Salva congruitate

Last updated

Salva congruitate [1] is a Latin scholastic term in logic, which means "without becoming ill-formed", [2] salva meaning rescue, salvation, welfare and congruitate meaning combine, coincide, agree. Salva Congruitate is used in logic to mean that two terms may be substituted for each other while preserving grammaticality in all contexts. [3] [4]

Latin Indo-European language of the Italic family

Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets, and ultimately from the Phoenician alphabet.

Logic study of inference and demonstration

Logic, is the systematic study of the form of valid inference, and the most general laws of truth. A valid inference is one where there is a specific relation of logical support between the assumptions of the inference and its conclusion. In ordinary discourse, inferences may be signified by words such as therefore, hence, ergo, and so on.

Substitution is a fundamental concept in logic. A substitution is a syntactic transformation on formal expressions. To apply a substitution to an expression means to consistently replace its variable, or placeholder, symbols by other expressions. The resulting expression is called a substitution instance, or short instance, of the original expression.

Contents

Remarks on salva congruitate

Timothy C. Potts

Timothy C. Potts describes salva congruitate as a form of replacement in the context of meaning. It is a replacement which preserves semantic coherence and should be distinguished from a replacement which preserves syntactic coherence but may yield an expression to which no meaning has been given. This means that supposing an original expression is meaningful, the new expression obtained by the replacement will also be meaningful, though it will not necessarily have the same meaning as the original one, nor, if the expression in question happens to be a proposition, will the replacement necessarily preserve the truth value of the original. [5]

In linguistics, syntax is the set of rules, principles, and processes that govern the structure of sentences in a given language, usually including word order. The term syntax is also used to refer to the study of such principles and processes. The goal of many syntacticians is to discover the syntactic rules common to all languages.

In the philosophy of language, the nature of meaning, its definition, elements, and types, was discussed by philosophers Aristotle, Augustine, and Aquinas. According to them "meaning is a relationship between two sorts of things: signs and the kinds of things they mean ". One term in the relationship of meaning necessarily causes something else to come to the mind. In other words: "a sign is defined as an entity that indicates another entity to some agent for some purpose". As Augustine states, a sign is "something that shows itself to the senses and something other than itself to the mind".

A proposition is a tentative and conjectural relationship between constructs that is stated in a declarative form. An example of a proposition is: “An increase in student intelligence causes an increase in their academic achievement.” This declarative statement does not have to be true, but must be empirically testable using data, so that we can judge whether it is true or false. Propositions are generally derived based on logic (deduction) or empirical observations (induction). Because propositions are associations between abstract constructs, they cannot be tested directly. Instead, they are tested indirectly by examining the relationship between corresponding measures (variables) of those constructs. The empirical formulation of propositions, stated as relationships between variables, is called hypotheses. The term proposition has a broad use in contemporary analytic philosophy. It is used to refer to some or all of the following: the primary bearers of truth-value, the objects of belief and other "propositional attitudes", the referents of that-clauses, and the meanings of declarative sentences. Propositions are the sharable objects of attitudes and the primary bearers of truth and falsity. This stipulation rules out certain candidates for propositions, including thought- and utterance-tokens which are not sharable, and concrete events or facts, which cannot be false.

Bob Hale

Bob Hale explains salva congruitate, as applied to singular terms, as substantival expressions in natural language, which are able to replace singular terms without destructive effect on the grammar of a sentence. [6] Thus the singular term 'Bob' may be replaced by the definite description 'the first man to swim the English Channel' salva congruitate. Such replacement may shift both meaning and reference, and so, if made in the context of a sentence, may cause a change in truth-value. Thus terms which may be interchanged salva congruitate may not be interchangeable salva veritate (preserving truth). More generally, expressions of any type are interchangeable salva congruitate if and only if they can replace one another preserving grammaticality or well-formedness.

