"paradox of free choice" redirects here. Not to be confused with The Paradox of Choice.
Free choice is a phenomenon in natural language where a linguistic disjunction appears to receive a logical conjunctive interpretation when it interacts with a modal operator. For example, the following English sentences can be interpreted to mean that the addressee can watch a movie and that they can also play video games, depending on their preference:[1]
You can watch a movie or play video games.
You can watch a movie or you can play video games.
Free choice inferences are a major topic of research in formal semantics and philosophical logic because they are not valid in classical systems of modal logic. If they were valid, then the semantics of natural language would validate the Free Choice Principle.
Free Choice Principle:
This symbolic logic formula above is not valid in classical modal logic: Adding this principle as an axiom to standard modal logics would allow one to conclude from , for any and . This observation is known as the Paradox of Free Choice.[1][2] To resolve this paradox, some researchers have proposed analyses of free choice within nonclassical frameworks such as dynamic semantics, linear logic, alternative semantics, and inquisitive semantics.[1][3][4] Others have proposed ways of deriving free choice inferences as scalar implicatures which arise on the basis of classical lexical entries for disjunction and modality.[1][5][6][7]
Free choice inferences are most widely studied for deontic modals, but also arise with other flavors of modality as well as imperatives, conditionals, and other kinds of operators.[1][8][9][4]Indefinite noun phrases give rise to a similar inference which is also referred to as "free choice" though researchers disagree as to whether it forms a natural class with disjunctive free choice.[9][10]
↑ Kamp, Hans (1973). "Free choice permission". Proceedings of the Aristotelian Society. 74: 57–74. doi:10.1093/aristotelian/74.1.57.
↑ Simons, Mandy (2005). "Dividing things up: The semantics of or and the modal/or interaction". Natural Language Semantics. 13 (3): 271–316. doi:10.1007/s11050-004-2900-7. S2CID14338992.
↑ Schulz, Katrin (2007). Minimal models in semantics and pragmatics: Free choice, exhaustivity, and conditionals (Thesis). University of Amsterdam ILLC.
↑ Fox, Danny (2007). "Free choice and the theory of scalar implicatures". In Sauerland, U.; Stateva, P. (eds.). Presupposition and implicature in compositional semantics. Palgrave Macmillan. pp.71–120. doi:10.1057/9780230210752_4. ISBN978-1-349-28206-7.
↑ Zimmerman, Thomas Ede (2000). "Free choice disjunction and epistemic possibility". Natural Language Semantics. 8 (4): 255–290. doi:10.1023/A:1011255819284. S2CID122826485.
In logic, disjunction, also known as logical disjunction or logical or or logical addition or inclusive disjunction, is a logical connective typically notated as and read aloud as "or". For instance, the English language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula , assuming that abbreviates "it is sunny" and abbreviates "it is warm".
In classical logic, disjunctive syllogism is a valid argument form which is a syllogism having a disjunctive statement for one of its premises.
A false dilemma, also referred to as false dichotomy or false binary, is an informal fallacy based on a premise that erroneously limits what options are available. The source of the fallacy lies not in an invalid form of inference but in a false premise. This premise has the form of a disjunctive claim: it asserts that one among a number of alternatives must be true. This disjunction is problematic because it oversimplifies the choice by excluding viable alternatives, presenting the viewer with only two absolute choices when, in fact, there could be many.
In logic, a logical connective is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective can be used to join the two atomic formulas and , rendering the complex formula .
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ. With multiple inputs, XOR is true if and only if the number of true inputs is odd.
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.
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as identical to the philosophy of logic, which includes additional topics like how to define logic or a discussion of the fundamental concepts of logic. The current article treats philosophical logic in the narrow sense, in which it forms one field of inquiry within the philosophy of logic.
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.
Paraconsistent logic is a type of non-classical logic that allows for the coexistence of contradictory statements without leading to a logical explosion where anything can be proven true. Specifically, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" systems of logic, purposefully excluding the principle of explosion.
In classical logic, intuitionistic logic, and similar logical systems, the principle of explosion is the law according to which any statement can be proven from a contradiction. That is, from a contradiction, any proposition can be inferred; this is known as deductive explosion.
The material conditional is an operation commonly used in logic. When the conditional symbol is interpreted as material implication, a formula is true unless is true and is false. Material implication can also be characterized inferentially by modus ponens, modus tollens, conditional proof, and classical reductio ad absurdum.
Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It can be used to formalize imperative logic, or directive modality in natural languages. Typically, a deontic logic uses OA to mean it is obligatory that A, and PA to mean it is permitted that A, which is defined as .
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.
Imperative logic is the field of logic concerned with imperatives. In contrast to declaratives, it is not clear whether imperatives denote propositions or more generally what role truth and falsity play in their semantics. Thus, there is almost no consensus on any aspect of imperative logic.
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.
Alternative semantics is a framework in formal semantics and logic. In alternative semantics, expressions denote alternative sets, understood as sets of objects of the same semantic type. For instance, while the word "Lena" might denote Lena herself in a classical semantics, it would denote the singleton set containing Lena in alternative semantics. The framework was introduced by Charles Leonard Hamblin in 1973 as a way of extending Montague grammar to provide an analysis for questions. In this framework, a question denotes the set of its possible answers. Thus, if and are propositions, then is the denotation of the question whether or is true. Since the 1970s, it has been extended and adapted to analyze phenomena including focus, scope, disjunction, NPIs, presupposition, and implicature.
In formal semantics and philosophical logic, simplification of disjunctive antecedents (SDA) is the phenomenon whereby a disjunction in the antecedent of a conditional appears to distribute over the conditional as a whole. This inference is shown schematically below:
A non-normal modal logic is a variant of modal logic that deviates from the basic principles of normal modal logics.
This is a glossary of logic. Logic is the study of the principles of valid reasoning and argumentation.
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