181-526: Philosophy ('love of wisdom' in Ancient Greek ) is a systematic study of general and fundamental questions concerning topics like existence , reason , knowledge , value , mind , and language . It is a rational and critical inquiry that reflects on its own methods and assumptions. Historically, many of the individual sciences , such as physics and psychology , formed part of philosophy. However, they are considered separate academic disciplines in
362-501: 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
543-423: A linguistic therapy. According to Ludwig Wittgenstein , for instance, philosophy aims at dispelling misunderstandings to which humans are susceptible due to the confusing structure of ordinary language . Phenomenologists , such as Edmund Husserl , characterize philosophy as a "rigorous science" investigating essences . They practice a radical suspension of theoretical assumptions about reality to get back to
724-543: A pitch accent . In Modern Greek, all vowels and consonants are short. Many vowels and diphthongs once pronounced distinctly are pronounced as /i/ ( iotacism ). Some of the stops and glides in diphthongs have become fricatives , and the pitch accent has changed to a stress accent . Many of the changes took place in the Koine Greek period. The writing system of Modern Greek, however, does not reflect all pronunciation changes. The examples below represent Attic Greek in
905-505: 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 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
1086-445: 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
1267-480: 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
1448-573: 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,
1629-425: 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
1810-542: A doctor diagnoses a disease based on the observed symptoms. Logic also investigates incorrect forms of reasoning. They are called fallacies and are divided into formal and informal fallacies based on whether the source of the error lies only in the form of the argument or also in its content and context. Metaphysics is the study of the most general features of reality , such as existence, objects and their properties , wholes and their parts , space and time , events , and causation . There are disagreements about
1991-525: A fifth major dialect group, or it is Mycenaean Greek overlaid by Doric, with a non-Greek native influence. Regarding the speech of the ancient Macedonians diverse theories have been put forward, but the epigraphic activity and the archaeological discoveries in the Greek region of Macedonia during the last decades has brought to light documents, among which the first texts written in Macedonian , such as
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#17327657345732172-510: 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
2353-686: 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)} "
2534-415: 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
2715-551: 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
2896-444: A great variety of methods to arrive at philosophical knowledge. They include conceptual analysis , reliance on common sense and intuitions , use of thought experiments , analysis of ordinary language , description of experience , and critical questioning . Philosophy is related to many other fields, including the sciences, mathematics , business , law , and journalism . It provides an interdisciplinary perspective and studies
3077-402: 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
3258-614: 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
3439-699: A metaphysical foundation of ethics. The modern period in Chinese philosophy began in the early 20th century and was shaped by the influence of and reactions to Western philosophy. The emergence of Chinese Marxism —which focused on class struggle , socialism , and communism —resulted in a significant transformation of the political landscape. Another development was the emergence of New Confucianism , which aims to modernize and rethink Confucian teachings to explore their compatibility with democratic ideals and modern science. Traditional Japanese philosophy assimilated and synthesized ideas from different traditions, including
3620-458: A part of intellectual history , but it also investigates questions not covered by intellectual history such as whether the theories of past philosophers are true and have remained philosophically relevant. The history of philosophy is primarily concerned with theories based on rational inquiry and argumentation; some historians understand it in a looser sense that includes myths , religious teachings , and proverbial lore. Influential traditions in
3801-550: A prefix /e-/, called the augment . This was probably originally a separate word, meaning something like "then", added because tenses in PIE had primarily aspectual meaning. The augment is added to the indicative of the aorist, imperfect, and pluperfect, but not to any of the other forms of the aorist (no other forms of the imperfect and pluperfect exist). The two kinds of augment in Greek are syllabic and quantitative. The syllabic augment
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#17327657345733982-664: 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
4163-542: A strong Northwest Greek influence, and can in some respects be considered a transitional dialect, as exemplified in the poems of the Boeotian poet Pindar who wrote in Doric with a small Aeolic admixture. Thessalian likewise had come under Northwest Greek influence, though to a lesser degree. Pamphylian Greek , spoken in a small area on the southwestern coast of Anatolia and little preserved in inscriptions, may be either
4344-611: A variety of arguments. Deductive arguments are mainly studied by formal logic. An argument is deductively valid if the truth of its premises ensures the truth of its conclusion. Deductively valid arguments follow a rule of inference , like modus ponens , which has the following logical form : " p ; if p then q ; therefore q ". An example is the argument "today is Sunday; if today is Sunday then I don't have to go to work today; therefore I don't have to go to work today". The premises of non-deductive arguments also support their conclusion, although this support does not guarantee that
