asks why such a person goes on the Megara road to get to Megara from Athens, since on such a person's view it is just as true that any other road would get him to Megara.

3) Law of excluded middle: In logic, the law of the excluded middle states that the formula "P ∨ ¬P" ("P or not-P") can be deduced from the calculus under investigation. It is one of the defining properties of classical systems of logic. However, some systems of logic have different but analogous laws, while others reject the law of excluded middle entirely. The law of excluded middle is related to the principle of bivalence, which is a semantic principle instead of a law that can be deduced from the calculus. For some finite n-valued logics, there is an analogous law called the law of excluded n+1th. If negation is cyclic and '∨ ' is a "max operator", then the law can be expressed in the object language by (P ∨ ~P ∨ ~~P ∨ ... ∨ ~...~P), where '~...~' represents n-1 negation signs and '∨ ... ∨ ' n-1 disjunction signs. It is easy to check that the sentence must receive at least one of the n truth values (and not a value that is not one of the n).In rhetoric, the law of excluded middle is readily misapplied, leading to the formal fallacy of the excluded middle, also known as a false dilemma.

According to Locke: John Locke claimed that the principles of Identity and contradiction were general ideas and only occurred to people after considerable abstract, philosophical thought. He characterized the principle of identity as "Whatsoever is, is." The principle of contradiction was stated as "It is impossible for the same thing to be and not to be." To Locke, these were not innate or a priori principles.

According to Leibniz: Leibniz formulated two additional principles, either or both of which may sometimes be counted as a law of thought. 1) Principle of sufficient reason 2) Identity of indiscernibles

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In Leibniz's thought and generally in the approach of rationalism, the latter two principles are regarded as clear and incontestable axioms. They were widely recognized in European thought of the seventeenth, eighteenth, and (while subject to greater debate) nineteenth century. As turned out to be the case with another such (the so-called law of continuity), they involve matters which, in contemporary terms, are subject to much debate and analysis (respectively on determinism and extensionality). Leibniz's principles were particularly influential in German thought. In France the Port-Royal Logic was less swayed by them. Hegel quarrelled with the identity of indiscernibles in his Science of Logic (1812-1816). 1)Principle of sufficient reason: The principle of sufficient reason states that anything that happens does so for a definite reason. It is usually attributed to Gottfried Leibniz..

2) Identity of indiscernibles: The identity of indiscernibles is an ontological principle which states that two or more objects or entities are identical (are one and the same entity), if and only if they have all their properties in common. That is, entities x and y are identical if and only if any predicate possessed by x is also possessed by y and vice versa. The principle is also known as Leibniz's law since a form of it is attributed to the German philosopher Gottfried Wilhelm Leibniz. I t is one of his two great metaphysical principles, the other being the principle of sufficient reason. Both are famously used in his arguments with Newton and Clarke in the LeibnizClarke correspondence. Associated with this principle is also the question as to whether it is a logical principle, or merely an empirical principle.

According to Schopenhauer: Four Laws Schopenhauer succssed the laws of thought and tried to demonstrate that they are the basis of reason. He listed them in the following way in his On the Fourfold Root of the Principle of Sufficient Reason, §33: A subject is equal to the sum of its predicates, or a = a. No predicate can be simultaneously attributed and denied to a subject, or a = — a = 0. Of every two contradictorily opposite predicates one must belong to every subject. Truth is the reference of a judgment to something outside it as its sufficient reason or ground. Also: The laws of thought can be most intelligibly expressed thus: 1) Everything that is, exists. 2) Nothing can simultaneously be and not be. 3) Each and every thing either is or is not. 4) Of everything that is, it can be found why it is.

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There would then have to be added only the fact that once for all in logic the question is about what is thought and hence about concepts and not about real things. To show that they are the foundation of reason, he gave the following explanation: Through a reflection, which I might call a self-examination of the faculty of reason, we know that these judgments are the expression of the conditions of all thought and therefore have these as their ground. Thus by making vain attempts to think in opposition to these laws, the faculty of reason recognizes them as the conditions of the possibility of all thought. We then find that it is just as impossible to think in opposition to them as it is to move our limbs in a direction contrary to their joints. If the subject could know itself, we should know those laws immediately, and not first through experiments on objects, that is, representations (mental images). Schopenhauer's four laws can be schematically presented in the following manner: 1. A is A. 2. A is no t not-A. 3. A is either A or not-A. 4. If A then B. Two Laws. Later, In 1844, Schopenhauer claimed that the four laws of thought could be reduced to two. "It seems to me," he wrote in the second volume of The World as Will and Representation, Chapter 9, "that the doctrine of the laws of thought could be simplified by our setting up only two of them, namely, the law o f the excluded middle, and that of sufficient reason or ground." Here is Law 1: The first law thus: “Any predicate can be either attributed or denied of every subject.” Here already in the “either, or” is the fact that both cannot occur simultaneously, and consequently the very thing expressed by the laws of identity and of contradiction. Therefore these laws would be added as corollaries of that principle, which really states that any two concept-spheres are to be thought as either united or separated, but never as both simultaneously; consequently, that where words are joined together which express the latter, such words state a process of thought that is not feasible. The awareness of this want of feasibility is the feeling of contradiction. Law 2 is as follows: The second law of thought, the principle of sufficient reason, would state that the above attribution or denial must be determined by something different from the judgment itself, which may be a (pure or empirical) perception, or merely another judgment. This other and different thing is then called the ground or reason of the judgment. He further asserted that "In so far as a judgment satisfies the first law of thought, it is thinkable; in so far as it satisfies the second, it is true. "

According to bole: The title of George Boole's 1854 treatise on logic, An investigation on the Laws of Thought, indicates an alternate path. The laws are

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now incorporate into his boolean logic in which the classic Aristotelian laws come down to saying there are two and only two truth values. The Leibnizian principles are ignored, at the algebraic level, absent second-order logic.

According to welton: In the 19th century the Aristotelian, and sometimes the Leibnizian, laws of thought were standard material in logic textbooks, and J. Welton described them in this way: The Laws of Thought, Regulative Principles of Thought, or Postulates of Knowledge, are those fundamental, necessary, formal and a priori mental laws in agreement with which all valid thought must be carried on. They are a priori, that is, they result directly from the processes of reason exercised upon the facts of the real world. They are formal; for as the necessary laws of all thinking, they cannot, at the same time, ascertain the definite properties of any particular class of things, for it is optional whether we think of that class of things or not. They are necessary, for no one ever does, or can, conceive them reversed, or really violate them, because no one ever accepts a contradiction which presents itself to his mind as such.

According to Russell: Bertrand Russell discussed only the three classic Aristotelian laws of thought in his 1912 book The Problems of Philosophy. At this point, in the early twentieth century, the laws of thought were sliding out of pedagogy in the field of logic, and the law of excluded middle was shortly to be questioned by intuitionistic logic.

REFRENCES www.en.wikipedia.org

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