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161-615: Written in French, it became quite popular and was in use up to the twentieth century, introducing the reader to logic, and exhibiting strong Cartesian elements in its metaphysics and epistemology (Arnauld having been one of the main philosophers whose objections were published, with replies, in Descartes ' Meditations on First Philosophy ). The Port-Royal Logic is sometimes cited as a paradigmatic example of traditional term logic . The philosopher Louis Marin particularly studied it in

322-501: A r y ) ∧ Q ( J o h n ) ) {\displaystyle \exists Q(Q(Mary)\land Q(John))} " . In this case, the existential quantifier is applied to the predicate variable " Q {\displaystyle Q} " . The added expressive power is especially useful for mathematics since it allows for more succinct formulations of mathematical theories. But it has drawbacks in regard to its meta-logical properties and ontological implications, which

483-508: A relation between a knower and a known proposition , in the case above between the person Ravi and the proposition "kangaroos hop". It is use-independent since it is not tied to one specific purpose. It is a mental representation that relies on concepts and ideas to depict reality. Because of its theoretical nature, it is often held that only relatively sophisticated creatures, such as humans, possess propositional knowledge. Propositional knowledge contrasts with non-propositional knowledge in

644-412: A series of thought experiments that aimed to show that some justified true beliefs do not amount to knowledge. In one of them, a person is unaware of all the fake barns in their area. By coincidence, they stop in front of the only real barn and form a justified true belief that it is a real barn. Many epistemologists agree that this is not knowledge because the justification is not directly relevant to

805-442: A belief is information that favors or supports it. Epistemologists understand evidence primarily in terms of mental states, for example, as sensory impressions or as other propositions that a person knows. But in a wider sense, it can also include physical objects, like bloodstains examined by forensic analysts or financial records studied by investigative journalists. Evidence is often understood in terms of probability : evidence for

966-634: A belief is justified if it coheres with other beliefs. Foundationalists , by contrast, maintain that the justification of basic beliefs does not depend on other beliefs. Internalism and externalism disagree about whether justification is determined solely by mental states or also by external circumstances. Separate branches of epistemology are dedicated to knowledge found in specific fields, like scientific, mathematical, moral, and religious knowledge. Naturalized epistemology relies on empirical methods and discoveries, whereas formal epistemology uses formal tools from logic . Social epistemology investigates

1127-473: A belief is justified if the individual's evidence supports the belief and they hold the belief on the basis of this evidence. Reliabilism is an externalist theory asserting that a reliable connection between belief and truth is required for justification. Some reliabilists explain this in terms of reliable processes. According to this view, a belief is justified if it is produced by a reliable belief-formation process, like perception. A belief-formation process

1288-612: A belief makes it more likely that the belief is true. A defeater is evidence against a belief or evidence that undermines another piece of evidence. For instance, witness testimony connecting a suspect to a crime is evidence for their guilt while an alibi is a defeater. Evidentialists analyze justification in terms of evidence by saying that to be justified, a belief needs to rest on adequate evidence. The presence of evidence usually affects doubt and certainty , which are subjective attitudes toward propositions that differ regarding their level of confidence. Doubt involves questioning

1449-592: A belief, known as propositional justification , but also in whether the person holds the belief because or based on this reason, known as doxastic justification . For example, if a person has sufficient reason to believe that a neighborhood is dangerous but forms this belief based on superstition then they have propositional justification but lack doxastic justification. Sources of justification are ways or cognitive capacities through which people acquire justification. Often-discussed sources include perception , introspection , memory , reason , and testimony , but there

1610-445: A central role in many arguments found in everyday discourse and the sciences. Ampliative arguments are not automatically incorrect. Instead, they just follow different standards of correctness. The support they provide for their conclusion usually comes in degrees. This means that strong ampliative arguments make their conclusion very likely while weak ones are less certain. As a consequence, the line between correct and incorrect arguments

1771-480: A certain cost: the premises support the conclusion in the sense that they make its truth more likely but they do not ensure its truth. This means that the conclusion of an ampliative argument may be false even though all its premises are true. This characteristic is closely related to non-monotonicity and defeasibility : it may be necessary to retract an earlier conclusion upon receiving new information or in light of new inferences drawn. Ampliative reasoning plays

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1932-414: A common view, this means that the person has sufficient reasons for holding this belief because they have information that supports it. Another view states that a belief is justified if it is formed by a reliable belief formation process, such as perception. The terms reasonable , warranted , and supported are closely related to the idea of justification and are sometimes used as synonyms. Justification

2093-573: A complex argument to be successful, each link of the chain has to be successful. Arguments and inferences are either correct or incorrect. If they are correct then their premises support their conclusion. In the incorrect case, this support is missing. It can take different forms corresponding to the different types of reasoning . The strongest form of support corresponds to deductive reasoning . But even arguments that are not deductively valid may still be good arguments because their premises offer non-deductive support to their conclusions. For such cases,

2254-425: A conclusion. Logic is interested in whether arguments are correct, i.e. whether their premises support the conclusion. These general characterizations apply to logic in the widest sense, i.e., to both formal and informal logic since they are both concerned with assessing the correctness of arguments. Formal logic is the traditionally dominant field, and some logicians restrict logic to formal logic. Formal logic

2415-701: A definition with more qualifications or features (the intension) denotes a class with fewer members (the extension), and vice versa. The main idea traces back through the scholastic philosophers to Aristotle 's ideas about genus and species , and is fundamental in the philosophy of Leibniz . More recently, it has been related to mathematical lattice theory in formal concept analysis , and independently formalized similarly by Yu. Schreider 's group in Moscow , Jon Barwise & Jerry Seligman in Information Flow , and others. This logic -related article

2576-573: A disease helps a doctor cure their patient, and knowledge of when a job interview starts helps a candidate arrive on time. The usefulness of a known fact depends on the circumstances. Knowledge of some facts may have little to no uses, like memorizing random phone numbers from an outdated phone book. Being able to assess the value of knowledge matters in choosing what information to acquire and transmit to others. It affects decisions like which subjects to teach at school and how to allocate funds to research projects. Of particular interest to epistemologists

2737-510: A formal language together with a set of axioms and a proof system used to draw inferences from these axioms. In logic, axioms are statements that are accepted without proof. They are used to justify other statements. Some theorists also include a semantics that specifies how the expressions of the formal language relate to real objects. Starting in the late 19th century, many new formal systems have been proposed. A formal language consists of an alphabet and syntactic rules. The alphabet

2898-686: A formal language while informal logic investigates them in their original form. On this view, the argument "Birds fly. Tweety is a bird. Therefore, Tweety flies." belongs to natural language and is examined by informal logic. But the formal translation "(1) ∀ x ( B i r d ( x ) → F l i e s ( x ) ) {\displaystyle \forall x(Bird(x)\to Flies(x))} ; (2) B i r d ( T w e e t y ) {\displaystyle Bird(Tweety)} ; (3) F l i e s ( T w e e t y ) {\displaystyle Flies(Tweety)} "