4525-510: A vowel or /n s r/ ; final stops were lost, as in γάλα "milk", compared with γάλακτος "of milk" (genitive). Ancient Greek of the classical period also differed in both the inventory and distribution of original PIE phonemes due to numerous sound changes, notably the following: The pronunciation of Ancient Greek was very different from that of Modern Greek . Ancient Greek had long and short vowels ; many diphthongs ; double and single consonants; voiced, voiceless, and aspirated stops ; and
4706-420: 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
4887-493: Is a combination of different parts and attempts to identify what those parts are. An influential theory in this area claims that knowledge has three components: it is a belief that is justified and true . This theory is controversial and the difficulties associated with it are known as the Gettier problem . Alternative views state that knowledge requires additional components, like the absence of luck; different components, like
5068-509: Is a common issue in relation to the sources of knowledge and the justification they offer. It is based on the idea that beliefs require some kind of reason or evidence to be justified. The problem is that the source of justification may itself be in need of another source of justification. This leads to an infinite regress or circular reasoning . Foundationalists avoid this conclusion by arguing that some sources can provide justification without requiring justification themselves. Another solution
5249-476: 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
5430-441: 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
5611-559: Is a set of essential features shared by all parts of philosophy. Others see only weaker family resemblances or contend that it is merely an empty blanket term. Precise definitions are often only accepted by theorists belonging to a certain philosophical movement and are revisionistic according to Søren Overgaard et al. in that many presumed parts of philosophy would not deserve the title "philosophy" if they were true. Some definitions characterize philosophy in relation to its method, like pure reasoning. Others focus on its topic, for example, as
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5792-418: Is added to stems beginning with consonants, and simply prefixes e (stems beginning with r , however, add er ). The quantitative augment is added to stems beginning with vowels, and involves lengthening the vowel: Some verbs augment irregularly; the most common variation is e → ei . The irregularity can be explained diachronically by the loss of s between vowels, or that of the letter w , which affected
5973-464: Is also concerned with the moral evaluation of character traits and institutions. It explores what the standards of morality are and how to live a good life. Philosophical ethics addresses such basic questions as "Are moral obligations relative?"; "Which has priority: well-being or obligation?"; and "What gives life meaning?" The main branches of ethics are meta-ethics , normative ethics , and applied ethics . Meta-ethics asks abstract questions about
6154-416: 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
6335-453: 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
6516-480: Is an expression of the philosopher's love of wisdom and has the aim of improving one's well-being by leading a reflective life. For example, the Stoics saw philosophy as an exercise to train the mind and thereby achieve eudaimonia and flourish in life. As a discipline, the history of philosophy aims to provide a systematic and chronological exposition of philosophical concepts and doctrines. Some theorists see it as
6697-415: 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
6878-449: Is closely related to the disciplines of logic and linguistics. The philosophy of language rose to particular prominence in the early 20th century in analytic philosophy due to the works of Frege and Russell. One of its central topics is to understand how sentences get their meaning. There are two broad theoretical camps: those emphasizing the formal truth conditions of sentences and those investigating circumstances that determine when it
7059-421: 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
7240-405: Is concerned with meaning , understanding , or the clarification of language. According to one view, philosophy is conceptual analysis , which involves finding the necessary and sufficient conditions for the application of concepts. Another definition characterizes philosophy as thinking about thinking to emphasize its self-critical, reflective nature. A further approach presents philosophy as
7421-448: Is considered by some linguists to have been closely related to Greek . Among Indo-European branches with living descendants, Greek is often argued to have the closest genetic ties with Armenian (see also Graeco-Armenian ) and Indo-Iranian languages (see Graeco-Aryan ). Ancient Greek differs from Proto-Indo-European (PIE) and other Indo-European languages in certain ways. In phonotactics , ancient Greek words could end only in
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7602-407: 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
7783-453: 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
7964-610: 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
8145-432: 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
8326-415: 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
8507-460: Is itself a borrowing from the Latin philosophia . The term philosophy acquired the meanings of "advanced study of the speculative subjects ( logic , ethics , physics , and metaphysics )", "deep wisdom consisting of love of truth and virtuous living", "profound learning as transmitted by the ancient writers", and "the study of the fundamental nature of knowledge , reality , and existence , and
8688-447: 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,
8869-688: 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
9050-518: 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
9231-407: 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
