Cameron Miranda
The laws of thought are fundamental axiomatic rules that are often considered the basis of rational discourse. 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 debated and discussed since the time of the ancient Greeks, with contributions from notable philosophers such as Plato, Aristotle, and Leibniz. While these laws are considered descriptive of being and standards of correct thinking, modern developments in logic, such as intuitionistic logic and fuzzy logic, have questioned or rejected these traditional laws. The laws of thought are essential in understanding the limits of reason and guiding our thinking, thoughts, expressions, and discussions. However, the term laws of thought has become obsolete due to the variety of meanings associated with it and the acknowledgment that a viable system of logic cannot rely solely on these principles.
| Characteristics | Values |
|---|---|
| Number of Laws of Thought | 3 traditional laws, with a 4th proposed |
| The Three Laws | Identity, Non-Contradiction, Excluded Middle |
| The Fourth Law | Comparisons |
| Purpose | To guide and underlie everyone's thinking, thoughts, expressions, discussions, etc. |
| Nature | Axiomatic rules, fundamental to rational discourse |
| Applicability | Universal, applying to any subject matter of thought |
| History | Originated by Plato, developed by Aristotle, and ended with the schoolmen of the Middle Ages |
| Interpretations | Disputed, with modern logicians disagreeing with Boole's expression |
| Examples | Aristotle's "Metaphysics", Leibniz's "Monadology", Boole's "An Investigation of the Laws of Thought" |
| Limitations | Not sufficient to construct a viable system of logic, questioned by intuitionistic logic, dialetheism, and fuzzy logic |
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What You'll Learn
- The law of non-contradiction: 'Nothing can both be and not be'
- The law of identity: 'Everything is what it is'
- The law of excluded middle: 'Of two contradictory judgments, one must be true, the other false'
- The law of comparisons: 'Opposite assertions cannot be true at the same time'
- The principle of sufficient reason: 'Truths of reason are true in all possible worlds'
The law of non-contradiction: 'Nothing can both be and not be'
The law of non-contradiction, also known as the law of contradiction, is one of the three fundamental laws of logic, or the laws of thought. It 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". This law is often expressed as ¬(A∧¬A) or ¬(p ∧ ¬p) in formal logic.
The law of non-contradiction is a fundamental principle in logic and rational discourse. It helps us determine what is true and false by asserting that opposite assertions cannot both be true at the same time. For example, the statements "the house is white" and "the house is not white" cannot both be true at the same time and in the same sense. This law is considered a basic requirement for identification and reasoning, helping us distinguish between different entities and their properties.
The law of non-contradiction has a long history in philosophy and logic, dating back to ancient Indian logic and the works of Plato and Aristotle. Aristotle cited this law as an example of an axiom, a statement that is considered true without requiring proof. However, some philosophers, such as Heraclitus, have challenged this law, arguing that change and becoming are essential aspects of reality.
Despite its widespread acceptance, the law of non-contradiction is not without its critics. Some modern developments in logic, such as intuitionistic logic, dialetheism, and fuzzy logic, have questioned or rejected this law. Additionally, philosophers such as Graham Priest have argued that under certain conditions, some statements can be both true and false simultaneously, challenging the absolute nature of the law.
The law of non-contradiction is closely related to other laws of thought, such as the law of excluded middle and the law of identity. Together, these laws form the foundation of traditional logic and continue to be a subject of debate and discussion in philosophy and logic.
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The law of identity: 'Everything is what it is'
The law of identity, often expressed as "A is A", is a fundamental axiom of logic and one of the traditional three laws of thought. It states that each thing is identical to itself, and that a thing might be continuously changing yet maintain its status as the same thing. For example, "a man is a man" or "whatever is white is white".
The law of identity is often regarded as a tautology or a trivial statement, as it does not seem to provide any useful information. Friedrich Hegel, for instance, claimed that the law of identity "says very little in itself". The fact that "A equals A" appears to be a useless repetition that tells us little about the identity of a thing. However, the law of identity is significant as it underlies mathematics, reason, and logic. In mathematics, for instance, the expression "A = A" has a well-defined meaning.
The law of identity is also important as it allows us to distinguish between ourselves and other things or people. This intrinsic ability to sense and distinguish is known as the law of comparisons, which is considered by some to be a fourth law of thought that underlies the other three laws. According to Leibniz, the law of identity is the first primitive truth of reason that is affirmative. However, he also noted that identity in itself has no meaning unless thought of in relative terms to other things. This is in line with Eastern philosophical concepts, which state that the origin of an individual object cannot be itself, but is dependent on other objects.
The law of identity is the first of the three traditional laws of thought, the other two being the law of noncontradiction and the law of excluded middle. These laws are often questioned or rejected in more recent developments, such as intuitionistic logic, dialetheism, and fuzzy logic.
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The law of excluded middle: 'Of two contradictory judgments, one must be true, the other false'
The law of excluded middle is one of the three fundamental laws of logic, or the laws of thought, which are axiomatic rules that underlie everyone's thinking, thoughts, expressions, and discussions. The law states that of two contradictory judgments, one must be true, and the other must be false. This means that there cannot be an intermediate between contradictories, and of one subject, we must either affirm or deny any one predicate.
