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Presocratic Fragments and Testimonials adapted from passages in John Burnet's Early Greek Philosophy (1892).] Presocratic Fragments and Testimonials adapted from passages in John Burnet's Early Greek Philosophy (1892).

${\displaystyle \neg }$ ${\displaystyle \to }$ ${\displaystyle \forall }$ ${\displaystyle \exists }$

Wikipedia:WikiProject Logic/Standards for notation#Symbols

• (A) cf Wolfram 1989^[1]
• (B) ^[2]
• (C) ^[3]
• (D) ^{[refgroup 1]}

reflist

refgroup

&site=en.wikipedia.org Wannabe Kate

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In Aristotle's view, if X is the assertion that s is F and Y is the assertion that s is not-F, then (a) if s exists then X is true or false and Y the contrary depending of whether of not s is F, but (b) if s does not exist then X is false and Y is true ^{[1] [2]}

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• Theory (mathematical logic)
• Theory (mathematical logic)#Syntactic consequence in a first order theory
• talk:WikiProject Philosophy#WikiProject Logic
• Wikipedia talk:WikiProject Philosophy#WikiProject Logic

• First-order logic#Validity, satisfiability, and logical consequence
• formula

More information , ...

Name	Description/Usage	Symbol(s)	Preferred Symbol(s)	Template	<math>	See
Definition	${\displaystyle X{\stackrel {\rm {def}}{=}}y_{1},y_{2},\dots }$	${\displaystyle {\stackrel {\rm {def}}{=}}}$	${\displaystyle {\stackrel {\rm {def}}{=}}}$	none	\stackrel{\rm def}=	Definition
Theorem	${\displaystyle X\vdash Y}$, ${\displaystyle \vdash Z}$, ${\displaystyle A\vdash _{S}X}$	${\displaystyle \vdash }$	${\displaystyle \vdash }$	{{tee}}	\vdash	Turnstile (symbol)
Semantic Entailment	${\displaystyle A\models _{L}X}$, ${\displaystyle \models X}$	${\displaystyle \models }$	${\displaystyle \models }$	{{models}}	\models	Double turnstile
True, tautology	${\displaystyle \vDash \top }$	${\displaystyle \top }$ or T or 1	${\displaystyle \top }$	{{true}}	\top	Tee (symbol)
False, contradiction	${\displaystyle \vDash \neg \bot }$	${\displaystyle \bot }$ or F or 0	${\displaystyle \bot }$	{{false}}	\bot	Falsum

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• ${\displaystyle \vdash }$ \vdash Turnstile (symbol)
• cf ⊢
• Semantic Entailment , ${\displaystyle \models }$
• Definition none \stackrel{\rm def}= Definition
• Theorem , , ${\displaystyle \vdash }$ \vdash Turnstile (symbol)
• Semantic Entailment , ${\displaystyle \models }$ \models Double turnstile
• True, tautology or T or 1 ${\displaystyle \top }$ \top Tee (symbol)
• False, contradiction or F or 0 ${\displaystyle \bot }$ \bot Falsum

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Wikipedia talk:WikiProject Logic {{logic}}Wikipedia talk:WikiProject Philosophy#WikiProject Logic tst — Philogo (talk) 02:37, 13 February 2011 (UTC) tst — Philogos (talk) 02:38, 13 February 2011 (UTC)

We say that A is contradictory (according to quantification theory) iff ~A is logically valid, or, equivalently, iff A is false for every interpretation

1. Pn0, Pn1, Pn2, Pn3, … 2. For every integer n ≥ 0 there are infinitely many n-ary function symbols: f n0, f n1, f n2, f n3, … In contemporary mathematical logic, the 3. Pn0, Pn1, Pn2, Pn3, … f n0, f n1, f n2, f n3, …

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1. Sider, Theodore (1997). "Four-Dimensionalism". Philosophical Review (Oxford University Press) 106 (2): 197–231. http://tedsider.org/papers/4d.pdf.
2. "The Unreality of Time". Wikisource. http://en.wikisource.org/wiki/The_Unreality_of_Time. Retrieved 2008-12-15.
3. "Time". Stanford Encyclopedia of Philosophy. 2002-11-25. http://plato.stanford.edu/entries/time/#TimTra). Retrieved 2008-12-15.

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The following shows the lede before and after my recent edits Before In philosophy, four-dimensionalism may refer to either eternalism or perdurantism. The former is a theory of time, while the latter is a theory about the identity of objects over time. Sider (1997), for example, uses the term four-dimensionalism to refer to perdurantism, the theory that objects (and people) are four dimensional (see below for explanation). Eternalism, by contrast, is the theory that the universe (but not necessarily its contents, e.g., objects and people) is four dimensional, with time being the fourth dimension. Nevertheless, both theories tend to be discussed together, as many philosophers hold the combination of eternalism and perdurantism, considering both as better theories than their counterparts, presentism and endurantism, respectively. Probably, nobody who accepts perdurantism rejects eternalism, and it is unclear if such a position would even be coherent.