Bob Hale, FRSE, was a British philosopher, known for his contributions to the development of the neo-Fregean (neo-logicist) philosophy of mathematics in collaboration with Crispin Wright, and for his works in modality and philosophy of language.

Noun part of speech in grammar denoting a figurative or real thing or person

A noun is a word that functions as the name of some specific thing or set of things, such as living creatures, objects, places, actions, qualities, states of existence, or ideas. Linguistically, a noun is a member of a large, open part of speech whose members can occur as the main word in the subject of a clause, the object of a verb, or the object of a preposition.

See also

The literal translation of the Latin "salva veritate" is "with unharmed truth", using ablative of manner: "salva" meaning "rescue," "salvation," or "welfare," and "veritate" meaning "reality" or "truth". Thus, Salva veritate is the logical condition by which two expressions may be interchanged without altering the truth-value of statements in which the expressions occur. Substitution salva veritate of co-extensional terms can fail in opaque contexts.

Crispin James Garth Wright is a British philosopher, who has written on neo-Fregean (neo-logicist) philosophy of mathematics, Wittgenstein's later philosophy, and on issues related to truth, realism, cognitivism, skepticism, knowledge, and objectivity. He is Professor of Philosophy at New York University and Professor of Philosophical Research at the University of Stirling, and taught previously at the University of St Andrews, University of Aberdeen, Princeton University and University of Michigan.

Peter Thomas Geach was a British philosopher and professor of logic at the University of Leeds. His areas of interest were the history of philosophy, philosophical logic, ethics, philosophy of religion, and the theory of identity.

Related Research Articles

Logical positivism and logical empiricism, which together formed neopositivism, was a movement in Western philosophy whose central thesis was verificationism, a theory of knowledge which asserted that only statements verifiable through empirical observation are meaningful. The movement flourished in the 1920s and 1930s in several European centers.

Semantics is the linguistic and philosophical study of meaning, in language, programming languages, formal logics, and semiotics. It is concerned with the relationship between signifiers—like words, phrases, signs, and symbols—and what they stand for in reality, their denotation.

An ontological commitment refers to a relation between a language and certain objects postulated to be extant by that language. The 'existence' referred to need not be 'real', but exist only in a universe of discourse. As an example, legal systems use vocabulary referring to 'legal persons' that are collective entities that have rights. One says the legal doctrine has an ontological commitment to non-singular individuals. In information systems and artificial intelligence, where an ontology refers to a specific vocabulary and a set of explicit assumptions about the meaning and usage of these words, then an ontological commitment is an agreement to use the shared vocabulary in a coherent and consistent manner within a specific context. In philosophy a "theory is ontologically committed to an object only if that object occurs in all the ontologies of that theory"

"Two Dogmas of Empiricism" is a paper by analytic philosopher Willard Van Orman Quine published in 1951. According to City University of New York professor of philosophy Peter Godfrey-Smith, this "paper [is] sometimes regarded as the most important in all of twentieth-century philosophy". The paper is an attack on two central aspects of the logical positivists' philosophy. One is the analytic–synthetic distinction between analytic truths and synthetic truths, explained by Quine as truths grounded only in meanings and independent of facts, and truths grounded in facts. The other is reductionism, the theory that each meaningful statement gets its meaning from some logical construction of terms that refers exclusively to immediate experience.

David Benjamin Kaplan is the Hans Reichenbach Professor of Scientific Philosophy at the University of California, Los Angeles Department of Philosophy. His philosophical work focuses on the philosophy of language, logic, metaphysics, epistemology and the philosophy of Frege and Russell. He is best known for his work on demonstratives, propositions, and reference in intensional contexts. He was elected a Fellow of the American Academy of Arts & Sciences in 1983 and a Corresponding Fellow of the British Academy in 2007.

In philosophy of language, a context in which a sub-sentential expression e appears is called extensional if and only if e can be replaced by an expression with the same extension and necessarily preserve truth-value. The extension of a term is the set of objects that that term denotes.