3059-415: A given argument is valid. Because of the reliance on formal language, natural language arguments cannot be studied directly. Instead, they need to be translated into formal language before their validity can be assessed. The term "logic" can also be used in a slightly different sense as a countable noun. In this sense, a logic is a logical formal system. Distinct logics differ from each other concerning

3220-551: A given conclusion based on a set of premises. This distinction does not just apply to logic but also to games. In chess , for example, the definitory rules dictate that bishops may only move diagonally. The strategic rules, on the other hand, describe how the allowed moves may be used to win a game, for instance, by controlling the center and by defending one's king . It has been argued that logicians should give more emphasis to strategic rules since they are highly relevant for effective reasoning. A formal system of logic consists of

3381-402: A great variety of topics. They include metaphysical theses about ontological categories and problems of scientific explanation. But in a more narrow sense, it is identical to term logic or syllogistics. A syllogism is a form of argument involving three propositions: two premises and a conclusion. Each proposition has three essential parts: a subject , a predicate, and a copula connecting

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3542-452: A letter, a newspaper, and a blog. Rationality is closely related to justification and the terms rational belief and justified belief are sometimes used as synonyms. However, rationality has a wider scope that encompasses both a theoretical side, covering beliefs, and a practical side, covering decisions , intentions , and actions . There are different conceptions about what it means for something to be rational. According to one view,

3703-614: A logical connective like "and" to form a new complex proposition. In Aristotelian logic, the subject can be universal , particular , indefinite , or singular . For example, the term "all humans" is a universal subject in the proposition "all humans are mortal". A similar proposition could be formed by replacing it with the particular term "some humans", the indefinite term "a human", or the singular term "Socrates". Aristotelian logic only includes predicates for simple properties of entities. But it lacks predicates corresponding to relations between entities. The predicate can be linked to

3864-416: A mental state is rational if it is based on or responsive to good reasons. Another view emphasizes the role of coherence, stating that rationality requires that the different mental states of a person are consistent and support each other. A slightly different approach holds that rationality is about achieving certain goals. Two goals of theoretical rationality are accuracy and comprehensiveness, meaning that

4025-410: A person already has, asserting that a person should only change their beliefs if they have a good reason to. One motivation for adopting epistemic conservatism is that the cognitive resources of humans are limited, meaning that it is not feasible to constantly reexamine every belief. Pragmatist epistemology is a form of fallibilism that emphasizes the close relation between knowing and acting. It sees

4186-744: A person has as few false beliefs and as many true beliefs as possible. Epistemic norms are criteria to assess the cognitive quality of beliefs, like their justification and rationality. Epistemologists distinguish between deontic norms, which are prescriptions about what people should believe or which beliefs are correct, and axiological norms, which identify the goals and values of beliefs. Epistemic norms are closely related to intellectual or epistemic virtues , which are character traits like open-mindedness and conscientiousness . Epistemic virtues help individuals form true beliefs and acquire knowledge. They contrast with epistemic vices and act as foundational concepts of virtue epistemology . Evidence for

4347-419: A person knows depends on the subjective criteria or social conventions used to assess epistemic status. The debate between empiricism and rationalism centers on the origins of human knowledge. Empiricism emphasizes that sense experience is the primary source of all knowledge. Some empiricists express this view by stating that the mind is a blank slate that only develops ideas about the external world through

4508-507: A posteriori knowledge. A priori knowledge is knowledge of non-empirical facts and does not depend on evidence from sensory experience. It belongs to fields such as mathematics and logic , like knowing that 2 + 2 = 4 {\displaystyle 2+2=4} . The contrast between a posteriori and a priori knowledge plays a central role in the debate between empiricists and rationalists on whether all knowledge depends on sensory experience. A closely related contrast

4669-664: A sentence like "yesterday was Sunday and the weather was good". It is only true if both of its input variables, p {\displaystyle p} ("yesterday was Sunday") and q {\displaystyle q} ("the weather was good"), are true. In all other cases, the expression as a whole is false. Other important logical connectives are ¬ {\displaystyle \lnot } ( not ), ∨ {\displaystyle \lor } ( or ), → {\displaystyle \to } ( if...then ), and ↑ {\displaystyle \uparrow } ( Sheffer stroke ). Given

4830-665: A set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to work". Premises and conclusions express propositions or claims that can be true or false. An important feature of propositions is their internal structure. For example, complex propositions are made up of simpler propositions linked by logical vocabulary like ∧ {\displaystyle \land } ( and ) or → {\displaystyle \to } ( if...then ). Simple propositions also have parts, like "Sunday" or "work" in

4991-412: A true or a false proposition. According to the correspondence theory of truth , to be true means to stand in the right relation to the world by accurately describing what it is like. This means that truth is objective: a belief is true if it corresponds to a fact . The coherence theory of truth says that a belief is true if it belongs to a coherent system of beliefs. A result of this view is that truth

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5152-402: Is and what types of knowledge there are. It further investigates the sources of knowledge, like perception , inference , and testimony , to determine how knowledge is created. Another topic is the extent and limits of knowledge, confronting questions about what people can and cannot know. Other central concepts include belief , truth , justification , evidence , and reason . Epistemology

5313-420: Is sound when its proof system cannot derive a conclusion from a set of premises unless it is semantically entailed by them. In other words, its proof system cannot lead to false conclusions, as defined by the semantics. A system is complete when its proof system can derive every conclusion that is semantically entailed by its premises. In other words, its proof system can lead to any true conclusion, as defined by

5474-447: Is a stub . You can help Misplaced Pages by expanding it . Epistemology Epistemology is the branch of philosophy that examines the nature, origin, and limits of knowledge . Also called theory of knowledge , it explores different types of knowledge, such as propositional knowledge about facts, practical knowledge in the form of skills, and knowledge by acquaintance as a familiarity through experience. Epistemologists study

5635-408: Is a closely related process focused not on external physical objects but on internal mental states . For example, seeing a bus at a bus station belongs to perception while feeling tired belongs to introspection. Rationalists understand reason as a source of justification for non-empirical facts. It is often used to explain how people can know about mathematical, logical, and conceptual truths. Reason

5796-409: Is a comparative term, meaning that to know something involves distinguishing it from relevant alternatives. For example, if a person spots a bird in the garden, they may know that it is a sparrow rather than an eagle but they may not know that it is a sparrow rather than an indistinguishable sparrow hologram. Epistemic conservatism is a view about belief revision . It gives preference to the beliefs

5957-476: Is a red planet". For most types of logic, it is accepted that premises and conclusions have to be truth-bearers . This means that they have a truth value : they are either true or false. Contemporary philosophy generally sees them either as propositions or as sentences . Propositions are the denotations of sentences and are usually seen as abstract objects . For example, the English sentence "the tree

6118-441: Is a restricted version of classical logic. It uses the same symbols but excludes some rules of inference. For example, according to the law of double negation elimination, if a sentence is not not true, then it is true. This means that A {\displaystyle A} follows from ¬ ¬ A {\displaystyle \lnot \lnot A} . This is a valid rule of inference in classical logic but it

