120-449: Thomas Morton may refer to: Thomas Morton (bishop) (1564–1659), Bishop of Durham and Chester in the 17th century Thomas Morton (playwright) (1764–1838), British playwright Thomas Morton (colonist) (c. 1579–1647), British lawyer & early colonist of Massachusetts Thomas Morton (journalist) (active 2014), American journalist Thomas Morton (shipwright) (1781–1832), inventor of
240-501: 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
360-444: 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 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
480-445: 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
600-480: 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
720-573: 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,
840-425: 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
960-510: 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
1080-686: 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)} "
1200-415: 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
1320-551: 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
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#17328697799721440-402: 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
1560-575: A later period were Friedrich Spanheim and Marco Antonio De Dominis . In 1610 he was nominated to one of the seventeen fellowships in Chelsea College . Preferments then followed: in July of the same year he was collated by Tobias Matthew , Archbishop of York , to the canonry of Husthwait in York Minster . In 1615, on the death of George Lloyd , James I nominated him Bishop of Chester ; his consecration
1680-614: 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
1800-550: A record of sympathetic treatment of Puritans as a diocesan, and underlying Calvinist beliefs shown in the Gagg controversy , his royalism saw him descend into poverty under the Commonwealth. Morton was born in York on 20 March 1564, the sixth of the nineteen children of Richard Morton, mercer, of York, and alderman of the city, by his wife Elizabeth All Saints' Church, Pavement, York . He
1920-664: 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
2040-420: 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
2160-471: 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
2280-441: 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
2400-416: 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
2520-453: 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
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#17328697799722640-415: 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
2760-421: 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
2880-407: 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
3000-453: 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
3120-424: Is different from Wikidata All article disambiguation pages All disambiguation pages Thomas Morton (bishop) Thomas Morton (20 March 1564 – 20 September 1659) was an English churchman, bishop of several dioceses . Well-connected and in favour with James I, he was also a significant polemical writer against Roman Catholic views. He rose to become Bishop of Durham , but despite
3240-606: 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
3360-432: 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
3480-415: 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
3600-447: 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,
3720-688: 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
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3840-518: 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
3960-407: 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
4080-541: 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
4200-430: 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
4320-410: 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
4440-528: Is the study of correct reasoning . It includes both formal and informal logic . Formal logic is the study of deductively valid inferences or logical truths . It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies , critical thinking , and argumentation theory . Informal logic examines arguments expressed in natural language whereas formal logic uses formal language . When used as
4560-432: 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
4680-540: 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
4800-599: 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)
4920-431: 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
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5040-494: The Bishop of Durham, in spite of all your votes;' asked where he was going, his answer was, 'To London, to live there a little while, and then to die.' Ultimately, Yelverton invited him to his house at Easton Maudit , ten miles from Northampton . Morton became a member of the family, and tutor to Henry, his eldest son. At Easton Maudit, Morton held secret ordinations . Yelverton died in 1654. Morton died there on 22 September 1659. He
5160-465: 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
5280-801: The Patent slip Thomas Morton (surgeon) (1813–1849), English surgeon Thomas Corsan Morton (1859–1928), Scottish artist of the Glasgow School Thomas Lewis Morton (1846–1914), English-born farmer and politician in Manitoba, Canada Thomas Morton (priest) (1894-1968), catholic priest and writer Thomas Morton (MP for Gloucestershire) , English Member of Parliament for Gloucestershire Thomas Morton (MP for Bishop's Lynn) , 14th-century English Member of Parliament Tom Morton (born 1955), Scottish journalist, author and BBC Radio Scotland broadcaster [REDACTED] Topics referred to by
5400-559: The Roman Catholic Church was hostile; he was one of the only three bishops who, according to a statement made to Gregorio Panzani , the papal envoy, by Richard Montagu, were 'counted violently bent against the Papists'. Morton corresponded with Sibrandus Lubbertus on matters concerning anti-papal polemic, and their views were close. Lubbertus was a leading contra-Remonstrant and Morton was one of his significant English supporters in
5520-418: 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
5640-399: 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
5760-495: 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
5880-487: 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
6000-645: 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
6120-495: 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,
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#17328697799726240-502: 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
6360-511: 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
6480-458: 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
6600-591: 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