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#17327657345739412-446: 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
9593-541: 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
9774-473: Is presented by coherentists , who state that a belief is justified if it coheres with other beliefs of the person. Many discussions in epistemology touch on the topic of philosophical skepticism , which raises doubts about some or all claims to knowledge. These doubts are often based on the idea that knowledge requires absolute certainty and that humans are unable to acquire it. Ethics, also known as moral philosophy, studies what constitutes right conduct . It
9955-417: Is sometimes understood as a proper science in its own right. According to some naturalistic philosophers , such as W. V. O. Quine , philosophy is an empirical yet abstract science that is concerned with wide-ranging empirical patterns instead of particular observations. Science-based definitions usually face the problem of explaining why philosophy in its long history has not progressed to the same extent or in
10136-430: 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
10317-461: Is suitable to use a sentence, the latter of which is associated with speech act theory . Ancient Greek Ancient Greek ( Ἑλληνῐκή , Hellēnikḗ ; [hellɛːnikɛ́ː] ) includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek ( c. 1400–1200 BC ), Dark Ages ( c. 1200–800 BC ),
10498-437: Is that actions are in tune with those duties and not what consequences they have. Virtue theorists judge actions based on how the moral character of the agent is expressed. According to this view, actions should conform to what an ideally virtuous agent would do by manifesting virtues like generosity and honesty . Logic is the study of correct reasoning . It aims to understand how to distinguish good from bad arguments . It
10679-467: Is the 1687 book Philosophiæ Naturalis Principia Mathematica by Isaac Newton . This book referred to natural philosophy in its title, but it is today considered a book of physics. The meaning of philosophy changed toward the end of the modern period when it acquired the more narrow meaning common today. In this new sense, the term is mainly associated with philosophical disciplines like metaphysics, epistemology, and ethics. Among other topics, it covers
10860-410: 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
11041-561: Is the study of correct reasoning and explores how good arguments can be distinguished from bad ones. Metaphysics examines the most general features of reality , existence, objects , and properties . Other subfields are aesthetics , philosophy of language , philosophy of mind , philosophy of religion , philosophy of science , philosophy of mathematics , philosophy of history , and political philosophy . Within each branch, there are competing schools of philosophy that promote different principles, theories, or methods. Philosophers use
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#173276573457311222-399: 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 the example. The truth of a proposition usually depends on
11403-432: 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
11584-460: Is truth established?"; and "Can we prove causal relations?" Epistemology is primarily interested in declarative knowledge or knowledge of facts, like knowing that Princess Diana died in 1997. But it also investigates practical knowledge , such as knowing how to ride a bicycle, and knowledge by acquaintance , for example, knowing a celebrity personally. One area in epistemology is the analysis of knowledge . It assumes that declarative knowledge
11765-540: 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
11946-599: 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)
12127-455: Is usually divided into formal and informal logic . Formal logic uses artificial languages with a precise symbolic representation to investigate arguments. In its search for exact criteria, it examines the structure of arguments to determine whether they are correct or incorrect. Informal logic uses non-formal criteria and standards to assess the correctness of arguments. It relies on additional factors such as content and context. Logic examines
12308-434: Is usually regarded as the first philosopher of this tradition. He translated and interpreted many works of Aristotle and Neoplatonists in his attempt to show that there is a harmony between reason and faith . Avicenna (980–1037 CE) also followed this goal and developed a comprehensive philosophical system to provide a rational understanding of reality encompassing science, religion, and mysticism. Al-Ghazali (1058–1111 CE)
12489-554: Is whether beauty is an objective feature of entities or a subjective aspect of experience. Aesthetic philosophers also investigate the nature of aesthetic experiences and judgments . Further topics include the essence of works of art and the processes involved in creating them. The philosophy of language studies the nature and function of language . It examines the concepts of meaning , reference , and truth. It aims to answer questions such as how words are related to things and how language affects human thought and understanding. It
12670-431: 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
12851-679: The Archaic or Epic period ( c. 800–500 BC ), and the Classical period ( c. 500–300 BC ). Ancient Greek was the language of Homer and of fifth-century Athenian historians, playwrights, and philosophers . It has contributed many words to English vocabulary and has been a standard subject of study in educational institutions of the Western world since the Renaissance . This article primarily contains information about
13032-606: The Epic and Classical periods of the language, which are the best-attested periods and considered most typical of Ancient Greek. From the Hellenistic period ( c. 300 BC ), Ancient Greek was followed by Koine Greek , which is regarded as a separate historical stage, though its earliest form closely resembles Attic Greek , and its latest form approaches Medieval Greek . There were several regional dialects of Ancient Greek; Attic Greek developed into Koine. Ancient Greek