6279-521: Is a special epistemic good that, unlike knowledge, is always intrinsically valuable. Wisdom is similar in this regard and is sometimes considered the highest epistemic good. It encompasses a reflective understanding with practical applications. It helps people grasp and evaluate complex situations and lead a good life. Philosophical skepticism questions the human ability to arrive at knowledge. Some skeptics limit their criticism to certain domains of knowledge. For example, religious skeptics say that it

6440-416: Is also known as symbolic logic and is widely used in mathematical logic . It uses a formal approach to study reasoning: it replaces concrete expressions with abstract symbols to examine the logical form of arguments independent of their concrete content. In this sense, it is topic-neutral since it is only concerned with the abstract structure of arguments and not with their concrete content. Formal logic

6601-439: Is also responsible for inferential knowledge, in which one or several beliefs are used as premises to support another belief. Memory depends on information provided by other sources, which it retains and recalls, like remembering a phone number perceived earlier. Justification by testimony relies on information one person communicates to another person. This can happen by talking to each other but can also occur in other forms, like

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6762-453: Is an example of the existential quantifier " ∃ {\displaystyle \exists } " applied to the individual variable " x {\displaystyle x} " . In higher-order logics, quantification is also allowed over predicates. This increases its expressive power. For example, to express the idea that Mary and John share some qualities, one could use the formula " ∃ Q ( Q ( M

6923-458: Is an oversimplification of much more complex psychological processes. Beliefs play a central role in various epistemological debates, which cover their status as a component of propositional knowledge, the question of whether people have control over and are responsible for their beliefs , and the issue of whether there are degrees of beliefs, called credences . As propositional attitudes, beliefs are true or false depending on whether they affirm

7084-495: 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 . Logic studies arguments, which consist of

7245-424: Is better because it is more stable. Another suggestion focuses on practical reasoning . It proposes that people put more trust in knowledge than in mere true beliefs when drawing conclusions and deciding what to do. A different response says that knowledge has intrinsic value, meaning that it is good in itself independent of its usefulness. Beliefs are mental states about what is the case, like believing that snow

7406-403: Is between analytic and synthetic truths . A sentence is analytically true if its truth depends only on the meaning of the words it uses. For instance, the sentence "all bachelors are unmarried" is analytically true because the word "bachelor" already includes the meaning "unmarried". A sentence is synthetically true if its truth depends on additional facts. For example, the sentence "snow is white"

7567-415: Is blurry in some cases, such as when the premises offer weak but non-negligible support. This contrasts with deductive arguments, which are either valid or invalid with nothing in-between. The terminology used to categorize ampliative arguments is inconsistent. Some authors, like James Hawthorne, use the term " induction " to cover all forms of non-deductive arguments. But in a more narrow sense, induction

7728-421: Is commonly defined in terms of arguments or inferences as the study of their correctness. An argument is a set of premises together with a conclusion. An inference is the process of reasoning from these premises to the conclusion. But these terms are often used interchangeably in logic. Arguments are correct or incorrect depending on whether their premises support their conclusion. Premises and conclusions, on

7889-407: Is controversial because it belongs to the field of psychology , not logic, and because appearances may be different for different people. Fallacies are usually divided into formal and informal fallacies. For formal fallacies, the source of the error is found in the form of the argument. For example, denying the antecedent is one type of formal fallacy, as in "if Othello is a bachelor, then he

8050-439: Is correct. Some philosophers, such as Timothy Williamson , reject the basic assumption underlying the analysis of knowledge by arguing that propositional knowledge is a unique state that cannot be dissected into simpler components. The value of knowledge is the worth it holds by expanding understanding and guiding action. Knowledge can have instrumental value by helping a person achieve their goals. For example, knowledge of

8211-453: Is deductively valid. For deductive validity, it does not matter whether the premises or the conclusion are actually true. So the argument "(1) all frogs are mammals; (2) no cats are mammals; (3) therefore no cats are frogs" is also valid because the conclusion follows necessarily from the premises. According to an influential view by Alfred Tarski , deductive arguments have three essential features: (1) they are formal, i.e. they depend only on

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8372-610: Is green" is different from the German sentence "der Baum ist grün" but both express the same proposition. Propositional theories of premises and conclusions are often criticized because they rely on abstract objects. For instance, philosophical naturalists usually reject the existence of abstract objects. Other arguments concern the challenges involved in specifying the identity criteria of propositions. These objections are avoided by seeing premises and conclusions not as propositions but as sentences, i.e. as concrete linguistic objects like

8533-416: Is important for explaining the nature of illusions. Constructivism in epistemology is the theory that how people view the world is not a simple reflection of external reality but an invention or a social construction. This view emphasizes the creative role of interpretation while undermining objectivity since social constructions may differ from society to society. According to contrastivism , knowledge

8694-460: Is impossible to have certain knowledge about the existence of deities or other religious doctrines. Similarly, moral skeptics challenge the existence of moral knowledge and metaphysical skeptics say that humans cannot know ultimate reality. Global skepticism is the widest form of skepticism, asserting that there is no knowledge in any domain. In ancient philosophy , this view was accepted by academic skeptics while Pyrrhonian skeptics recommended

8855-432: Is interested in deductively valid arguments, for which the truth of their premises ensures the truth of their conclusion. This means that it is impossible for the premises to be true and the conclusion to be false. For valid arguments, the logical structure of the premises and the conclusion follows a pattern called a rule of inference . For example, modus ponens is a rule of inference according to which all arguments of

9016-415: Is invalid in intuitionistic logic. Another classical principle not part of intuitionistic logic is the law of excluded middle . It states that for every sentence, either it or its negation is true. This means that every proposition of the form A ∨ ¬ A {\displaystyle A\lor \lnot A} is true. These deviations from classical logic are based on the idea that truth

9177-443: Is itself a knowledge claim. Another objection says that the abstract reasoning leading to skepticism is not convincing enough to overrule common sense. Fallibilism is another response to skepticism. Fallibilists agree with skeptics that absolute certainty is impossible. Most fallibilists disagree with skeptics about the existence of knowledge, saying that there is knowledge since it does not require absolute certainty. They emphasize

9338-447: Is male; Othello is not a bachelor; therefore Othello is not male". But most fallacies fall into the category of informal fallacies, of which a great variety is discussed in the academic literature. The source of their error is usually found in the content or the context of the argument. Informal fallacies are sometimes categorized as fallacies of ambiguity, fallacies of presumption, or fallacies of relevance. For fallacies of ambiguity,

9499-688: Is necessary, then it is also possible. This means that ◊ A {\displaystyle \Diamond A} follows from ◻ A {\displaystyle \Box A} . Another principle states that if a proposition is necessary then its negation is impossible and vice versa. This means that ◻ A {\displaystyle \Box A} is equivalent to ¬ ◊ ¬ A {\displaystyle \lnot \Diamond \lnot A} . Other forms of modal logic introduce similar symbols but associate different meanings with them to apply modal logic to other fields. For example, deontic logic concerns