6720-561: The conflict over the appointment of Conrad Vorstius at the University of Leiden . One of Morton's last acts before his death was to publish a denial that he had in a speech in the House of Lords acknowledged the fiction of the Nag's Head Consecration of Matthew Parker , Archbishop of Canterbury. By his will he left money to the poor of the parish in which he died, and his chalice to All Saints, York,
6840-438: 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
6960-451: 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
7080-409: 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
7200-434: 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
7320-485: 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
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#17328697799727440-508: 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
7560-523: 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
7680-419: 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
7800-421: 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
7920-455: The grander scope of the allegiance oath controversy to which he had devoted his efforts. Nicholas Byfield preached in Chester to a congregation including John Bruen . Morton tried to reason with his Puritanical clergy. His tenure as bishop coincided with a watershed moment in opinion, namely a changed view of the relative threat of Catholicism and Protestant nonconformity. Sabbatarianism
8040-553: The house of the usher of the black rod . After four months' imprisonment Morton was released without a trial, and remained unmolested at Durham House , in The Strand , till April 1645, when he was again brought before the bar of the House of Commons on the charges of baptising the infant daughter of the Earl of Rutland according to the rites of the Church of England, and of refusing to surrender
8160-406: 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
8280-407: 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
8400-534: The learnedest and best bishops that ever I knew". He gained a reputation as a Protestant controversialist, and published numerous works against Roman Catholicism , prominent among them being the Apologia catholica (1605) and A Catholicke Appeale (1609). Morton's major works were: Other works of the 1590s which have been ascribed to this Thomas Morton were the works of another Thomas Morton, of Berwick and Christ's College, Cambridge . Logic Logic
8520-519: The libraries of London. Through Richard Bancroft 's recommendation Morton was appointed one of James I 's chaplains, and in 1606 became Dean of Gloucester , and, on the nomination of his former patron, Lord Eure, the lord president, member of the Council of the Marches . On accepting the deanery he offered to resign the living of Long Marston in favour of his friend John Donne , not yet in holy orders , but
8640-522: 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
8760-549: The lords again. Two days later, 29 December, he joined in John Williams ' protest against the legality of all acts done in the enforced absence of the spiritual lords . For this he and his 11 associates were next day impeached of high treason on William Prynne 's motion; and the same night they were all committed to the Tower, with the exception of Morton and the aged Robert Wright , Bishop of Lichfield , who were allowed to remain in
8880-527: The offer was declined. In the same year he visited Oxford, where he was admitted to an ad eundem degree on 12 July. On this occasion he met eminent theologians, such as John King , John Rainolds , Henry Airey , and Daniel Featley . In 1609 James I made him Dean of Winchester , where Thomas Bilson , who conferred on him the living of Alresford . At Winchester he became the intimate friend of Arthur Lake , then master of St. Cross, and of John Harmar , head-master of Winchester School . In 1610 he preached
9000-534: The office of university lecturer in logic till in 1598 when he obtained the living of All Saints' Church, Long Marston , in Yorkshire. He was then chaplain to Henry Hastings, 3rd Earl of Huntingdon , Lord President of the North . In 1602, when the plague was raging at York, he devoted himself to the inmates of the pest-house. He conducted disputations with Roman Catholics; Herbert Croft , who became Bishop of Hereford ,
9120-409: 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
9240-444: 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
9360-450: The parish in which he was born. He also bequeathed a silver-gilt chalice and paten of large size for the use of the chapel recently added to the manor-house by Henry Yelverton. A codicil to his will contained a declaration of his faith and of his adhesion to the Church of England. In the 1680s Richard Baxter , who as a schoolboy received confirmation from Morton in Durham, called him "one of
9480-485: 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,
9600-413: 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
9720-470: 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
9840-485: 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
9960-406: 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
10080-417: 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
10200-571: The recommendation of Lancelot Andrewes . With the bishopric he held the living of Clifton Camville in commendam . In 1621, he served on the commission for granting a dispensation to George Abbot, Archbishop of Canterbury, for the casual homicide of a keeper in Bramshill Park . In February 1626, he took a leading part in the York House Conference on Richard Montagu 's incriminated books. With John Preston , Morton did his best to impugn
10320-606: The rest of the reformed churches except in church government,' and Edward Hyde, 1st Earl of Clarendon classes him with 'the less formal and more popular prelates'. He was a sincere episcopalian, regarding ordination by presbyters valid in case of necessity, no such necessity however warranting it in the Church of England. From the moderation of his ecclesiastical views he was at one time well regarded by William Prynne. Edmund Calamy recorded his liberal treatment of Puritans such as John Hieron , Richard Mather , and John Shawe of Christ's College, Cambridge . His attitude towards
10440-436: 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
10560-407: The same term This disambiguation page lists articles about people with the same name. If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Thomas_Morton&oldid=1178662745 " Category : Human name disambiguation pages Hidden categories: Short description
10680-492: 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
10800-468: The seal of the County palatine of Durham . He was committed to the custody of the serjeant-at-arms for six months. On the abolition of episcopacy in 1646 an annual income was assigned to him, but without indications of by whom it was to be paid not being specified. He obtained a sum of £1,000 from the committee at Goldsmiths' Hall , which he employed in paying his debts and purchasing an annuity. In 1648 he