13213-501: The Pella curse tablet , as Hatzopoulos and other scholars note. Based on the conclusions drawn by several studies and findings such as Pella curse tablet , Emilio Crespo and other scholars suggest that ancient Macedonian was a Northwest Doric dialect , which shares isoglosses with its neighboring Thessalian dialects spoken in northeastern Thessaly . Some have also suggested an Aeolic Greek classification. The Lesbian dialect
13394-603: The epic poems , the Iliad and the Odyssey , and in later poems by other authors. Homeric Greek had significant differences in grammar and pronunciation from Classical Attic and other Classical-era dialects. The origins, early form and development of the Hellenic language family are not well understood because of a lack of contemporaneous evidence. Several theories exist about what Hellenic dialect groups may have existed between
13575-501: The present , future , and imperfect are imperfective in aspect; the aorist , present perfect , pluperfect and future perfect are perfective in aspect. Most tenses display all four moods and three voices, although there is no future subjunctive or imperative. Also, there is no imperfect subjunctive, optative or imperative. The infinitives and participles correspond to the finite combinations of tense, aspect, and voice. The indicative of past tenses adds (conceptually, at least)
13756-418: The "things themselves", that is, as originally given in experience. They contend that this base-level of experience provides the foundation for higher-order theoretical knowledge, and that one needs to understand the former to understand the latter. An early approach found in ancient Greek and Roman philosophy is that philosophy is the spiritual practice of developing one's rational capacities. This practice
13937-1031: The 5th century BC. Ancient pronunciation cannot be reconstructed with certainty, but Greek from the period is well documented, and there is little disagreement among linguists as to the general nature of the sounds that the letters represent. /oː/ raised to [uː] , probably by the 4th century BC. Greek, like all of the older Indo-European languages , is highly inflected. It is highly archaic in its preservation of Proto-Indo-European forms. In ancient Greek, nouns (including proper nouns) have five cases ( nominative , genitive , dative , accusative , and vocative ), three genders ( masculine , feminine , and neuter ), and three numbers (singular, dual , and plural ). Verbs have four moods ( indicative , imperative , subjunctive , and optative ) and three voices (active, middle, and passive ), as well as three persons (first, second, and third) and various other forms. Verbs are conjugated through seven combinations of tenses and aspect (generally simply called "tenses"):
14118-409: The 5th century CE. Its focus was on religious topics and many thinkers used ancient philosophy to explain and further elaborate Christian doctrines . The Renaissance period started in the 14th century and saw a renewed interest in schools of ancient philosophy, in particular Platonism . Humanism also emerged in this period. The modern period started in the 17th century. One of its central concerns
14299-495: The Archaic period of ancient Greek (see Homeric Greek for more details): Μῆνιν ἄειδε, θεά, Πηληϊάδεω Ἀχιλῆος οὐλομένην, ἣ μυρί' Ἀχαιοῖς ἄλγε' ἔθηκε, πολλὰς δ' ἰφθίμους ψυχὰς Ἄϊδι προΐαψεν ἡρώων, αὐτοὺς δὲ ἑλώρια τεῦχε κύνεσσιν οἰωνοῖσί τε πᾶσι· Διὸς δ' ἐτελείετο βουλή· ἐξ οὗ δὴ τὰ πρῶτα διαστήτην ἐρίσαντε Ἀτρεΐδης τε ἄναξ ἀνδρῶν καὶ δῖος Ἀχιλλεύς. The beginning of Apology by Plato exemplifies Attic Greek from
14480-669: The Classical period of ancient Greek. (The second line is the IPA , the third is transliterated into the Latin alphabet using a modern version of the Erasmian scheme .) Ὅτι [hóti Hóti μὲν men mèn ὑμεῖς, hyːmêːs hūmeîs, 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
14661-545: The Dorians. The Greeks of this period believed there were three major divisions of all Greek people – Dorians, Aeolians, and Ionians (including Athenians), each with their own defining and distinctive dialects. Allowing for their oversight of Arcadian, an obscure mountain dialect, and Cypriot, far from the center of Greek scholarship, this division of people and language is quite similar to the results of modern archaeological-linguistic investigation. One standard formulation for
14842-417: 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
15023-418: 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
15204-550: The aorist. Following Homer 's practice, the augment is sometimes not made in poetry , especially epic poetry. The augment sometimes substitutes for reduplication; see below. Almost all forms of the perfect, pluperfect, and future perfect reduplicate the initial syllable of the verb stem. (A few irregular forms of perfect do not reduplicate, whereas a handful of irregular aorists reduplicate.) The three types of reduplication are: Irregular duplication can be understood diachronically. For example, lambanō (root lab ) has
15385-399: 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
15566-419: The augment when it was word-initial. In verbs with a preposition as a prefix, the augment is placed not at the start of the word, but between the preposition and the original verb. For example, προσ(-)βάλλω (I attack) goes to προσ έ βαλoν in the aorist. However compound verbs consisting of a prefix that is not a preposition retain the augment at the start of the word: αὐτο(-)μολῶ goes to ηὐ τομόλησα in
15747-438: The basic limits of human understanding". Before the modern age, the term philosophy was used in a wide sense. It included most forms of rational inquiry, such as the individual sciences , as its subdisciplines. For instance, natural philosophy was a major branch of philosophy. This branch of philosophy encompassed a wide range of fields, including disciplines like physics, chemistry , and biology . An example of this usage
15928-495: 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
16109-438: The beginning of the 20th century. It discusses topics such as ethnophilosophy , négritude , pan-Africanism , Marxism, postcolonialism , the role of cultural identity, relativism , epistemological dualism , and the critique of Eurocentrism . Philosophical questions can be grouped into several branches. These groupings allow philosophers to focus on a set of similar topics and interact with other thinkers who are interested in