After In philosophy, four-dimensionalism (also known as the the doctrine of temporal parts and the theory that objects "perdure") is the philosophical theory that persistanmce through time is like extension through space and an object that exists in time has temporal parts in the various subregions of the total region of time it occupies. (Sider (1997, page 1)) ^[1] Contemporary four-dimensionalists include, according to Sider (1997), Armstrong (1980), Hughes (1986) , Heller (1884, 1990,1992,1992) and Lewis (1983, 1986).

Four-dimensionalism may refer to either eternalism or perdurantism. Eternalism is a philosophical approach to the ontological nature of time, according to which all points in time are equally "real", as opposed to the presentist idea that only the present is real.^[2] Perdurantism or perdurance theory is a philosophical theory of persistence and identity.^[3] according to which an individual has distinct temporal parts throughout its existence. Thus eternalism is a theory of time, while perdurantism is a theory about the identity of objects over time. Sider (1997) uses the term four-dimensionalism to refer to perdurantism. Eternalism and perdurantism tend to be discussed together because many philosophers argue for a combination of eternalism and perdurantism, considering both as better theories than their counterparts, presentism and endurantism, respectively. It may be argued that the acceptance of perdurantism and rejection of eternalism would would be incoherent.

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test template Please do not add or change content without verifying it by citing reliable sources, as you did to [[test]]. Please review the guidelines at Wikipedia:Citing sources and take this opportunity to add references to the article. Thank you. —

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In logic, entailment is a relation between a set of sentences (meaningfully declarative sentences or truthbearers) and another sentence. If a sentence, S1, is the conjunction of all the elements of a set of one or more sentences, Γ, then, Γ entails another sentence, S2, if and only if S1 and not-S2 are logically inconsistent. Using ${\displaystyle \models }$ to stand for entailment we can write:

• If Γ =${\displaystyle \{A_{1},A_{2},\ldots ,A_{n}\}}$ ${\displaystyle \wedge }$ ${\displaystyle S1=A_{1}\wedge A_{2}\wedge \ldots \wedge A_{n}}$ then Γ ${\displaystyle \models }$ S2 ${\displaystyle {\stackrel {\rm {def}}{=}}}$ (S1 ${\displaystyle \wedge }$ ${\displaystyle \neg }$S2) ${\displaystyle \models }$ ${\displaystyle \bot }$.

If a set of one or more sentences, Γ, entails a sentence, S2, then S2 is called the logical consequent of the conjunction of the elements of Γ, S1,and the conjunction of the elements of Γ, S1, is said to logically imply S2.

jlkjklj In logic, entailment is a relation between logical propositions: a set of propositions ${\displaystyle \{A_{1},A_{2},\ldots ,A_{n}\}}$ entails a proposition ${\displaystyle B}$ if and only if the conjunction ${\displaystyle A=A_{1}\wedge A_{2}\wedge \ldots \wedge A_{n}}$ logically contradicts the negation ${\displaystyle \neg B}$. When this is the case, we say that A logically implies B, or that B is a logical consequent of A.

A set of propositions Γ = ${\displaystyle \{A_{1},A_{2},\ldots ,A_{n}\}}$ entails a sentence ${\displaystyle S2}$ if and only if the conjunction ${\displaystyle S1=A_{1}\wedge A_{2}\wedge \ldots \wedge A_{n}}$ logically contradicts the negation ${\displaystyle \neg S2}$. When this is the case, we say that S1 logically implies S2, or that S2 is a logical consequent of S1.

Γ = ${\displaystyle \{A_{1},A_{2},\ldots ,A_{n}\}}$ entails a sentence ${\displaystyle S2}$ if and only if the conjunction ${\displaystyle S1=A_{1}\wedge A_{2}\wedge \ldots \wedge A_{n}}$ logically contradicts the negation ${\displaystyle \neg S2}$. When this is the case, we say that S1 logically implies S2, or that S2 is a logical consequent of S1.

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test test--31.49.82.106 (talk) 16:52, 16 October 2014 (UTC) test— Philogos (talk) 16:57, 16 October 2014 (UTC) test--— Philogos (talk) 17:01, 16 October 2014 (UTC)

^[4]

sider refs

Sider (1997), Armstrong (1980): Armstrong, David M. (1980). “Identity Through Time.” In Peter van Inwagen (ed.), Time and Cause, 67-68 Dordrecht: D. Reidel.

