Philosophy of logic
Philosophy of logic is the branch of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application. This involves questions about how logic is to be defined and how different logical systems are connected to each other. It includes the study of the nature of the fundamental concepts used by logic and the relation of logic to other disciplines. According to a common characterisation, philosophical logic is the part of the philosophy of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. But other theorists draw the distinction between the philosophy of logic and philosophical logic differently or not at all. Metalogic is closely related to the philosophy of logic as the discipline investigating the properties of formal logical systems, like consistency and completeness.
Various characterizations of the nature of logic are found in the academic literature. Logic is often seen as the study of correct reasoning, valid inference, or logical consequence. It is a formal science that investigates how conclusions follow from premises in a topic-neutral manner, i.e. independent of the specific subject matter discussed. One form of inquiring into the nature of logic focuses on the commonalities between various logical formal systems and on how they differ from non-logical formal systems. Important considerations in this respect are whether the formal system in question is compatible with fundamental logical intuitions and whether it is complete. Different conceptions of logic can be distinguished according to whether they define logic as the study of valid inference or logical truth. A further distinction among conceptions of logic is based on whether the criteria of valid inference and logical truth are specified in terms of syntax or semantics.
Different [|types of logic] are often distinguished. Logic is usually understood as formal logic and is treated as such for most of this article. Formal logic is only interested in the form of arguments, expressed in a formal language, and focuses on deductive inferences. Informal logic, on the other hand, addresses a much wider range of arguments found also in natural language, which include non-deductive arguments. The correctness of arguments may depend on other factors than their form, like their content or their context. Various logical formal systems or logics have been developed in the 20th century and it is the task of the philosophy of logic to classify them, to show how they are related to each other, and to address the problem of how there can be a manifold of logics in contrast to one universally true logic. These logics can be divided into classical logic, usually identified with first-order logic, extended logics, and deviant logics. Extended logics accept the basic formalism and the axioms of classical logic but extend them with new logical vocabulary. Deviant logics, on the other hand, reject certain core assumptions of classical logic and are therefore incompatible with it.
The philosophy of logic also investigates the nature and philosophical implications of the [|fundamental concepts of logic]. This includes the problem of truth, especially of logical truth, which may be defined as truth depending only on the meanings of the logical terms used. Another question concerns the nature of premises and conclusions, i.e. whether to understand them as thoughts, propositions, or sentences, and how they are composed of simpler constituents. Together, premises and a conclusion constitute an inference, which can be either deductive and ampliative depending on whether it is necessarily truth-preserving or introduces new and possibly false information. A central concern in logic is whether a deductive inference is valid. Validity is often defined in terms of necessity, i.e. an inference is valid if and only if it is impossible for the premises to be true and the conclusion to be false. Incorrect inferences and arguments, on the other hand, fail to support their conclusion. They can be categorized as formal or informal fallacies depending on whether they belong to formal or informal logic. Logic has mostly been concerned with definitory rules, i.e. with the question of which rules of inference determine whether an argument is valid. A separate topic of inquiry concerns the strategic rules of logic: the rules governing how to reach an intended conclusion given a certain set of premises, i.e. which inferences need to be drawn to arrive there.
The [|metaphysics of logic] is concerned with the metaphysical status of the laws and objects of logic. An important dispute in this field is between realists, who hold that logic is based on facts that have mind-independent existence, and anti-realists like conventionalists, who hold that the laws of logic are based on the conventions governing the use of language. Logic is closely related to [|various disciplines]. A central issue in regard to ontology concerns the ontological commitments associated with the use of logic, for example, with singular terms and existential quantifiers. An important question in mathematics is whether all mathematical truths can be grounded in the axioms of logic together with set theory. Other related fields include computer science and psychology.