16290-487: 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
16471-645: 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
16652-495: 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,
16833-511: 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
17014-459: The conclusion is true. One form is inductive reasoning . It starts from a set of individual cases and uses generalization to arrive at a universal law governing all cases. An example is the inference that "all ravens are black" based on observations of many individual black ravens. Another form is abductive reasoning . It starts from an observation and concludes that the best explanation of this observation must be true. This happens, for example, when
17195-458: 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
17376-591: 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
17557-612: The consequences of the general theories developed by normative ethics in specific situations, for example, in the workplace or for medical treatments. Within contemporary normative ethics, consequentialism, deontology , and virtue ethics are influential schools of thought. Consequentialists judge actions based on their consequences. One such view is utilitarianism , which argues that actions should increase overall happiness while minimizing suffering. Deontologists judge actions based on whether they follow moral duties, such as abstaining from lying or killing. According to them, what matters
17738-438: 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
17919-451: 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
18100-615: The dialect of Sparta ), and Northern Peloponnesus Doric (including Corinthian ). All the groups were represented by colonies beyond Greece proper as well, and these colonies generally developed local characteristics, often under the influence of settlers or neighbors speaking different Greek dialects. After the conquests of Alexander the Great in the late 4th century BC, a new international dialect known as Koine or Common Greek developed, largely based on Attic Greek , but with influence from other dialects. This dialect slowly replaced most of
18281-530: The dialects is: West vs. non-West Greek is the strongest-marked and earliest division, with non-West in subsets of Ionic-Attic (or Attic-Ionic) and Aeolic vs. Arcadocypriot, or Aeolic and Arcado-Cypriot vs. Ionic-Attic. Often non-West is called 'East Greek'. Arcadocypriot apparently descended more closely from the Mycenaean Greek of the Bronze Age. Boeotian Greek had come under
18462-510: The divergence of early Greek-like speech from the common Proto-Indo-European language and the Classical period. They have the same general outline but differ in some of the detail. The only attested dialect from this period is Mycenaean Greek , but its relationship to the historical dialects and the historical circumstances of the times imply that the overall groups already existed in some form. Scholars assume that major Ancient Greek period dialect groups developed not later than 1120 BC, at
18643-421: The emergence and application of formal logic , the focus on the role of language as well as pragmatism , and movements in continental philosophy like phenomenology, existentialism , and post-structuralism . The 20th century saw a rapid expansion of academic philosophy in terms of the number of philosophical publications and philosophers working at academic institutions . There was also a noticeable growth in
18824-478: The emergence of non-Vedic teachings, like Buddhism and Jainism . Buddhism was founded by Gautama Siddhartha (563–483 BCE), who challenged the Vedic idea of a permanent self and proposed a path to liberate oneself from suffering . Jainism was founded by Mahavira (599–527 BCE), who emphasized non-violence as well as respect toward all forms of life. The subsequent classical period started roughly 200 BCE and
19005-441: The exploration of the nature of reality and the ways of arriving at knowledge. Chinese philosophy focuses principally on practical issues in relation to right social conduct, government, and self-cultivation . Major branches of philosophy are epistemology , ethics , logic , and metaphysics . Epistemology studies what knowledge is and how to acquire it. Ethics investigates moral principles and what constitutes right conduct. Logic
19186-406: The features that all entities have in common. Specific metaphysics is interested in different kinds of being, the features they have, and how they differ from one another. An important area in metaphysics is ontology . Some theorists identify it with general metaphysics. Ontology investigates concepts like being , becoming , and reality. It studies the categories of being and asks what exists on
19367-434: 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
19548-485: 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
19729-513: 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
19910-523: 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
20091-419: 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
20272-421: 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
20453-537: The history of philosophy include Western , Arabic–Persian , Indian , and Chinese philosophy . Other philosophical traditions are Japanese philosophy , Latin American philosophy , and African philosophy . Western philosophy originated in Ancient Greece in the 6th century BCE with the pre-Socratics . They attempted to provide rational explanations of the cosmos as a whole. The philosophy following them
20634-417: The importance of a strong state and strict laws. Buddhism was introduced to China in the 1st century CE and diversified into new forms of Buddhism . Starting in the 3rd century CE, the school of Xuanxue emerged. It interpreted earlier Daoist works with a specific emphasis on metaphysical explanations. Neo-Confucianism developed in the 11th century CE. It systematized previous Confucian teachings and sought