9660-518: Is necessary. For example, if the formula B ( s ) {\displaystyle B(s)} stands for the sentence "Socrates is a banker" then the formula ◊ B ( s ) {\displaystyle \Diamond B(s)} articulates the sentence "It is possible that Socrates is a banker". To include these symbols in the logical formalism, modal logic introduces new rules of inference that govern what role they play in inferences. One rule of inference states that, if something

9821-469: Is no universal agreement to what extent they all provide valid justification. Perception relies on sensory organs to gain empirical information. There are various forms of perception corresponding to different physical stimuli, such as visual , auditory , haptic , olfactory , and gustatory perception. Perception is not merely the reception of sense impressions but an active process that selects, organizes, and interprets sensory signals . Introspection

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9982-407: Is not the best or most likely explanation. Not all arguments live up to the standards of correct reasoning. When they do not, they are usually referred to as fallacies . Their central aspect is not that their conclusion is false but that there is some flaw with the reasoning leading to this conclusion. So the argument "it is sunny today; therefore spiders have eight legs" is fallacious even though

10143-497: Is one of the main branches of philosophy besides fields like ethics , logic , and metaphysics . The term is also used in a slightly different sense to refer not to the branch of philosophy but to a particular position within that branch, as in Plato 's epistemology and Immanuel Kant 's epistemology. As a normative field of inquiry, epistemology explores how people should acquire beliefs. This way, it determines which beliefs fulfill

10304-541: Is only one type of ampliative argument alongside abductive arguments . Some philosophers, like Leo Groarke, also allow conductive arguments as another type. In this narrow sense, induction is often defined as a form of statistical generalization. In this case, the premises of an inductive argument are many individual observations that all show a certain pattern. The conclusion then is a general law that this pattern always obtains. In this sense, one may infer that "all elephants are gray" based on one's past observations of

10465-408: Is relative since it depends on other beliefs. Further theories of truth include pragmatist , semantic , pluralist , and deflationary theories . Truth plays a central role in epistemology as a goal of cognitive processes and a component of propositional knowledge. In epistemology, justification is a property of beliefs that fulfill certain norms about what a person should believe. According to

10626-407: Is relevant to many descriptive and normative disciplines, such as the other branches of philosophy and the sciences, by exploring the principles of how they may arrive at knowledge. The word epistemology comes from the ancient Greek terms ἐπιστήμη (episteme, meaning knowledge or understanding ) and λόγος (logos, meaning study of or reason ), literally, the study of knowledge. The word

10787-412: Is reliable if most of the beliefs it causes are true. A slightly different view focuses on beliefs rather than belief-formation processes, saying that a belief is justified if it is a reliable indicator of the fact it presents. This means that the belief tracks the fact: the person believes it because it is a fact but would not believe it otherwise. Virtue epistemology is another type of externalism and

10948-420: Is sometimes understood as a form of reliabilism. It says that a belief is justified if it manifests intellectual virtues. Intellectual virtues are capacities or traits that perform cognitive functions and help people form true beliefs. Suggested examples include faculties like vision, memory, and introspection. In the epistemology of perception, direct and indirect realists disagree about the connection between

11109-430: Is studied by formal logic. The study of natural language arguments comes with various difficulties. For example, natural language expressions are often ambiguous, vague, and context-dependent. Another approach defines informal logic in a wide sense as the normative study of the standards, criteria, and procedures of argumentation. In this sense, it includes questions about the role of rationality , critical thinking , and

11270-405: Is synthetically true because its truth depends on the color of snow in addition to the meanings of the words snow and white . A priori knowledge is primarily associated with analytic sentences while a posteriori knowledge is primarily associated with synthetic sentences. However, it is controversial whether this is true for all cases. Some philosophers, such as Willard Van Orman Quine , reject

11431-462: Is taken by radical skeptics , who argue that there is no knowledge at all. Epistemologists distinguish between different types of knowledge. Their primary interest is in knowledge of facts, called propositional knowledge . It is a theoretical knowledge that can be expressed in declarative sentences using a that-clause, like "Ravi knows that kangaroos hop". For this reason, it is also called knowledge-that . Epistemologists often understand it as

11592-416: Is the dream argument . It starts from the observation that, while people are dreaming, they are usually unaware of this. This inability to distinguish between dream and regular experience is used to argue that there is no certain knowledge since a person can never be sure that they are not dreaming. Some critics assert that global skepticism is a self-refuting idea because denying the existence of knowledge

11753-414: Is the case if the beliefs are consistent and support each other. According to coherentism, justification is a holistic aspect determined by the whole system of beliefs, which resembles an interconnected web. The view of foundherentism is an intermediary position combining elements of both foundationalism and coherentism. It accepts the distinction between basic and non-basic beliefs while asserting that

11914-405: Is the question of whether knowledge is more valuable than a mere opinion that is true. Knowledge and true opinion often have a similar usefulness since both are accurate representations of reality. For example, if a person wants to go to Larissa , a true opinion about how to get there may help them in the same way as knowledge does. Plato already considered this problem and suggested that knowledge

12075-410: Is the set of basic symbols used in expressions . The syntactic rules determine how these symbols may be arranged to result in well-formed formulas. For instance, the syntactic rules of propositional logic determine that " P ∧ Q {\displaystyle P\land Q} " is a well-formed formula but " ∧ Q {\displaystyle \land Q} " is not since

12236-432: Is to study the criteria according to which an argument is correct or incorrect. A fallacy is committed if these criteria are violated. In the case of formal logic, they are known as rules of inference . They are definitory rules, which determine whether an inference is correct or which inferences are allowed. Definitory rules contrast with strategic rules. Strategic rules specify which inferential moves are necessary to reach

12397-540: Is unable to address. Both provide criteria for assessing the correctness of arguments and distinguishing them from fallacies. Many characterizations of informal logic have been suggested but there is no general agreement on its precise definition. The most literal approach sees the terms "formal" and "informal" as applying to the language used to express arguments. On this view, informal logic studies arguments that are in informal or natural language. Formal logic can only examine them indirectly by translating them first into

12558-599: Is used to represent the ideas of knowing something in contrast to merely believing it to be the case. Higher-order logics extend classical logic not by using modal operators but by introducing new forms of quantification. Quantifiers correspond to terms like "all" or "some". In classical first-order logic, quantifiers are only applied to individuals. The formula " ∃ x ( A p p l e ( x ) ∧ S w e e t ( x ) ) {\displaystyle \exists x(Apple(x)\land Sweet(x))} " ( some apples are sweet)

12719-427: Is wet. According to foundationalism, basic beliefs are the foundation on which all other knowledge is built while non-basic beliefs constitute the superstructure resting on this foundation. Coherentists reject the distinction between basic and non-basic beliefs, saying that the justification of any belief depends on other beliefs. They assert that a belief must be in tune with other beliefs to amount to knowledge. This