Definition and related disciplines
Philosophy of logic is the area of philosophy that studies the nature of logic. Like many other disciplines, logic involves various philosophical presuppositions which are addressed by the philosophy of logic. The philosophy of logic can be understood in analogy to other discipline-specific branches of philosophy: just like the philosophy of science investigates philosophical problems raised by science, so the philosophy of logic investigates philosophical problems raised by logic.An important question studied by the philosophy of logic is how logic is to be defined, for example, in terms of valid inference or of logical truth. This includes the issue of how to distinguish logical from non-logical formal systems. It is especially relevant for clarifying the relation between the various proposed logical systems, both classical and non-classical, and for evaluating whether all of these systems actually qualify as logical systems. The philosophy of logic also investigates how to understand the most fundamental concepts of logic, like truth, premises, conclusions, inference, argument, and validity. It tries to clarify the relation between logic and other fields, such as ontology, mathematics, and psychology.
The philosophy of logic is closely related to philosophical logic but there is no general agreement about how these disciplines stand to each other. Some theorists use these two terms for the same discipline while others see them as distinct disciplines. According to the latter view, philosophical logic contrasts with the philosophy of logic in that it is usually seen as the application of logical methods to philosophical problems, often by developing deviant or extended logics. In this sense, philosophical logic is one area of inquiry within the philosophy of logic, i.e. a part of the general study of philosophical problems raised by logic. But this form of distinction is not universally accepted and some authors have proposed different characterizations. The intimate connection between logic and philosophy is also reflected in the fact that many famous logicians were also philosophers. The philosophy of logic is closely related to metalogic but not identical to it. Metalogic investigates the properties of formal logical systems, like whether a given logical system is consistent or complete. It usually includes the study of the semantics and syntax of formal languages and formal systems.
Nature of logic
The term "logic" is based on the Greek word "logos", which is associated with various different senses, such as reason, discourse, or language. There are many disagreements about what logic is and how it should be defined. Various characteristics are generally ascribed to logic, like that it studies the relation between premises and conclusions and that it does so in a topic-neutral manner. An important task of the philosophy of logic is to investigate the criteria according to which a formal system should count as logic. Different conceptions of logic understand it as either based on valid inference or logical truth. The criteria of valid inference and logical truth can themselves be specified in different ways: based on syntactic or semantic considerations.General characteristics
Traditionally, logic is often understood as the discipline investigating laws of thought. One problem for this characterization is that logic is not an empirical discipline studying the regularities found in actual human thinking: this subject belongs to psychology. This is better captured by another characterization sometimes found in the literature: that logic concerns the laws of correct thinking or, more specifically, correct reasoning. This reflects the practical significance of logic as a tool to improve one's reasoning by drawing good inferences and becoming aware of possible mistakes. Logic has also been defined as the science of valid argumentation. This mirrors the definition in terms of reasoning since argumentation may be understood as an outward expression of inward reasoning.Logic is often seen as a formal foundation of all knowledge. As a formal science, it stands in contrast to the material or empirical sciences, like physics or biology, since it is mainly concerned with entailment relations between propositions but not with whether these propositions actually are true. For example, deducing from the proposition "all moons are made of cheese" that "Earth's moon is made of cheese" is a valid inference. The error in this example is due to a false premise belonging to empirical astronomy.
A central feature of logic is that it is topic-neutral. This means that it is concerned with the validity of arguments independent of the subject matter of these arguments. In this sense, regular sciences are concerned with correct reasoning within a specific area of inquiry, for example, concerning material bodies for classical mechanics or living beings for biology, while logic is concerned with correct reasoning in general as applicable to all these disciplines. One problem with this characterization is that it is not always clear how the terms "topic-neutral" and "subject matter" are to be understood in this context. For example, it could be argued that first-order logic has individuals as its subject matter, due to its usage of singular terms and quantifiers, and is therefore not completely topic-neutral. A closely related characterization holds that logic is concerned with the form of arguments rather than their contents. On this view, the regular sciences could be seen as seeking true premises while logic studies how to draw conclusions from these or any premises. But this characterization also has its problems due to difficulties in distinguishing between form and content. For example, since temporal logic talks about time, this would lead to the implausible conclusion that time belongs to the form and not to the content of arguments. These difficulties have led some theorists to doubt that logic has a clearly specifiable scope or an essential character.
There is wide agreement that logic is a normative discipline. This means that the laws it investigates determine how people should think and that violating these laws is irrational. But there have been individual challenges to this idea. For example, Gilbert Harman claims that deductive logic investigates relations between propositions rather than correct reasoning. He argues that these relations do not directly determine how people should change their beliefs.