10920-418: 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
11040-604: 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
11160-518: 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
11280-543: The sermon ad clerum at the opening of Convocation . When in London he lodged at the deanery of St Paul's Cathedral with John Overall , in whose house he enjoyed the society of Isaac Casaubon , who became a friend; and met Abraham Scultetus , Giovanni Diodati , and Pierre Du Moulin . On Casaubon's death in 1614 Morton had a monument erected to him in Westminster Abbey at his own cost. Among his associates from abroad at
11400-404: 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
11520-415: 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
11640-870: 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
11760-474: 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
11880-500: The statements contained in them on predestination and freewill. In June 1632, Morton became Bishop of Durham , which he held by canonical right until his death in 1659, although parliament claimed to deprive him of it in 1647. Complaints were later made against him to the House of Commons by his prebendary, Peter Smart . He showed forbearance in claiming the rights of the palatinate, was liberal in almsgiving, and maintained poor scholars at
12000-418: 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
12120-437: 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
12240-550: 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
12360-438: 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
12480-700: 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
12600-417: 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
12720-423: 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
12840-409: 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
12960-399: 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"
13080-479: 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
13200-636: The universities. On his journey to Scotland in 1633, Charles I and his suite were received by Morton in princely style; six years later, in May 1639, he again entertained Charles at the beginning of the First Bishops' War . The next year, in the month of August, the Scots crossed the River Tweed , and pushed on to the city of Durham . The cathedral clergy fled, and Morton himself retired into Yorkshire . Early in 1641 he
13320-606: Was a patron of foreign Reformed theologians , whom he received into his house and treated generously. He favoured the work of John Durie for reconciling Protestants. He numbered Richard Hooker among his friends as well as Hooker's biographer Isaak Walton , who wrote of the information he derived from Morton. William Laud was one of his correspondents. In theology he belonged to the school of James Ussher and William Bedell , and had little sympathy with Laudianism . Richard Baxter speaks of him as 'belonging to that class of episcopal divines who differ in nothing considerable from
13440-554: Was at issue, with an attempt by the magistrates to suppress the diversions customary on Sunday afternoons. James I asked advice from Morton, who recommended: James based the substance of his subsequent declaration on these points; but his publication of the Book of Sports in the following year led to new disturbances. Morton's own dealings with nonconformist clergy were marked by moderation. In 1618, on John Overall's translation to Norwich, Morton became Bishop of Coventry and Lichfield , on
13560-407: Was brought up and grammar school educated in the city and nearby Halifax . In 1582, he became a pensioner at St John's College, Cambridge from which he graduated with a BA in 1584 and an MA in 1590. William Whitaker picked him out for a Fellow of the college, and he proceeded to the degree of BD in 1598, and that of DD 'with great distinction' in 1606. Morton was ordained in 1592, and held
13680-534: Was buried in the Yelverton chapel of the parish church. His chaplain, John Barwick , preached the funeral sermon. He died unmarried. Morton was a patron of learned men. At the beginning of the First English Civil War , he offered Thomas Fuller a home and maintenance. Isaac Basire was one of the scholars whom he brought forward. Ralph Brownrig , Henry Ferne and John Barwick were among his chaplains. He
13800-778: Was claimed as Morton's convert to the Church of England . In 1602 he was selected, with Richard Crakanthorpe as his colleague, to accompany Ralph Eure, 3rd Baron Eure when sent by Elizabeth as ambassador extraordinary to Rudolf II, Holy Roman Emperor and Christian IV of Denmark . He made the acquaintance of foreign scholars and theologians, including Jesuits , and collected books at Frankfurt and elsewhere. He met Hugh Broughton , then residing at Middelburg , to whom he proposed scriptural difficulties. On Elizabeth's death Morton returned to England, and became chaplain to Roger Manners, 5th Earl of Rutland . He had time for theological writing, and residence at Belvoir Castle enabled him to consult
13920-445: Was delayed until 7 July 1616. The ceremony, of unusual stateliness, was performed at Lambeth Palace by George Abbot , Archbishop of Canterbury , assisted by Christopher Hampton , Archbishop of Armagh ; Alexander Forbes , Bishop of Caithness ; John King, Bishop of London ; and John Overall, Bishop of Coventry and Lichfield . While the palace at Chester was readied he stayed with Christopher Hatton at Clay Hall, Essex , where he
14040-405: 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
14160-482: Was driven from Durham House soldiers, who took forcible possession of it. He then resided with his friends, the Earl and Countess of Rutland, at Exeter House in The Strand; and the passed his time with royalist lay friends. Returning to London on horseback, he fell in with Christopher, son and heir of Henry Yelverton . Christopher did not recognise the bishop. To his inquiry who he was, Morton replied, 'I am that old man,
14280-484: Was in London attending Parliament, and was nominated a member of the sub-committee to prepare matters for the consideration of the abortive committee of the lords appointed on 1 March—the day of William Laud 's committal to the Tower of London —to take cognisance of innovations in religion. In the following December a mob threatened to drag him out of his coach when on his way to the House of Lords . Morton never took his seat in
14400-455: Was seriously ill. He had resigned Alresford, but during his episcopate he held the living of Stopford , given him by James I in commendam . Morton's see was large: Cheshire and Lancashire , the north-western portion of Yorkshire , and large parts of Cumberland and Westmoreland . Lancashire had a Catholic majority and Calvinist minority. Two significant works came out of this period, in which Morton had to deal with local issues outside
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