Philosophical logic in the context of "Logical consequence"

Reality is the state of everything that exists, not how they might be imagined. Different cultures and academic disciplines conceptualize it in various ways.

Philosophical questions about the nature of reality, existence, or being are considered under the rubric of ontology, a major branch of metaphysics in the Western intellectual tradition. Ontological questions also feature in diverse branches of philosophy, including the philosophy of science, religion, mathematics, and logic. These include questions about whether only physical objects are real (e.g., physicalism), whether reality is fundamentally immaterial (e.g., idealism), whether hypothetical unobservable entities posited by scientific theories exist (e.g., scientific realism), whether God exists, whether numbers and other abstract objects exist, and whether possible worlds exist. Skeptics question whether any of those claims are true, and suggest more extreme postulates.

Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components (other than its logical constants). Thus, logical truths such as "if p, then p" can be considered tautologies. Logical truths are thought to be the simplest case of statements which are analytically true (or in other words, true by definition). All of philosophical logic can be thought of as providing accounts of the nature of logical truth, as well as logical consequence.

Logical truths are generally considered to be necessarily true. This is to say that they are such that no situation could arise in which they could fail to be true. The view that logical statements are necessarily true is sometimes treated as equivalent to saying that logical truths are true in all possible worlds. However, the question of which statements are necessarily true remains the subject of continued debate.

In logic and philosophy, a formal fallacy is a pattern of reasoning with a flaw in its logical structure (the logical relationship between the premises and the conclusion). In other words:

• It is a pattern of reasoning in which the conclusion may not be true even if all the premises are true.
• It is a pattern of reasoning in which the premises do not entail the conclusion.
• It is a pattern of reasoning that is invalid.
• It is a fallacy in which deduction goes wrong, and is no longer a logical process.

A formal fallacy is contrasted with an informal fallacy which may have a valid logical form and yet be unsound because one or more premises are false. A formal fallacy, however, may have a true premise, but a false conclusion. The term 'logical fallacy' is sometimes used in everyday conversation, and refers to a formal fallacy.

Non-classical logics (and sometimes alternative logics or non-Aristotelian logics) are formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is commonly the case, including by way of extensions, deviations, and variations. The aim of these departures is to make it possible to construct different models of logical consequence and logical truth.

Philosophical logic is understood to encompass and focus on non-classical logics, although the term has other meanings as well. In addition, some parts of theoretical computer science can be thought of as using non-classical reasoning, although this varies according to the subject area. For example, the basic boolean functions (e.g. AND, OR, NOT, etc) in computer science are very much classical in nature, as is clearly the case given that they can be fully described by classical truth tables. However, in contrast, some computerized proof methods may not use classical logic in the reasoning process.

Counterfactual conditionals (also contrafactual, subjunctive or X-marked) are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with indicatives, which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of fake tense morphology, which some languages use in combination with other kinds of morphology including aspect and mood.

Counterfactuals are one of the most studied phenomena in philosophical logic, formal semantics, and philosophy of language. They were first discussed as a problem for the material conditional analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic possible world approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as causal models and dynamic semantics. Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.

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 (or it ought to be (the case) that A), and PA to mean it is permitted (or permissible) that A, which is defined as ${\displaystyle PA\equiv \neg O\neg A}$.

In natural language, the statement "You may go to the zoo OR the park" should be understood as ${\displaystyle Pz\land Pp}$ instead of ${\displaystyle Pz\lor Pp}$, as both options are permitted by the statement. When there are multiple agents involved in the domain of discourse, the deontic modal operator can be specified to each agent to express their individual obligations and permissions. For example, by using a subscript ${\displaystyle O_{i}}$ for agent ${\displaystyle a_{i}}$, ${\displaystyle O_{i}A}$ means that "It is an obligation for agent ${\displaystyle a_{i}}$ (to bring it about/make it happen) that ${\displaystyle A}$". Note that ${\displaystyle A}$ could be stated as an action by another agent; One example is "It is an obligation for Adam that Bob doesn't crash the car", which would be represented as ${\displaystyle O_{Adam}B}$, where B="Bob doesn't crash the car".

Gertrude Elizabeth Margaret Anscombe FBA (/ˈænskəm/; 18 March 1919 – 5 January 2001), usually cited as G. E. M. Anscombe or Elizabeth Anscombe, was a British analytic philosopher. She wrote on the philosophy of mind, philosophy of action, philosophical logic, philosophy of language, and ethics. She was a prominent figure of analytical Thomism, a fellow of Somerville College, Oxford, and a professor of philosophy at the University of Cambridge.

Anscombe was a student of Ludwig Wittgenstein and became an authority on his work and edited and translated many books drawn from his writings, above all his Philosophical Investigations. Anscombe's 1958 article "Modern Moral Philosophy" introduced the term consequentialism into the language of analytic philosophy, and had a seminal influence on contemporary virtue ethics. Her monograph Intention (1957) was described by Donald Davidson as "the most important treatment of action since Aristotle". It is "widely considered a foundational text in contemporary philosophy of action" and has also had influence in the philosophy of practical reason."