The law of excluded middle is often attributed to Aristotle, who cited it as an example of an axiom in his work, Metaphysics, Book IV, Part 7. In this work, Aristotle states that "since it is impossible that contradictories should be at the same time true of the same thing, obviously contraries also cannot belong at the same time to the same thing". He further states that "there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate".
However, it is important to note that Aristotle's formulation of the law of excluded middle has been debated and interpreted in various ways. In his work "On Interpretation", Aristotle seems to deny the law of excluded middle in the case of future contingents, such as in his discussion of a potential sea battle, where he holds that it is not yet determined whether there will be a battle tomorrow, but that the complex proposition that either there will be a battle or there will not is true.
The law of excluded middle has been a subject of discussion and disagreement among modern logicians and philosophers. Some, like Brouwer, the originator of mathematical intuitionism, have rejected the use of the law in certain mathematical proofs. Others, like Jan Łukasiewicz, a leading member of the Polish school of logic, have formulated propositional calculi that introduce a third truth-value, neither truth nor falsity, for future contingents, in which the law of excluded middle fails.
Despite these debates and interpretations, the law of excluded middle remains a fundamental principle in logic and the laws of thought, providing a basis for rational discourse and valid inference.
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The law of comparisons: 'Opposite assertions cannot be true at the same time'
The law of comparisons is the fourth law of thought, in addition to the three traditional laws of thought: the law of contradiction, the law of excluded middle, and the law of identity. The three traditional laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based. The law of comparisons, which states that opposite assertions cannot be true at the same time, is necessary to satisfy the law of identity.
The law of identity, according to Leibniz, is the first primitive truth of reason that is affirmative. However, the identity of an entity in itself has no meaning unless it is thought of in terms relative to other things. Thus, to satisfy the law of identity, entities must be compared with all other entities to determine if they are identical with themselves or if there are other entities identical with them. For example, to know if an entity is identical with itself, it must be compared with itself. Therefore, comparisons are necessary to satisfy the law of identity, and the law of comparisons underlies the other three laws of thought.
The law of comparisons, or the law of non-contradiction, is one of the oldest rules of logic, dating back to ancient Indian logic in the Shrauta Sutras, the grammar of Pāṇini, and the Brahma Sutras attributed to Vyasa. It was later elaborated on by medieval commentators such as Madhvacharya. The law of non-contradiction states that contradictory statements cannot both be true in the same sense at the same time. In other words, "nothing can both be and not be." This law is also found in the Buddhist Tripitaka, attributed to Nigaṇṭha Nātaputta, who lived in the 6th century BCE.
The law of non-contradiction is one of the three traditional laws of thought, along with the law of excluded middle and the law of identity. These laws are often referred to as the laws of logic or the laws of thought. The law of non-contradiction is considered the firmest of all principles by Aristotle, who concluded that "opposite assertions are not true at the same time." This law is also known as the principle of non-contradiction (PNC) or the principle of contradiction. It is a fundamental rule that guides everyone's thinking, thoughts, expressions, and discussions.
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The principle of sufficient reason: 'Truths of reason are true in all possible worlds'
The principle of sufficient reason, as conceived by Leibniz, states that for every entity X, if X exists, then there is a sufficient explanation for why X exists. This can be extended to events and propositions as well. A sufficient explanation can be understood in terms of reasons or causes. This principle is based on two other principles: non-contradiction and sufficient reason. According to Leibniz, these two principles are the basis of all truths, which can be either necessary or contingent.
Leibniz argues for the principle of sufficient reason (PSR) in three ways: from the concept of a sufficient reason and the concept of a "requisite", from his theory of truth, and inductively. According to his theory of truth, a proposition is true if the concept of the predicate is contained in the concept of the subject. For example, the statement "bachelors are unmarried" is true because the concept "unmarried" is contained in the concept "bachelor". Leibniz controversially claims that all true statements are true for this reason, even historical statements like "Caesar crossed the Rubicon".
Leibniz's PSR is connected with the Principle of the Best, which says that for any proposition, it is true if it holds in the best possible world. This can be interpreted as saying that the sufficient reason for every choice is that the chooser perceives it to be the best, and that God, who chooses the actual world, perceives something to be what is best just in case it is the best.
The principle of sufficient reason can be seen as a description of a closed system, in which there is no 'outside' to provide unexplained events with causes. This principle is essential to rational discourse and underlies everyone's thinking, thoughts, expressions, and discussions. However, it is important to note that classical ideas like these are often questioned or rejected in more recent developments, such as intuitionistic logic, dialetheism, and fuzzy logic.
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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 three traditional laws of thought are: the law of contradiction, the law of excluded middle, and 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 contradictory judgments (e.g., A is B, A is not B), one must be true and the other must be false.
The principle of identity, also known as the law of identity, states that everything is what it is. According to Leibniz, this law involves the assumption that entities must be compared with all other entities to determine if they are identical to themselves or if there are other entities identical to them.