12880-407: Is what distinguishes justified beliefs from superstition and lucky guesses. However, justification does not guarantee truth. For example, if a person has strong but misleading evidence, they may form a justified belief that is false. Epistemologists often identify justification as one component of knowledge. Usually, they are not only interested in whether a person has a sufficient reason to hold

13041-601: Is white or that God exists . In epistemology, they are often understood as subjective attitudes that affirm or deny a proposition , which can be expressed in a declarative sentence . For instance, to believe that snow is white is to affirm the proposition "snow is white". According to this view, beliefs are representations of what the world is like. They are kept in memory and can be retrieved when actively thinking about reality or when deciding how to act. A different view understands beliefs as behavioral patterns or dispositions to act rather than as representational items stored in

13202-431: Is why first-order logic is still more commonly used. Deviant logics are logical systems that reject some of the basic intuitions of classical logic. Because of this, they are usually seen not as its supplements but as its rivals. Deviant logical systems differ from each other either because they reject different classical intuitions or because they propose different alternatives to the same issue. Intuitionistic logic

13363-543: The knowledge base of an expert system . Knowledge contrasts with ignorance , which is often simply defined as the absence of knowledge. Knowledge is usually accompanied by ignorance since people rarely have complete knowledge of a field, forcing them to rely on incomplete or uncertain information when making decisions. Even though many forms of ignorance can be mitigated through education and research, there are certain limits to human understanding that are responsible for inevitable ignorance. Some limitations are inherent in

13524-436: The suspension of belief to achieve a state of tranquility . Overall, not many epistemologists have explicitly defended global skepticism. The influence of this position derives mainly from attempts by other philosophers to show that their theory overcomes the challenge of skepticism. For example, René Descartes used methodological doubt to find facts that cannot be doubted. One consideration in favor of global skepticism

13685-547: The 20th century ( La Critique du discours , Éditions de Minuit, 1975), while Michel Foucault considered it, in The Order of Things , one of the bases of the classical épistémè . Among the contributions of the Port-Royal Logic is the popularization of the distinction between comprehension and extension , which would later become a more refined distinction between intension and extension . Roughly speaking:

13846-469: The Greek word "logos", which has a variety of translations, such as reason , discourse , or language . Logic is traditionally defined as the study of the laws of thought or correct reasoning , and is usually understood in terms of inferences or arguments . Reasoning is the activity of drawing inferences. Arguments are the outward expression of inferences. An argument is a set of premises together with

14007-418: The ambiguity and vagueness of natural language are responsible for their flaw, as in "feathers are light; what is light cannot be dark; therefore feathers cannot be dark". Fallacies of presumption have a wrong or unjustified premise but may be valid otherwise. In the case of fallacies of relevance, the premises do not support the conclusion because they are not relevant to it. The main focus of most logicians

14168-399: The assessment of arguments. Premises and conclusions are the basic parts of inferences or arguments and therefore play a central role in logic. In the case of a valid inference or a correct argument, the conclusion follows from the premises, or in other words, the premises support the conclusion. For instance, the premises "Mars is red" and "Mars is a planet" support the conclusion "Mars

14329-495: The basic principles of classical logic. They introduce additional symbols and principles to apply it to fields like metaphysics , ethics , and epistemology . Modal logic is an extension of classical logic. In its original form, sometimes called "alethic modal logic", it introduces two new symbols: ◊ {\displaystyle \Diamond } expresses that something is possible while ◻ {\displaystyle \Box } expresses that something

14490-419: The belief following it and is supported by the belief preceding it. The disagreement between internalism and externalism is about the sources of justification. Internalists say that justification depends only on factors within the individual. Examples of such factors include perceptual experience, memories, and the possession of other beliefs. This view emphasizes the importance of the cognitive perspective of

14651-430: The belief in the right way. Another theory states that the belief is the product of a reliable belief formation process. Further approaches require that the person would not have the belief if it was false, that the belief is not inferred from a falsehood, that the justification cannot be undermined , or that the belief is infallible. There is no consensus on which of the proposed modifications and reconceptualizations

14812-487: The best explanation, for example, when a doctor concludes that a patient has a certain disease which explains the symptoms they suffer. Arguments that fall short of the standards of correct reasoning often embody fallacies . Systems of logic are theoretical frameworks for assessing the correctness of arguments. Logic has been studied since antiquity . Early approaches include Aristotelian logic , Stoic logic , Nyaya , and Mohism . Aristotelian logic focuses on reasoning in

14973-522: The circumstances under which they observed the cup. Evidentialism is an influential internalist view. It says that justification depends on the possession of evidence . In this context, evidence for a belief is any information in the individual's mind that supports the belief. For example, the perceptual experience of rain is evidence for the belief that it is raining. Evidentialists have suggested various other forms of evidence, including memories, intuitions, and other beliefs. According to evidentialism,

15134-645: The claim "either it is raining, or it is not". These two definitions of formal logic are not identical, but they are closely related. For example, if the inference from p to q is deductively valid then the claim "if p then q " is a logical truth. Formal logic uses formal languages to express and analyze arguments. They normally have a very limited vocabulary and exact syntactic rules . These rules specify how their symbols can be combined to construct sentences, so-called well-formed formulas . This simplicity and exactness of formal logic make it capable of formulating precise rules of inference. They determine whether

15295-495: The color of elephants. A closely related form of inductive inference has as its conclusion not a general law but one more specific instance, as when it is inferred that an elephant one has not seen yet is also gray. Some theorists, like Igor Douven, stipulate that inductive inferences rest only on statistical considerations. This way, they can be distinguished from abductive inference. Abductive inference may or may not take statistical observations into consideration. In either case,

15456-525: The communal aspect of knowledge and historical epistemology examines its historical conditions. Epistemology is closely related to psychology , which describes the beliefs people hold, while epistemology studies the norms governing the evaluation of beliefs. It also intersects with fields such as decision theory , education , and anthropology . Early reflections on the nature, sources, and scope of knowledge are found in ancient Greek , Indian , and Chinese philosophy . The relation between reason and faith

15617-548: The concepts of belief , truth , and justification to understand the nature of knowledge. To discover how knowledge arises, they investigate sources of justification, such as perception , introspection , memory , reason , and testimony . The school of skepticism questions the human ability to attain knowledge while fallibilism says that knowledge is never certain. Empiricists hold that all knowledge comes from sense experience, whereas rationalists believe that some knowledge does not depend on it. Coherentists argue that

15778-511: The conclusion "all ravens are black". A further approach is to define informal logic as the study of informal fallacies . Informal fallacies are incorrect arguments in which errors are present in the content and the context of the argument. A false dilemma , for example, involves an error of content by excluding viable options. This is the case in the fallacy "you are either with us or against us; you are not with us; therefore, you are against us". Some theorists state that formal logic studies

