Logic > Mashad > Presentation

Logic assignment Laws of thought

Submitted to: Miss Fozia Akram Submitted by: Mashhad Javaid

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.

LAW OF THOUGHT 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

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.

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 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.

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 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 indiscernible

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..

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.