Law of thought
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For the formalized account of these laws see Rule of inference
The laws of thought are fundamental axiomatic rules upon which rational discourse itself is based. The rules have a long tradition in the history of philosophy.they are laws that guides and underline everyone thinking and thoughts and expressions, discusses etc. The "laws of thought" are said to comprise the following:
1. The law of identity. 2. The law of non-contradiction 3. The law of the excluded middle
1. The law of identity In philosophy, the law [of identity] is often mistakenly attributed to Aristotle,[1] who actually wrote: "Now 'why a thing is itself' is a meaningless inquiry (for—to give meaning to the question 'why'—the fact 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.)" Metaphysics, Book VII, Part 17 (1)
2. The law of non-contradiction
In logic, the law of non-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". (2)
[Note Aristotle's use of indices (respect & time).]
3. The law of the excluded middle
Aristotle wrote that ambiguity can arise from the use of ambiguous names, but cannot exist in the "facts" themselves:
It is impossible, then, that 'being a man' should mean precisely 'not being a man', if 'man' not only signifies something about one subject but also has one significance. … And it will not be possible to be and not to be the same thing, except in virtue of an ambiguity, just as if one whom we call 'man', and others were to call 'not-man'; but the point in question is not this, whether the same thing can at the same time be and not be a man in name, but whether it can be in fact. (Metaphysics 4.4, W.D. Ross (trans.), GBWW 8, 525–526). (3)
Plato
Socrates, in a Platonic dialogue, described three principles derived from introspection. He asserted that these three axioms contradict each other.
[F]irst , 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.
— Plato, Theaetetus, 155
Indian logic
The law of noncontradiction is found in ancient Indian logic as a meta-rule in the Shrauta Sutras, the grammar of Pāṇini,[1] and the Brahma Sutras attributed to Vyasa. It was later elaborated on by medieval commentators such as Madhvacharya.[2]
Aristotle
The three classic laws of thought are attributed to Aristotle and were foundational in scholastic logic. They are:
Avicenna and Persian Logic
The Persian philosopher, Ibn Sina (Avicenna), once wrote the following response to opponents of the law of noncontradiction:
"Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned." (Avicenna, Metaphysics)[3]
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.
Leibniz
Gottfried Leibniz formulated two additional principles, either or both of which may sometimes be counted as a law of thought:
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).
Schopenhauer
Four Laws
Arthur Schopenhauer discussed 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:
- Everything that is, exists.
- Nothing can simultaneously be and not be.
- Each and every thing either is or is not.
- Of everything that is, it can be found why it is.
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.
— Schopenhauer, Manuscript Remains, Vol. 4, "Pandectae II," §163
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:
- A is A.
- A is not both B and not-B.
- A is either B or not-B.
- 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 of 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 "Insofar as a judgment satisfies the first law of thought, it is thinkable; insofar as it satisfies the second, it is true … ."
Boole
The title of George Boole's 1854 treatise on logic, An Investigation on the Laws of Thought, indicates an alternate path. The laws are now incorporated 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.
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.
— Welton, A Manual of Logic, 1891, Vol. I, p. 30.
References
- ^ Frits Staal (1988), Universals: Studies in Indian Logic and Linguistics, Chicago, pp. 109–28 (cf. Bull, Malcolm (1999), Seeing Things Hidden, Verso, p. 53, ISBN 1859842631)
- ^ Dasgupta, Surendranath (1991), A History of Indian Philosophy, Motilal Banarsidass, p. 110, ISBN 8120804155
- ^ Avicenna, Metaphysics, I; commenting on Aristotle, Topics I.11.105a4–5
- Aristotle, "The Categories", Harold P. Cooke (trans.), pp. 1–109 in Aristotle, Vol. 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
- Aristotle, "On Interpretation", Harold P. Cooke (trans.), pp. 111–179 in Aristotle, Vol. 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
- Aristotle, "Prior Analytics", Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Vol. 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
- Boole, George, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Macmillan, 1854. Reprinted with corrections, Dover Publications, New York, NY, 1958.
- Russell, Bertrand, The Problems of Philosophy, Williams and Norgate, London, 1912.
- Arthur Schopenhauer, The World as Will and Representation, Volume 2, Dover Publications, New York, 1966, ISBN 0-486-21762-0