In propositional logic, transposition is a valid rule of replacement that permits one to switch the antecedent with the consequent of a conditional statement in a logical proof if they are also both negated. It is the inference from the truth of "A implies B" the truth of "Not-B implies not-A", and conversely. It is very closely related to the rule of inference modus tollens. It is the rule that:

The indeterminacy of translation is a thesis propounded by 20th-century American analytic philosopher W. V. Quine. The classic statement of this thesis can be found in his 1960 book Word and Object, which gathered together and refined much of Quine's previous work on subjects other than formal logic and set theory. The indeterminacy of translation is also discussed at length in his Ontological Relativity. Crispin Wright suggests that this "has been among the most widely discussed and controversial theses in modern analytical philosophy". This view is endorsed by Putnam who states that it is "the most fascinating and the most discussed philosophical argument since Kant's Transcendental Deduction of the Categories".

The history of logic as a subject has been characterised by many disputes over what the topic deals with, and the main article 'Logic' has as a result been hesitant to commit to a particular definition of logic. This article surveys various definitions of the subject that have appeared over the centuries through to modern times, and puts them in context as reflecting rival conceptions of the subject.

<i>Language, Truth, and Logic</i> philosophical book by A. J. Ayer

Language, Truth, and Logic is a 1936 work of philosophy by Alfred Jules Ayer. It brought some of the ideas of the Vienna Circle and the logical empiricists to the attention of the English-speaking world.

Logical truth is one of the most fundamental concepts in logic, and there are different theories on its nature. A logical truth is a statement which is true, and remains true under all reinterpretations of its components other than its logical constants. It is a type of analytic statement. All of philosophical logic can be thought of as providing accounts of the nature of logical truth, as well as logical consequence.

An opaque context or referentially opaque context is a linguistic context in which it is not always possible to substitute "co-referential" expressions without altering the truth of sentences. The expressions involved are usually grammatically singular terms. So, substitution of co-referential expressions into an opaque context does not always preserve truth. For example, "Lois believes x is a hero" is an opaque context because "Lois believes Superman is a hero" is true while "Lois believes Clark Kent is a hero" is false, even though 'Superman' and 'Clark Kent' are co-referential expressions.

A truth-bearer is an entity that is said to be either true or false and nothing else. The thesis that some things are true while others are false has led to different theories about the nature of these entities. Since there is divergence of opinion on the matter, the term truth-bearer is used to be neutral among the various theories. Truth-bearer candidates include propositions, sentences, sentence-tokens, statements, concepts, beliefs, thoughts, intuitions, utterances, and judgements but different authors exclude one or more of these, deny their existence, argue that they are true only in a derivative sense, assert or assume that the terms are synonymous, or seek to avoid addressing their distinction or do not clarify it.

Following the developments in formal logic with symbolic logic in the late nineteenth century and mathematical logic in the twentieth, topics traditionally treated by logic not being part of formal logic have tended to be termed either philosophy of logic or philosophical logic if no longer simply logic.

<i>Word and Object</i> 1960 book by Willard Van Orman Quine

Word and Object is a 1960 work by philosopher Willard Van Orman Quine, in which the author expands upon the line of thought of his earlier writings in From a Logical Point of View (1953), and reformulates some of his earlier arguments, such as his attack in "Two Dogmas of Empiricism" on the analytic-synthetic distinction. The thought experiment of radical translation and the accompanying notion of indeterminacy of translation are original to Word and Object, which is Quine's most famous book.

References

  1. W.V.O. Quine, Philosophy of logic
  2. Dr. Benjamin Schnieder, Canonical Property Designators, P9
  3. W.V.O. Quine, Quiddities, P204
  4. W.V.O. Quine, Philosophy of Logic, P18
  5. Timothy C. Potts, Structures and categories for the representation of meaning, p57
  6. Bob Hale, Singular Terms, P34