20815-418: The indigenous Shinto religion and Chinese and Indian thought in the forms of Confucianism and Buddhism, both of which entered Japan in the 6th and 7th centuries. Its practice is characterized by active interaction with reality rather than disengaged examination. Neo-Confucianism became an influential school of thought in the 16th century and the following Edo period and prompted a greater focus on language and
20996-480: The interconnectedness of all things. Latin American philosophy during the colonial period , starting around 1550, was dominated by religious philosophy in the form of scholasticism . Influential topics in the post-colonial period were positivism , the philosophy of liberation , and the exploration of identity and culture. Early African philosophy, like Ubuntu philosophy , was focused on community, morality, and ancestral ideas. Systematic African philosophy emerged at
21177-406: 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
21358-407: 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
21539-522: 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
21720-548: The manifestation of cognitive virtues instead of justification; or they deny that knowledge can be analyzed in terms of other phenomena. Another area in epistemology asks how people acquire knowledge. Often-discussed sources of knowledge are perception , introspection , memory , inference , and testimony . According to empiricists , all knowledge is based on some form of experience. Rationalists reject this view and hold that some forms of knowledge, like innate knowledge , are not acquired through experience. The regress problem
21901-454: 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 the strongest form of support: if their premises are true then their conclusion must also be true. This
22082-496: The modern sense of the term. Influential traditions in the history of philosophy include Western , Arabic–Persian , Indian , and Chinese philosophy . Western philosophy originated in Ancient Greece and covers a wide area of philosophical subfields. A central topic in Arabic–Persian philosophy is the relation between reason and revelation . Indian philosophy combines the spiritual problem of how to reach enlightenment with
22263-594: The most fundamental level. Another subfield of metaphysics is philosophical cosmology . It is interested in the essence of the world as a whole. It asks questions including whether the universe has a beginning and an end and whether it was created by something else. A key topic in metaphysics concerns the question of whether reality only consists of physical things like matter and energy. Alternative suggestions are that mental entities (such as souls and experiences ) and abstract entities (such as numbers) exist apart from physical things. Another topic in metaphysics concerns
22444-402: The most influential philosophers of the subsequent period. The increasing influence of Western thought and institutions in the 19th and 20th centuries gave rise to the intellectual movement of Islamic modernism , which aims to understand the relation between traditional Islamic beliefs and modernity. One of the distinguishing features of Indian philosophy is that it integrates the exploration of
22625-470: The natural and social sciences, religion, and mathematics. Epistemology is the branch of philosophy that studies knowledge. It is also known as theory of knowledge and aims to understand what knowledge is, how it arises, what its limits are, and what value it has. It further examines the nature of truth , belief , justification , and rationality . Some of the questions addressed by epistemologists include "By what method(s) can one acquire knowledge?"; "How
22806-501: The natural world. The Kyoto School emerged in the 20th century and integrated Eastern spirituality with Western philosophy in its exploration of concepts like absolute nothingness ( zettai-mu ), place ( basho ), and the self . Latin American philosophy in the pre-colonial period was practiced by indigenous civilizations and explored questions concerning the nature of reality and the role of humans. It has similarities to indigenous North American philosophy , which covered themes such as
22987-454: The nature and sources of morality. It analyzes the meaning of ethical concepts, like right action and obligation . It also investigates whether ethical theories can be true in an absolute sense and how to acquire knowledge of them. Normative ethics encompasses general theories of how to distinguish between right and wrong conduct. It helps guide moral decisions by examining what moral obligations and rights people have. Applied ethics studies
23168-469: The nature of reality, the ways of arriving at knowledge, and the spiritual question of how to reach enlightenment . It started around 900 BCE when the Vedas were written. They are the foundational scriptures of Hinduism and contemplate issues concerning the relation between the self and ultimate reality as well as the question of how souls are reborn based on their past actions . This period also saw
23349-534: The number of female philosophers , but they still remained underrepresented. Arabic–Persian philosophy arose in the early 9th century CE as a response to discussions in the Islamic theological tradition . Its classical period lasted until the 12th century CE and was strongly influenced by ancient Greek philosophers. It employed their ideas to elaborate and interpret the teachings of the Quran . Al-Kindi (801–873 CE)
23530-508: The older dialects, although the Doric dialect has survived in the Tsakonian language , which is spoken in the region of modern Sparta. Doric has also passed down its aorist terminations into most verbs of Demotic Greek . By about the 6th century AD, the Koine had slowly metamorphosed into Medieval Greek . Phrygian is an extinct Indo-European language of West and Central Anatolia , which
23711-409: 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
23892-444: 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
24073-487: The perfect stem eilēpha (not * lelēpha ) because it was originally slambanō , with perfect seslēpha , becoming eilēpha through compensatory lengthening. Reduplication is also visible in the present tense stems of certain verbs. These stems add a syllable consisting of the root's initial consonant followed by i . A nasal stop appears after the reduplication in some verbs. The earliest extant examples of ancient Greek writing ( c. 1450 BC ) are in
