De dicto and de re

Last updated

De dicto and de re are two phrases used to mark a distinction in intensional statements, associated with the intensional operators in many such statements. The distinction is used regularly in analytical metaphysics and in philosophy of language. [1]

Contents

The literal translation of the phrase de dicto is "about what is said", [2] whereas de re translates as "about the thing". [3] The original meaning of the Latin locutions may help to elucidate the living meaning of the phrases, in the distinctions they mark. The distinction can be understood by examples of intensional contexts of which three are considered here: a context of thought, a context of desire, and a context of modality.

Context of thought

There are two possible interpretations of the sentence "Peter believes someone is out to get him":

On the de dicto interpretation, 'someone' is unspecific and Peter suffers a general paranoia; he believes that it is true that a person is out to get him, but does not necessarily have any beliefs about who this person may be. What Peter believes is that the predication 'someone is out to get Peter' is satisfied.

On the de re interpretation, 'someone' is specific, picking out some particular individual. There is some person Peter has in mind, and Peter believes that person is out to get him.

In the context of thought, the distinction helps us explain how people can hold seemingly self-contradictory beliefs. [4] Say Lois Lane believes Clark Kent is weaker than Superman. Since Clark Kent is Superman, taken de re, Lois's belief is untenable; the names 'Clark Kent' and 'Superman' pick out an individual in the world, and a person (or super-person) cannot be stronger than himself. Understood de dicto, however, this may be a perfectly reasonable belief, since Lois is not aware that Clark and Superman are one and the same.

Context of desire

Consider the sentence "Jana wants to marry the tallest man in Fulsom County". It could be read either de dicto or de re; the meanings would be different. One interpretation is that Jana wants to marry the tallest man in Fulsom County, whoever he might be. On this interpretation, what the statement tells us is that Jana has a certain unspecific desire; what she desires is for Jana is marrying the tallest man in Fulsom County to be true. The desire is directed at that situation, regardless of how it is to be achieved. The other interpretation is that Jana wants to marry a certain man, who in fact happens to be the tallest man in Fulsom County. Her desire is for that man, and she desires herself to marry him. The first interpretation is the de dicto interpretation, because Jana's desire relates to the words "the tallest man in Fulsom County", and the second interpretation is the de re interpretation, because Jana's desire relates to the man those words refer to.

Another way to understand the distinction is to ask what Jana would want if a nine-foot-tall immigrant moved to Fulsom county. If she continued to want to marry the same man and perceived this as representing no change in her desires then she could be taken to have meant the original statement in a de re sense. If she no longer wanted to marry that man but instead wanted to marry the new tallest man in Fulsom County, and saw this as a continuation of her earlier desire, then she meant the original statement in a de dicto sense.

Context of modality

The number of discovered chemical elements is 118. Take the sentence "The number of chemical elements is necessarily greater than 100". Again, there are two interpretations as per the de dicto/de re distinction.

Another example: "The President of the US in 2001 could not have been Al Gore".

Representing de dicto and de re in modal logic

In modal logic the distinction between de dicto and de re is one of scope. In de dicto claims, any existential quantifiers are within the scope of the modal operator, whereas in de re claims the modal operator falls within the scope of the existential quantifier. For example:

De dicto:Necessarily, some x is such that it is A
De re:Some x is such that it is necessarily A

Generally speaking, is logically equivalent to , both meaning that all x in all the possible worlds are A (assuming that the range of quantification/domain of discourse is the same in all the accessible possible worlds); However, means that each accessible possible world has its own x that is A, but they are not necessarily the same, whereas means that there is a special x that is A in all accessible possible worlds.

Similarly, is logically equivalent to , both meaning that in some accessible possible world, there is some x that is A; However, means that in some accessible possible world, all x are A, whereas means that for each x in the range of quantification/domain of discourse, there is some accessible possible world where x is A, but it can be true that no world has two x that are both A.

See also

Related Research Articles

Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development that goes back to Anselm of Canterbury (1033–1109). St. Anselm's ontological argument, in its most succinct form, is as follows: "God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist." A more elaborate version was given by Gottfried Leibniz (1646–1716); this is the version that Gödel studied and attempted to clarify with his ontological argument.

<span class="mw-page-title-main">Saul Kripke</span> American philosopher and logician (1940–2022)

Saul Aaron Kripke was an American analytic philosopher and logician. He was Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emeritus professor at Princeton University. From the 1960s until his death, he was a central figure in a number of fields related to mathematical and modal logic, philosophy of language and mathematics, metaphysics, epistemology, and recursion theory.

In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts with Hilbert-style systems, which instead use axioms as much as possible to express the logical laws of deductive reasoning.

Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems of intuitionistic logic do not assume the law of the excluded middle and double negation elimination, which are fundamental inference rules in classical logic.

In quantified modal logic, the Barcan formula and the converse Barcan formula (i) syntactically state principles of interchange between quantifiers and modalities; (ii) semantically state a relation between domains of possible worlds. The formulas were introduced as axioms by Ruth Barcan Marcus, in the first extensions of modal propositional logic to include quantification.

Modal logic is a kind of logic used to represent statements about necessity and possibility. It plays a major role in philosophy and related fields as a tool for understanding concepts such as knowledge, obligation, and causation. For instance, in epistemic modal logic, the formula can be used to represent the statement that is known. In deontic modal logic, that same formula can represent that is a moral obligation. Modal logic considers the inferences that modal statements give rise to. For instance, most epistemic modal logics treat the formula as a tautology, representing the principle that only true statements can count as knowledge. However, this formula is not a tautology in deontic modal logic, since what ought to be true can be false.

