Law of thought

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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 thought (for example, to contradict oneself) is to be irrational.

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[edit] 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, Theatetus, 155

[edit] Aristotle

The three classic laws of thought are attributed to Aristotle and were foundational in scholastic logic. They are:

[edit] 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.

[edit] Leibniz

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).

[edit] Schopenhauer

[edit] Four Laws

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:

  1. A subject is equal to the sum of its predicates, or a = a.
  2. No predicate can be simultaneously attributed and denied to a subject, or a = — a = 0.
  3. Of every two contradictorily opposite predicates one must belong to every subject.
  4. 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.
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,On the Fourfold Root of the Principle of Sufficient Reason, §33.

Schopenhauer's four laws can be schematically presented in the following manner:

  1. A is A.
  2. A is not not-A.
  3. A is either A or not-A.
  4. If A then B.

[edit] 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 … ."

[edit] 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.

[edit] 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.

[edit] 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.

[edit] Bibliography

[edit] See also