24254-433: The philosophical sense is the field that studies the nature and appreciation of beauty and other aesthetic properties, like the sublime . Although it is often treated together with the philosophy of art , aesthetics is a broader category that encompasses other aspects of experience, such as natural beauty. In a more general sense, aesthetics is "critical reflection on art, culture, and nature ". A key question in aesthetics
24435-415: The precise definition of the term and its meaning has changed throughout the ages. Metaphysicians attempt to answer basic questions including " Why is there something rather than nothing? "; "Of what does reality ultimately consist?"; and "Are humans free?" Metaphysics is sometimes divided into general metaphysics and specific or special metaphysics. General metaphysics investigates being as such. It examines
24616-485: 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,
24797-413: 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
24978-470: 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
25159-449: The problem of identity . One question is how much an entity can change while still remaining the same entity. According to one view, entities have essential and accidental features . They can change their accidental features but they cease to be the same entity if they lose an essential feature. A central distinction in metaphysics is between particulars and universals . Universals, like the color red, can exist at different locations at
25340-485: 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
25521-406: 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
25702-426: The provocative, vexing, and enduring problems central to the human condition. The philosophical pursuit of wisdom involves asking general and fundamental questions. It often does not result in straightforward answers but may help a person to better understand the topic, examine their life, dispel confusion, and overcome prejudices and self-deceptive ideas associated with common sense. For example, Socrates stated that "
25883-417: 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
26064-434: The rational study of reality, knowledge, and values. It is distinguished from other disciplines of rational inquiry such as the empirical sciences and mathematics . The practice of philosophy is characterized by several general features: it is a form of rational inquiry, it aims to be systematic, and it tends to critically reflect on its own methods and presuppositions. It requires attentively thinking long and carefully about
26245-436: 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
26426-486: The same questions. Epistemology, ethics, logic, and metaphysics are sometimes listed as the main branches. There are many other subfields besides them and the different divisions are neither exhaustive nor mutually exclusive. For example, political philosophy, ethics, and aesthetics are sometimes linked under the general heading of value theory as they investigate normative or evaluative aspects. Furthermore, philosophical inquiry sometimes overlaps with other disciplines in
26607-506: The same time. This is not the case for particulars including individual persons or specific objects. Other metaphysical questions are whether the past fully determines the present and what implications this would have for the existence of free will . There are many other subfields of philosophy besides its core branches. Some of the most prominent are aesthetics, philosophy of language, philosophy of mind, philosophy of religion, philosophy of science, and political philosophy. Aesthetics in
26788-407: The same way as the sciences. This problem is avoided by seeing philosophy as an immature or provisional science whose subdisciplines cease to be philosophy once they have fully developed. In this sense, philosophy is sometimes described as "the midwife of the sciences". Other definitions focus on the contrast between science and philosophy. A common theme among many such conceptions is that philosophy
26969-505: The scope and fundamental concepts of these fields. It also investigates their methods and ethical implications. The word philosophy comes from the Ancient Greek words φίλος ( philos ) ' love ' and σοφία ( sophia ) ' wisdom ' . Some sources say that the term was coined by the pre-Socratic philosopher Pythagoras , but this is not certain. The word entered the English language primarily from Old French and Anglo-Norman starting around 1175 CE. The French philosophie
27150-492: 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
27331-418: 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
27512-604: 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
27693-518: 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
27874-404: 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
28055-415: 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
28236-870: 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
28417-474: 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
28598-418: 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
28779-437: 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
28960-403: The structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies , critical thinking , and argumentation theory . Informal logic examines arguments expressed in natural language whereas formal logic uses formal language . When used as a countable noun , the term "a logic" refers to a specific logical formal system that articulates
29141-438: 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
29322-594: The study of the biggest patterns of the world as a whole or as the attempt to answer the big questions. Such an approach is pursued by Immanuel Kant , who holds that the task of philosophy is united by four questions: "What can I know?"; "What should I do?"; "What may I hope?"; and "What is the human being?" Both approaches have the problem that they are usually either too wide, by including non-philosophical disciplines, or too narrow, by excluding some philosophical sub-disciplines. Many definitions of philosophy emphasize its intimate relation to science. In this sense, philosophy