Hughes (1986): Hughes, C. (1986)). “Is a Thing Just the Sum of Its Parts?” Proceedings of the Aristotelian Society 85: 213-33.

Heller (1984, 1990,1992,1993) Heller, Mark (1984). “Temporal Parts of Four Dimensional Objects.” Philo- sophical Studies 46: 323-34. Reprinted in Rea 1997: 12.-330. Heller, Mark (1990). The Ontology of Physical Objects: Four-dimensional Hunks of Matter. Cambridge: Cambridge University Press. Heller, Mark (1992). “Things Change.” Philosophy and Phenomenological Research 52: 695-304 Heller, Mark (1993). “Varieties of Four Dimensionalism.” Australasian Journal of Philosophy 71: 47-59.

Lewis (1983, 1986). Lewis, David (1983). “Survival and Identity.” In Philosophical Papers, Volume 1, 55-7. Oxford: Oxford University Press. With postscripts. Originally published in Amelie O. Rorty, ed., The Identities of Persons (Berkeley: University of California Press, 1976), 17-40. Lewis, David (1986a). On the Plurality of Worlds. Oxford: Basil Blackwell. Lewis, David (1986b). Philosophical Papers, Volume 2. Oxford: Oxford University Press.

Adams, Robert Merrihew †). “Time and Thisness.” In French et al. (1986), 315™. Armstrong, David M. €). “Identity Through Time.” In Peter van Inwagen (ed.), Time and Cause, 67À. Dordrecht: D. Reidel. Chisholm, Roderick ~). Person and Object: A Metaphysical Study. La Salle, Illinois: Open Court Publishing Co. Dau, Paolo †). “Part-Time Objects.” In French et al. (1986), 459¼. Evans, Gareth €). “Can There Be Vague Objects?” Analysis 38: 208. Fine, Kit Œ). “Compounds and Aggregates.” Noûs 28_): 137p. French, Peter, Theodore E. Uehling, Jr. and Howard K. Wettstein (eds.) †). Midwest Studies in Philosophy XI: Studies in Essentialism. Minneapolis: University of Minnesota Press. Geach, Peter z). “Some Problems about Time.” 302. Berkeley: Uni- versity of California Press. Graham, George ). “Persons and Time.” Southern Journal of Philosophy 15: 308. Haslanger, Sally Œ). “Humean Supervenience and Enduring Things.” Australasian Journal of Philosophy 72: 339±. Haslanger, Sally and Roxanne Marie Kurtz (eds.) _). Persistence: Contempo- rary Readings. Cambridge, MA: MIT Press. Heller, Mark „). “Temporal Parts of Four Dimensional Objects.” Philo- sophical Studies 46: 323œ. Reprinted in Rea 1997: 320Ø. — ˆ). The Ontology of Physical Objects: Four-dimensional Hunks of Matter. Cambridge: Cambridge University Press. 31

— Š). “Things Change.” Philosophy and Phenomenological Research 52: 695Ä. — ‹). “Varieties of Four Dimensionalism.” Australasian Journal of Philosophy 71: 47±. Hirsch, Eli ‚). The Concept of Identity. Oxford: Oxford University Press. Hughes, C. †). “Is a Thing Just the Sum of Its Parts?” Proceedings of the Aristotelian Society 85: 213›. Kazmi, Ali Akhtar ˆ). “Parthood and Persistence.” Canadian Journal of Philosophy, Supplementary Volume 16: 227¨. Leonard, Henry S. and Nelson Goodman ‘). “The Calculus of Individuals and its Uses.” Journal of Symbolic Logic 5: 45­. Lewis, David ƒ). “Survival and Identity.” In Philosophical Papers, Volume 1 , 55•7. Oxford: Oxford University Press. With postscripts. Originally published in Amelie O. Rorty, ed., The Identities of Persons (Berkeley: University of California Press, 1976), 17-40. — † a). On the Plurality of Worlds. Oxford: Basil Blackwell. — † b). Philosophical Papers, Volume 2. Oxford: Oxford University Press. Markosian, Ned ). “Brutal Composition.” Philosophical Studies 92: 211©. Mellor, D. H. ). Real Time. Cambridge: Cambridge University Press. Merricks, Trenton Œ). “Endurance and Indiscernibility.” Journal of Philoso- phy 91: 165Ä. — ). “On the Incompatibility of Enduring and Perduring Entities.” Mind 104: 523Y. Perry, John (ed.) }). Personal Identity. Berkeley: University of California Press. Prior, A.N. x). “Changes in Events and Changes in Things.” In Papers on Time and Tense, 7‘. London: Oxford University Press. 32