15939-458: The conclusion is true. Some theorists, like John Stuart Mill , give a more restrictive definition of fallacies by additionally requiring that they appear to be correct. This way, genuine fallacies can be distinguished from mere mistakes of reasoning due to carelessness. This explains why people tend to commit fallacies: because they have an alluring element that seduces people into committing and accepting them. However, this reference to appearances

16100-591: The conditional proposition p → q {\displaystyle p\to q} , one can form truth tables of its converse q → p {\displaystyle q\to p} , its inverse ( ¬ p → ¬ q {\displaystyle \lnot p\to \lnot q} ) , and its contrapositive ( ¬ q → ¬ p {\displaystyle \lnot q\to \lnot p} ) . Truth tables can also be defined for more complex expressions that use several propositional connectives. Logic

16261-438: The contrast between necessity and possibility and the problem of ethical obligation and permission. Similarly, it does not address the relations between past, present, and future. Such issues are addressed by extended logics. They build on the basic intuitions of classical logic and expand it by introducing new logical vocabulary. This way, the exact logical approach is applied to fields like ethics or epistemology that lie beyond

16422-451: The depth level. But they can be highly informative on the surface level by making implicit information explicit. This happens, for example, in mathematical proofs. Ampliative arguments are arguments whose conclusions contain additional information not found in their premises. In this regard, they are more interesting since they contain information on the depth level and the thinker may learn something genuinely new. But this feature comes with

16583-405: The distinction, saying that there are no analytic truths. The analysis of knowledge is the attempt to identify the essential components or conditions of all and only propositional knowledge states. According to the so-called traditional analysis , knowledge has three components: it is a belief that is justified and true. In the second half of the 20th century, this view was put into doubt by

16744-409: The example. The truth of a proposition usually depends on the meanings of all of its parts. However, this is not the case for logically true propositions. They are true only because of their logical structure independent of the specific meanings of the individual parts. Arguments can be either correct or incorrect. An argument is correct if its premises support its conclusion. Deductive arguments have

16905-434: The field of ethics and introduces symbols to express the ideas of obligation and permission , i.e. to describe whether an agent has to perform a certain action or is allowed to perform it. The modal operators in temporal modal logic articulate temporal relations. They can be used to express, for example, that something happened at one time or that something is happening all the time. In epistemology, epistemic modal logic

17066-485: The form "(1) p , (2) if p then q , (3) therefore q " are valid, independent of what the terms p and q stand for. In this sense, formal logic can be defined as the science of valid inferences. An alternative definition sees logic as the study of logical truths . A proposition is logically true if its truth depends only on the logical vocabulary used in it. This means that it is true in all possible worlds and under all interpretations of its non-logical terms, like

17227-411: The form of knowledge-how and knowledge by acquaintance . Knowledge-how is a practical ability or skill, like knowing how to read or how to prepare lasagna . It is usually tied to a specific goal and not mastered in the abstract without concrete practice. To know something by acquaintance means to be familiar with it as a result of experiental contact. Examples are knowing the city of Perth , knowing

17388-513: The form of syllogisms . It was considered the main system of logic in the Western world until it was replaced by modern formal logic, which has its roots in the work of late 19th-century mathematicians such as Gottlob Frege . Today, the most commonly used system is classical logic . It consists of propositional logic and first-order logic . Propositional logic only considers logical relations between full propositions. First-order logic also takes

17549-523: The form of the premises and the conclusion: how they have to be structured for the inference to be valid. Arguments that do not follow any rule of inference are deductively invalid. The modus ponens is a prominent rule of inference. It has the form " p ; if p , then q ; therefore q ". Knowing that it has just rained ( p {\displaystyle p} ) and that after rain the streets are wet ( p → q {\displaystyle p\to q} ), one can use modus ponens to deduce that

17710-419: The form of the premises and the conclusion; (2) they are a priori, i.e. no sense experience is needed to determine whether they obtain; (3) they are modal, i.e. that they hold by logical necessity for the given propositions, independent of any other circumstances. Because of the first feature, the focus on formality, deductive inference is usually identified with rules of inference. Rules of inference specify

17871-421: The general form of arguments while informal logic studies particular instances of arguments. Another approach is to hold that formal logic only considers the role of logical constants for correct inferences while informal logic also takes the meaning of substantive concepts into account. Further approaches focus on the discussion of logical topics with or without formal devices and on the role of epistemology for

18032-427: The human cognitive faculties themselves, such as the inability to know facts too complex for the human mind to conceive. Others depend on external circumstances when no access to the relevant information exists. Epistemologists disagree on how much people know, for example, whether fallible beliefs about everyday affairs can amount to knowledge or whether absolute certainty is required. The most stringent position

18193-417: The individual in the form of their mental states. It is commonly associated with the idea that the relevant factors are accessible, meaning that the individual can become aware of their reasons for holding a justified belief through introspection and reflection. Externalism rejects this view, saying that at least some relevant factors are external to the individual. This means that the cognitive perspective of

18354-405: The individual is less central while other factors, specifically the relation to truth, become more important. For instance, when considering the belief that a cup of coffee stands on the table, externalists are not only interested in the perceptual experience that led to this belief but also consider the quality of the person's eyesight, their ability to differentiate coffee from other beverages, and

18515-406: The internal parts of propositions into account, like predicates and quantifiers . Extended logics accept the basic intuitions behind classical logic and apply it to other fields, such as metaphysics , ethics , and epistemology . Deviant logics, on the other hand, reject certain classical intuitions and provide alternative explanations of the basic laws of logic. The word "logic" originates from

18676-407: The internal structure of propositions. This happens through devices such as singular terms, which refer to particular objects, predicates , which refer to properties and relations, and quantifiers, which treat notions like "some" and "all". For example, to express the proposition "this raven is black", one may use the predicate B {\displaystyle B} for the property "black" and

18837-405: The justification of non-basic beliefs depends on coherence with other beliefs. Infinitism presents another approach to the structure of knowledge. It agrees with coherentism that there are no basic beliefs while rejecting the view that beliefs can support each other in a circular manner . Instead, it argues that beliefs form infinite justification chains, in which each link of the chain supports

18998-522: The logical conjunction ∧ {\displaystyle \land } requires terms on both sides. A proof system is a collection of rules to construct formal proofs. It is a tool to arrive at conclusions from a set of axioms. Rules in a proof system are defined in terms of the syntactic form of formulas independent of their specific content. For instance, the classical rule of conjunction introduction states that P ∧ Q {\displaystyle P\land Q} follows from

19159-440: The main topic in epistemology, some theorists focus on understanding rather than knowledge. Understanding is a more holistic notion that involves a wider grasp of a subject. To understand something, a person requires awareness of how different things are connected and why they are the way they are. For example, knowledge of isolated facts memorized from a textbook does not amount to understanding. According to one view, understanding

19320-457: The mind possesses inborn ideas which it can access without the help of the senses. Others hold that there is an additional cognitive faculty, sometimes called rational intuition , through which people acquire nonempirical knowledge. Some rationalists limit their discussion to the origin of concepts, saying that the mind relies on inborn categories to understand the world and organize experience. Foundationalists and coherentists disagree about

