Keith Mack
The laws of thought are fundamental axiomatic rules that are said to guide everyone's thinking, thoughts, expressions, and discussions. They are traditionally the three fundamental laws of logic: the law of contradiction, the law of excluded middle, and the principle of identity. These laws have been discussed since the time of the Greeks, with key contributions from Plato and Aristotle, and have been the subject of debate and interpretation by many philosophers and logicians, including George Boole, whose work founded the discipline of algebraic logic. While some modern logicians disagree with Boole's interpretation, the laws of thought continue to be a relevant topic in philosophy and logic, with ongoing discussions about their validity and applicability in understanding the world and our thoughts.
| Characteristics | Values |
|---|---|
| Traditional laws | Contradiction, Excluded Middle, Identity |
| Traditional principles | Identity, Contradiction, Excluded Middle, Sufficient Reason |
| Three traditional laws | Nothing can become greater or less while remaining equal to itself, without addition or subtraction there is only equality, what was not before cannot be afterwards without becoming and having become |
| Fourth law | Comparisons |
| Two types of truths | Truths of fact, truths of reason |
| Two types of logical argument | Induction, Deduction |
| Logic | Study of valid inference |
| Philosophy | Pursuit of basic understanding through reason |
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What You'll Learn
The laws of contradiction and excluded middle
The law of contradiction, also known as the law of non-contradiction, states that nothing can both be and not be. In other words, two or more contradictory statements cannot both be true in the same sense at the same time. Aristotle, who discussed the laws of thought in his works, provided the following statement: "it will not be possible to be and not to be the same thing". This is equivalent to the propositional logic statement ~(P ∧ ~P).
The law of excluded middle, also known as the principle of excluded third, states that there exists no P such that P is neither true nor false, but some third state. In classical logic, this is a tautology. In modern mathematical logic, the excluded middle has been argued to result in possible self-contradiction. A common example of this is the "Liar's paradox", the statement "this statement is false", which is argued to be neither true nor false.
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The law of identity
In his "Tractatus Logico-Philosophicus", Ludwig Wittgenstein writes that "to say of one thing that it is identical with itself is to say nothing". This suggests that the law of identity is a trivial statement that conveys no new information. Despite this, the law of identity has been proclaimed by Afrikan Spir as the fundamental law of knowledge, which is opposed to the changing appearance of empirical reality.
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The law of non-contradiction
Plato's law of non-contradiction is the empirically derived necessary starting point for all else he has to say. It logically separates the Platonic world of constant change from the formally knowable world of momentarily fixed physical objects. However, according to both Plato and Aristotle, Heraclitus denied the law of non-contradiction. This is because, as Plato pointed out, the law of non-contradiction does not hold for changing things in the world.
In contrast to Plato, Aristotle begins a priori with the law of non-contradiction as the fundamental axiom of an analytic philosophical system. This axiom then necessitates the fixed, realist model. According to John Locke, the principles of identity and contradiction were general ideas that occurred to people after considerable abstract, philosophical thought.
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The laws of thought as a foundation for logic
The laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based. The formulation and clarification of such rules have a long tradition in the history of philosophy and logic. The laws of thought are rules that apply without exception to any subject matter of thought and are often said to be the object of logic.
The laws of thought are traditionally the three fundamental laws of logic: the law of contradiction, the law of excluded middle (or third), and the principle of identity. The law of non-contradiction, or the law of contradiction, states that "nothing can both be and not be" or "two or more contradictory statements cannot both be true in the same sense at the same time". The law of excluded middle and certain related laws have been rejected by some, such as the Dutch mathematician L.E.J. Brouwer, who originated mathematical intuitionism. Aristotle, however, cited the laws of contradiction and of excluded middle as examples of axioms.
The principle of identity, or the law of identity, was characterized by John Locke as "Whatsoever is, is". According to Gottfried Wilhelm Leibniz, the law of identity is the first primitive truth of reason that is affirmative. Leibniz regarded it as a necessary and sufficient condition for a truth to be a truth of reason and thus logically necessary that its analysis should reveal it to depend wholly on propositions whose negation involves a contradiction.
The laws of thought also include the principle of sufficient reason, which, unlike the others, cannot be interpreted as a principle of formal logic. The laws of thought are often questioned or rejected in more recent developments, such as intuitionistic logic, dialetheism, and fuzzy logic.
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The laws of thought in relation to truth and reason
The laws of thought refer to a set of fundamental axiomatic rules that are believed to govern rational discourse and thought processes. These laws have been a topic of discussion in philosophy and logic for centuries, with their origins traced back to ancient Greek philosophers such as Plato and Aristotle.
One of the key laws of thought is the law of non-contradiction, also known as the law of contradiction. This law states that "nothing can both be and not be" or, in other words, "two or more contradictory statements cannot both be true in the same sense at the same time". Aristotle provided seven "proofs" to demonstrate the importance of this law, showing that its negation implies any proposition. The law of contradiction is considered a fundamental principle in logic and has been referenced by many philosophers and logicians throughout history.
Another important law of thought is the law of excluded middle, which states that a statement is either true or false, with no intermediate value. However, this law has been rejected by some, such as the Dutch mathematician L.E.J. Brouwer, who argued that it may not apply to infinite classes. In addition to these, there is also the principle of identity, which John Locke characterised as "Whatsoever is, is".
The laws of thought can be understood as descriptive, prescriptive, or formal. Descriptive laws describe the nature of "being", the subject matter common to all sciences, or the activity of thinking or reasoning. Prescriptive laws express absolute or conventional standards of correct thinking or reasoning. Formal laws are propositions that are true based on their form, independently of their content, and are true in all possible worlds.
While the laws of thought have traditionally been seen as the foundation of logic, modern mathematical logic has challenged their privileged status. However, the choice between different logical theories still depends on philosophical arguments. Additionally, the term "laws of thought" has become less commonly used due to the variety of meanings associated with it and the acknowledgment that a viable system of logic cannot be constructed solely on the principles of identity, contradiction, and excluded middle.
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Frequently asked questions
The laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based. The laws of thought are traditionally the three fundamental laws of logic: (1) the law of contradiction, (2) the law of excluded middle (or third), and (3) the principle of identity.
The law of contradiction, also known as the law of non-contradiction, states that "nothing can both be and not be." In other words, two or more contradictory statements cannot both be true in the same sense at the same time.
The law of excluded middle states that of two contradictories, one subject must either be affirmed or denied. For example, it is false to say of what is that it is not, or of what is not that it is.
The principle of identity states that a necessary and sufficient condition for two entities, x and y, to be identical (the same) is that they share the same properties. In other words, for all x and all y, if x has a certain property, then y must also have that property, and vice versa.
The fourth law of thought, proposed by Arthur Schopenhauer, is the law of comparisons. This law states that knowledge about comparisons must precede the other three laws, as without it, we cannot know what is and what is not.