29503-700: 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
29684-417: 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
29865-517: The syllabic script Linear B . Beginning in the 8th century BC, however, the Greek alphabet became standard, albeit with some variation among dialects. Early texts are written in boustrophedon style, but left-to-right became standard during the classic period. Modern editions of ancient Greek texts are usually written with accents and breathing marks , interword spacing , modern punctuation , and sometimes mixed case , but these were all introduced later. The beginning of Homer 's Iliad exemplifies
30046-423: 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
30227-409: 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
30408-466: The teachings of Advaita Vedanta to argue that all the different religions are valid paths toward the one divine. Chinese philosophy is particularly interested in practical questions associated with right social conduct, government, and self-cultivation . Many schools of thought emerged in the 6th century BCE in competing attempts to resolve the political turbulence of that period. The most prominent among them were Confucianism and Daoism . Confucianism
30589-399: 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"
30770-467: The time of the Dorian invasions —and that their first appearances as precise alphabetic writing began in the 8th century BC. The invasion would not be "Dorian" unless the invaders had some cultural relationship to the historical Dorians . The invasion is known to have displaced population to the later Attic-Ionic regions, who regarded themselves as descendants of the population displaced by or contending with
30951-479: 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
31132-596: The unexamined life is not worth living " to highlight the role of philosophical inquiry in understanding one's own existence. And according to Bertrand Russell , "the man who has no tincture of philosophy goes through life imprisoned in the prejudices derived from common sense, from the habitual beliefs of his age or his nation, and from convictions which have grown up in his mind without the cooperation or consent of his deliberate reason." Attempts to provide more precise definitions of philosophy are controversial and are studied in metaphilosophy . Some approaches argue that there
31313-480: Was Aeolic. For example, fragments of the works of the poet Sappho from the island of Lesbos are in Aeolian. Most of the dialect sub-groups listed above had further subdivisions, generally equivalent to a city-state and its surrounding territory, or to an island. Doric notably had several intermediate divisions as well, into Island Doric (including Cretan Doric ), Southern Peloponnesus Doric (including Laconian ,
31494-452: Was a pluricentric language , divided into many dialects. The main dialect groups are Attic and Ionic , Aeolic , Arcadocypriot , and Doric , many of them with several subdivisions. Some dialects are found in standardized literary forms in literature , while others are attested only in inscriptions. There are also several historical forms. Homeric Greek is a literary form of Archaic Greek (derived primarily from Ionic and Aeolic) used in
31675-470: Was a strong critic of the idea that reason can arrive at a true understanding of reality and God. He formulated a detailed critique of philosophy and tried to assign philosophy a more limited place besides the teachings of the Quran and mystical insight. Following Al-Ghazali and the end of the classical period, the influence of philosophical inquiry waned. Mulla Sadra (1571–1636 CE) is often regarded as one of
31856-435: Was characterized by the emergence of the six orthodox schools of Hinduism : Nyāyá , Vaiśeṣika , Sāṃkhya , Yoga , Mīmāṃsā , and Vedanta . The school of Advaita Vedanta developed later in this period. It was systematized by Adi Shankara ( c. 700 –750 CE), who held that everything is one and that the impression of a universe consisting of many distinct entities is an illusion . A slightly different perspective
32037-656: Was defended by Ramanuja (1017–1137 CE), who founded the school of Vishishtadvaita Vedanta and argued that individual entities are real as aspects or parts of the underlying unity. He also helped to popularize the Bhakti movement , which taught devotion toward the divine as a spiritual path and lasted until the 17th to 18th centuries CE. The modern period began roughly 1800 CE and was shaped by encounters with Western thought. Philosophers tried to formulate comprehensive systems to harmonize diverse philosophical and religious teachings. For example, Swami Vivekananda (1863–1902 CE) used
32218-405: 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
32399-508: Was founded by Confucius (551–479 BCE). It focused on different forms of moral virtues and explored how they lead to harmony in society. Daoism was founded by Laozi (6th century BCE) and examined how humans can live in harmony with nature by following the Dao or the natural order of the universe. Other influential early schools of thought were Mohism , which developed an early form of altruistic consequentialism , and Legalism , which emphasized
32580-509: Was how philosophical and scientific knowledge are created. Specific importance was given to the role of reason and sensory experience . Many of these innovations were used in the Enlightenment movement to challenge traditional authorities. Several attempts to develop comprehensive systems of philosophy were made in the 19th century, for instance, by German idealism and Marxism . Influential developments in 20th-century philosophy were
32761-447: Was shaped by Socrates (469–399 BCE), Plato (427–347 BCE), and Aristotle (384–322 BCE). They expanded the range of topics to questions like how people should act , how to arrive at knowledge , and what the nature of reality and mind is. The later part of the ancient period was marked by the emergence of philosophical movements, for example, Epicureanism , Stoicism , Skepticism , and Neoplatonism . The medieval period started in
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