19481-409: The mind. This view says that to believe that there is mineral water in the fridge is nothing more than a group of dispositions related to mineral water and the fridge. Examples are the dispositions to answer questions about the presence of mineral water affirmatively and to go to the fridge when thirsty. Some theorists deny the existence of beliefs, saying that this concept borrowed from folk psychology

19642-417: The need to keep an open and inquisitive mind since doubt can never be fully excluded, even for well-established knowledge claims like thoroughly tested scientific theories. Epistemic relativism is a related view. It does not question the existence of knowledge in general but rejects the idea that there are universal epistemic standards or absolute principles that apply equally to everyone. This means that what

19803-409: The other hand, are true or false depending on whether they are in accord with reality. In formal logic, a sound argument is an argument that is both correct and has only true premises. Sometimes a distinction is made between simple and complex arguments. A complex argument is made up of a chain of simple arguments. This means that the conclusion of one argument acts as a premise of later arguments. For

19964-444: The other hand, do not have propositional parts. But they can also be conceived as having an internal structure: they are made up of subpropositional parts, like singular terms and predicates . For example, the simple proposition "Mars is red" can be formed by applying the predicate "red" to the singular term "Mars". In contrast, the complex proposition "Mars is red and Venus is white" is made up of two simple propositions connected by

20125-453: The perceiver and the perceived object. Direct realists say that this connection is direct, meaning that there is no difference between the object present in perceptual experience and the physical object causing this experience. According to indirect realism, the connection is indirect since there are mental entities, like ideas or sense data, that mediate between the perceiver and the external world. The contrast between direct and indirect realism

20286-485: The premises P {\displaystyle P} and Q {\displaystyle Q} . Such rules can be applied sequentially, giving a mechanical procedure for generating conclusions from premises. There are different types of proof systems including natural deduction and sequent calculi . A semantics is a system for mapping expressions of a formal language to their denotations. In many systems of logic, denotations are truth values. For instance,

20447-413: The premises offer support for the conclusion because the conclusion is the best explanation of why the premises are true. In this sense, abduction is also called the inference to the best explanation . For example, given the premise that there is a plate with breadcrumbs in the kitchen in the early morning, one may infer the conclusion that one's house-mate had a midnight snack and was too tired to clean

20608-470: The premises. But this point is not always accepted since it would mean, for example, that most of mathematics is uninformative. A different characterization distinguishes between surface and depth information. The surface information of a sentence is the information it presents explicitly. Depth information is the totality of the information contained in the sentence, both explicitly and implicitly. According to this view, deductive inferences are uninformative on

20769-485: The propositional connective "and". Whether a proposition is true depends, at least in part, on its constituents. For complex propositions formed using truth-functional propositional connectives, their truth only depends on the truth values of their parts. But this relation is more complicated in the case of simple propositions and their subpropositional parts. These subpropositional parts have meanings of their own, like referring to objects or classes of objects. Whether

20930-406: The propositions are formed. For example, the syllogism "all men are mortal; Socrates is a man; therefore Socrates is mortal" is valid. The syllogism "all cats are mortal; Socrates is mortal; therefore Socrates is a cat", on the other hand, is invalid. Classical logic is distinct from traditional or Aristotelian logic. It encompasses propositional logic and first-order logic. It is "classical" in

21091-417: The psychology of argumentation. Another characterization identifies informal logic with the study of non-deductive arguments. In this way, it contrasts with deductive reasoning examined by formal logic. Non-deductive arguments make their conclusion probable but do not ensure that it is true. An example is the inductive argument from the empirical observation that "all ravens I have seen so far are black" to

21252-459: The pursuit of knowledge as an ongoing process guided by common sense and experience while always open to revision. 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

21413-436: The rules of inference they accept as valid and the formal languages used to express them. Starting in the late 19th century, many new formal systems have been proposed. There are disagreements about what makes a formal system a logic. For example, it has been suggested that only logically complete systems, like first-order logic , qualify as logics. For such reasons, some theorists deny that higher-order logics are logics in

21574-492: The scope of mathematics. Propositional logic comprises formal systems in which formulae are built from atomic propositions using logical connectives . For instance, propositional logic represents the conjunction of two atomic propositions P {\displaystyle P} and Q {\displaystyle Q} as the complex formula P ∧ Q {\displaystyle P\land Q} . Unlike predicate logic where terms and predicates are

21735-418: The semantics for classical propositional logic assigns the formula P ∧ Q {\displaystyle P\land Q} the denotation "true" whenever P {\displaystyle P} and Q {\displaystyle Q} are true. From the semantic point of view, a premise entails a conclusion if the conclusion is true whenever the premise is true. A system of logic

21896-604: The semantics. Thus, soundness and completeness together describe a system whose notions of validity and entailment line up perfectly. Systems of logic are theoretical frameworks for assessing the correctness of reasoning and arguments. For over two thousand years, Aristotelian logic was treated as the canon of logic in the Western world, but modern developments in this field have led to a vast proliferation of logical systems. One prominent categorization divides modern formal logical systems into classical logic , extended logics, and deviant logics . Aristotelian logic encompasses

22057-644: The sense data it receives from the sensory organs. According to them, the mind can arrive at various additional insights by comparing impressions, combining them, generalizing to arrive at more abstract ideas, and deducing new conclusions from them. Empiricists say that all these mental operations depend on material from the senses and do not function on their own. Even though rationalists usually accept sense experience as one source of knowledge, they also say that important forms of knowledge come directly from reason without sense experience, like knowledge of mathematical and logical truths. According to some rationalists,

22218-518: The sense that it is based on basic logical intuitions shared by most logicians. These intuitions include the law of excluded middle , the double negation elimination , the principle of explosion , and the bivalence of truth. It was originally developed to analyze mathematical arguments and was only later applied to other fields as well. Because of this focus on mathematics, it does not include logical vocabulary relevant to many other topics of philosophical importance. Examples of concepts it overlooks are

22379-404: The simple proposition "Mars is red", are true or false. In such cases, the truth is called a logical truth: a proposition is logically true if its truth depends only on the logical vocabulary used in it. This means that it is true under all interpretations of its non-logical terms. In some modal logics , this means that the proposition is true in all possible worlds. Some theorists define logic as

22540-415: The simple proposition they form is true depends on their relation to reality, i.e. what the objects they refer to are like. This topic is studied by theories of reference . Some complex propositions are true independently of the substantive meanings of their parts. In classical logic, for example, the complex proposition "either Mars is red or Mars is not red" is true independent of whether its parts, like

22701-870: The singular term r {\displaystyle r} referring to the raven to form the expression B ( r ) {\displaystyle B(r)} . To express that some objects are black, the existential quantifier ∃ {\displaystyle \exists } is combined with the variable x {\displaystyle x} to form the proposition ∃ x B ( x ) {\displaystyle \exists xB(x)} . First-order logic contains various rules of inference that determine how expressions articulated this way can form valid arguments, for example, that one may infer ∃ x B ( x ) {\displaystyle \exists xB(x)} from B ( r ) {\displaystyle B(r)} . Extended logics are logical systems that accept