Kripke semantics is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joyal. It was first conceived for modal logics, and later adapted to intuitionistic logic and other non-classical systems. The development of Kripke semantics was a breakthrough in the theory of non-classical logics, because the model theory of such logics was almost non-existent before Kripke.

<span class="mw-page-title-main">Method of analytic tableaux</span> Tool for proving a logical formula

In proof theory, the semantic tableau, also called an analytic tableau, truth tree, or simply tree, is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. An analytic tableau is a tree structure computed for a logical formula, having at each node a subformula of the original formula to be proved or refuted. Computation constructs this tree and uses it to prove or refute the whole formula. The tableau method can also determine the satisfiability of finite sets of formulas of various logics. It is the most popular proof procedure for modal logics.

In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category are included in another. The study of arguments using categorical statements forms an important branch of deductive reasoning that began with the Ancient Greeks.

In logic, predicate abstraction is the result of creating a predicate from a formula. If Q is any formula then the predicate abstract formed from that sentence is (λx.Q), where λ is an abstraction operator and in which every occurrence of x that is free in Q is bound by λ in (λx.Q). The resultant predicate is a monadic predicate capable of taking a term t as argument as in (t), which says that the object denoted by 't' has the property of being such that Q.

A fallacy of necessity is a fallacy in the logic of a syllogism whereby a degree of unwarranted necessity is placed in the conclusion.

In philosophical logic, the concept of an impossible world is used to model certain phenomena that cannot be adequately handled using ordinary possible worlds. An impossible world, , is the same sort of thing as a possible world , except that it is in some sense "impossible." Depending on the context, this may mean that some contradictions, statements of the form are true at , or that the normal laws of logic, metaphysics, and mathematics, fail to hold at , or both. Impossible worlds are controversial objects in philosophy, logic, and semantics. They have been around since the advent of possible world semantics for modal logic, as well as world based semantics for non-classical logics, but have yet to find the ubiquitous acceptance, that their possible counterparts have found in all walks of philosophy.

Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applications in many fields, including philosophy, theoretical computer science, artificial intelligence, economics, and linguistics. While philosophers since Aristotle have discussed modal logic, and Medieval philosophers such as Avicenna, Ockham, and Duns Scotus developed many of their observations, it was C. I. Lewis who created the first symbolic and systematic approach to the topic, in 1912. It continued to mature as a field, reaching its modern form in 1963 with the work of Kripke.

A modal connective is a logical connective for modal logic. It is an operator which forms propositions from propositions. In general, a modal operator has the "formal" property of being non-truth-functional in the following sense: The truth-value of composite formulae sometimes depend on factors other than the actual truth-value of their components. In the case of alethic modal logic, a modal operator can be said to be truth-functional in another sense, namely, that of being sensitive only to the distribution of truth-values across possible worlds, actual or not. Finally, a modal operator is "intuitively" characterized by expressing a modal attitude about the proposition to which the operator is applied.

In logic, general frames are Kripke frames with an additional structure, which are used to model modal and intermediate logics. The general frame semantics combines the main virtues of Kripke semantics and algebraic semantics: it shares the transparent geometrical insight of the former, and robust completeness of the latter.

In logic, Hilbert's epsilon calculus is an extension of a formal language by the epsilon operator, where the epsilon operator substitutes for quantifiers in that language as a method leading to a proof of consistency for the extended formal language. The epsilon operator and epsilon substitution method are typically applied to a first-order predicate calculus, followed by a demonstration of consistency. The epsilon-extended calculus is further extended and generalized to cover those mathematical objects, classes, and categories for which there is a desire to show consistency, building on previously-shown consistency at earlier levels.

In philosophy, specifically in the area of metaphysics, counterpart theory is an alternative to standard (Kripkean) possible-worlds semantics for interpreting quantified modal logic. Counterpart theory still presupposes possible worlds, but differs in certain important respects from the Kripkean view. The form of the theory most commonly cited was developed by David Lewis, first in a paper and later in his book On the Plurality of Worlds.

In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic Logic. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. It is formed with propositional calculus formulas and tautologies, and inference apparatus with substitution and modus ponens, but extending the syntax with the modal operator necessarily and its dual possibly.

An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics.

In quantified modal logic, the Buridan formula and the converse Buridan formula (i) syntactically state principles of interchange between quantifiers and modalities; (ii) semantically state a relation between domains of possible worlds. The formulas are named in honor of the medieval philosopher Jean Buridan by analogy with the Barcan formula and the converse Barcan formula introduced as axioms by Ruth Barcan Marcus.

References

  1. Semantics Archive discussion
  2. "De Dicto | Definition of De Dicto by Oxford Dictionary on Lexico.com also meaning of De Dicto". Lexico Dictionaries | English. Archived from the original on May 18, 2021.
  3. "De Re | Definition of De Re by Oxford Dictionary on Lexico.com also meaning of De Re". Lexico Dictionaries | English. Archived from the original on May 12, 2021.
  4. Salmani Nodoushan, M. A. (2018). "Which view of indirect reports do Persian data corroborate?" International Review of Pragmatics, 10(1), 76-100.

Bibliography