22862-474: The smallest units, propositional logic takes full propositions with truth values as its most basic component. Thus, propositional logics can only represent logical relationships that arise from the way complex propositions are built from simpler ones. But it cannot represent inferences that result from the inner structure of a proposition. First-order logic includes the same propositional connectives as propositional logic but differs from it because it articulates

23023-411: The standards or epistemic goals of knowledge and which ones fail, thereby providing an evaluation of beliefs. Descriptive fields of inquiry, like psychology and cognitive sociology , are also interested in beliefs and related cognitive processes. Unlike epistemology, they study the beliefs people have and how people acquire them instead of examining the evaluative norms of these processes. Epistemology

23184-418: The streets are wet ( q {\displaystyle q} ). The third feature can be expressed by stating that deductively valid inferences are truth-preserving: it is impossible for the premises to be true and the conclusion to be false. Because of this feature, it is often asserted that deductive inferences are uninformative since the conclusion cannot arrive at new information not already present in

23345-437: The strict sense. When understood in a wide sense, logic encompasses both formal and informal logic. Informal logic uses non-formal criteria and standards to analyze and assess the correctness of arguments. Its main focus is on everyday discourse. Its development was prompted by difficulties in applying the insights of formal logic to natural language arguments. In this regard, it considers problems that formal logic on its own

23506-550: The strongest form of support: if their premises are true then their conclusion must also be true. This is not the case for ampliative arguments, which arrive at genuinely new information not found in the premises. Many arguments in everyday discourse and the sciences are ampliative arguments. They are divided into inductive and abductive arguments. Inductive arguments are statistical generalizations, such as inferring that all ravens are black based on many individual observations of black ravens. Abductive arguments are inferences to

23667-407: The structure of knowledge. Foundationalism distinguishes between basic and non-basic beliefs. A belief is basic if it is justified directly, meaning that its validity does not depend on the support of other beliefs. A belief is non-basic if it is justified by another belief. For example, the belief that it rained last night is a non-basic belief if it is inferred from the observation that the street

23828-438: The study of logical truths. Truth tables can be used to show how logical connectives work or how the truth values of complex propositions depends on their parts. They have a column for each input variable. Each row corresponds to one possible combination of the truth values these variables can take; for truth tables presented in the English literature, the symbols "T" and "F" or "1" and "0" are commonly used as abbreviations for

23989-700: The subject in two ways: either by affirming it or by denying it. For example, the proposition "Socrates is not a cat" involves the denial of the predicate "cat" to the subject "Socrates". Using combinations of subjects and predicates, a great variety of propositions and syllogisms can be formed. Syllogisms are characterized by the fact that the premises are linked to each other and to the conclusion by sharing one predicate in each case. Thus, these three propositions contain three predicates, referred to as major term , minor term , and middle term . The central aspect of Aristotelian logic involves classifying all possible syllogisms into valid and invalid arguments according to how

24150-417: The subject to the predicate. For example, the proposition "Socrates is wise" is made up of the subject "Socrates", the predicate "wise", and the copula "is". The subject and the predicate are the terms of the proposition. Aristotelian logic does not contain complex propositions made up of simple propositions. It differs in this aspect from propositional logic, in which any two propositions can be linked using

24311-423: The symbols displayed on a page of a book. But this approach comes with new problems of its own: sentences are often context-dependent and ambiguous, meaning an argument's validity would not only depend on its parts but also on its context and on how it is interpreted. Another approach is to understand premises and conclusions in psychological terms as thoughts or judgments. This position is known as psychologism . It

24472-409: The table. This conclusion is justified because it is the best explanation of the current state of the kitchen. For abduction, it is not sufficient that the conclusion explains the premises. For example, the conclusion that a burglar broke into the house last night, got hungry on the job, and had a midnight snack, would also explain the state of the kitchen. But this conclusion is not justified because it

24633-421: The taste of tsampa , and knowing Marta Vieira da Silva personally. Another influential distinction is between a posteriori and a priori knowledge. A posteriori knowledge is knowledge of empirical facts based on sensory experience, like seeing that the sun is shining and smelling that a piece of meat has gone bad. Knowledge belonging to the empirical science and knowledge of everyday affairs belongs to

24794-399: The term ampliative or inductive reasoning is used. Deductive arguments are associated with formal logic in contrast to the relation between ampliative arguments and informal logic. A deductively valid argument is one whose premises guarantee the truth of its conclusion. For instance, the argument "(1) all frogs are amphibians; (2) no cats are amphibians; (3) therefore no cats are frogs"

24955-479: The truth values "true" and "false". The first columns present all the possible truth-value combinations for the input variables. Entries in the other columns present the truth values of the corresponding expressions as determined by the input values. For example, the expression " p ∧ q {\displaystyle p\land q} " uses the logical connective ∧ {\displaystyle \land } ( and ). It could be used to express

25116-409: The truth. More specifically, this and similar counterexamples involve some form of epistemic luck, that is, a cognitive success that results from fortuitous circumstances rather than competence. Following these thought experiments , philosophers proposed various alternative definitions of knowledge by modifying or expanding the traditional analysis. According to one view, the known fact has to cause

25277-400: The validity or truth of a proposition. Certainty, by contrast, is a strong affirmative conviction, meaning that the person is free of doubt that the proposition is true. In epistemology, doubt and certainty play central roles in attempts to find a secure foundation of all knowledge and in skeptical projects aiming to establish that no belief is immune to doubt. While propositional knowledge is

25438-405: The world. While this core sense is of particular interest to epistemologists, the term also has other meanings. Understood on a social level, knowledge is a characteristic of a group of people that share ideas, understanding, or culture in general. The term can also refer to information stored in documents, such as "knowledge housed in the library" or knowledge stored in computers in the form of

25599-434: Was a central topic in the medieval period . The modern era was characterized by the contrasting perspectives of empiricism and rationalism. Epistemologists in the 20th century examined the components, structure, and value of knowledge while integrating insights from the natural sciences and linguistics . Epistemology is the philosophical study of knowledge . Also called theory of knowledge , it examines what knowledge

25760-405: Was discussed at length around the turn of the 20th century but it is not widely accepted today. Premises and conclusions have an internal structure. As propositions or sentences, they can be either simple or complex. A complex proposition has other propositions as its constituents, which are linked to each other through propositional connectives like "and" or "if...then". Simple propositions, on

25921-454: Was only coined in the 19th century to label this field and conceive it as a distinct branch of philosophy. Knowledge is an awareness, familiarity, understanding, or skill. Its various forms all involve a cognitive success through which a person establishes epistemic contact with reality. Knowledge is typically understood as an aspect of individuals, generally as a cognitive mental state that helps them understand, interpret, and interact with

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