Quine, W. V. O. ~). “Whither Physical Objects.” In R.S. Cohen, P.K. Feyerabend and M.W. Wartofsky (eds.), Essays in Memory of Imre Lakatos, 497D. Dordrecht: D. Reidel Publishing Company. — ). Theories and Things. Cambridge, MA: Harvard University Press. Rea, Michael (ed.) ). Material Constitution. Lanham, Maryland: Rowman & Little_eld. Sider, Theodore ‹). “Van Inwagen and the Possibility of Gunk.” Analysis 53: 285É. — Ž a). “All the World’s a Stage.” Australasian Journal of Philosophy 74: 433+. Reprinted in Haslanger and Kurtz 2006: 91O. — Ž b). “Merricks on Perdurance/Endurance Incompatibility.” Never published; but material from this paper appeared in chapter 3 of Sider (2001). — _). Four-Dimensionalism. Oxford: Clarendon. Simons, Peter ‡). Parts: A Study in Ontology. Oxford: Clarendon. Thomson, Judith Jarvis ƒ). “Parthood and Identity across Time.” Journal of Philosophy 80: 201. Reprinted in Rea 1997: 25£. Unger, Peter ). “I Do Not Exist.” In G. F. Macdonald (ed.), Perception and Identity: Essays Presented to A. J. Ayer with His Replies to Them, 235©. New York: Macmillan. Reprinted in Rea 1997: 175È. van Inwagen, Peter ). “The Doctrine of Arbitrary Undetached Parts.” Paci_c Philosophical Quarterly 62: 123_. Reprinted in van Inwagen 2001: 75Ì. — ˆ a). “Four-Dimensional Objects.” Noûs 24: 245­. Reprinted in van Inwagen 2001: 111Q. — ˆ b). Material Beings. Ithaca, NY: Cornell University Press. — _). Ontology, Identity and Modality. Cambridge: Cambridge University Press. 33

Wiggins, David ). “Mereological Essentialism: Asymmetrical Essential Dependence and the Nature of Continuants.” In Ernest Sosa (ed.), Essays on the Philosophy of Roderick Chisholm, 297Í. Amsterdam: Rodopi. — €). Sameness and Substance. Cambridge, Mass.: Harvard University Press. Williamson, Timothy Œ). Vagueness. London: Routledge.

Argument: Prevailing usage in logic

The prevailing use of the term argument in logic is that it (a) consists of one or more premises and a conclusion (b) the premises purport to support the conclusion (c) in the case of deductive argument, the premises are purported to entail the conclusion (d) Various terms are used in the literature when saying what the premises and the conclusion are including statements, sentences (by which are meant declarative or indicative sentences), propositions, claims. All authors agree that whichever terms they have used , they are referring to whatever it is they consider to be either true or false (i.e. truthbearers ).

The following citations from reliable sources are offered in evidence for the above:

• The Cambridge Dictionary of Philosophy, 2nd Ed. CUM, 1995: "Argument: a sequence of statements such that some of them (the premises) purport to give reason to accept another of them, the conclusion"; Stanford Enc. Phil., Classical Logic;
• Internet Encyclopedia of Philosophy."Argument", <http://www.iep.utm.edu/argument/>: "An argument is a connected series of statements or propositions, some of which are intended to provide support, justification or evidence for the truth of another statement or proposition. Arguments consist of one or more premises and a conclusion. The premises are those statements that are taken to provide the support or evidence; the conclusion is that which the premises allegedly support."
• Standford Encyclopedia Of Philosophy, Informal Logic : "The premises of a valid deductive argument guarantee the truth of the conclusion. If the premises are true, the conclusion cannot be false. Informal logic tends to categorize arguments in terms of a consequent distinction between "deductive" and "inductive" arguments (a distinction that Govier [1987] aptly calls "the great divide"). In contrast with valid deductive arguments, the premises of a good inductive argument render a conclusion only probable, leaving it possible that the premises are true and the conclusion false (identifying poor arguments as deductive or inductive is inherently problematic: perhaps it can best be said that poor deductive and inductive arguments are arguments that in some way approximate good deductive and inductive forms)."
• Wesley Salman, Logic, PH 1963. pp 2,3 : "Arguments are often used to convince, and this is one of those important and legitimate function; however logic is not concerned with the persuasive power of argument. ..Roughly speaking, an argument is a conclusion standing in relation to its supporting evidence." More precisely, an argument is a group of statements standing in relation to each other. (Footnote: The term "statement" is used to refer to components of arguments because it is philosophically more neutral than alternatives such as "sentence" or "proposition". No technical definition of "statement is offered here, because any definition would raise controversies in the philosophy of language which need not trouble the beginner. More sophisticated readers may supply whatever technical definition seems most appropriate to them.) An argument consists of one statement which is the conclusion and one or more statements of supporting evidence. The statements of evidence are called "premises".
• Mates, Elementary Logic, 1972, p 4, 5 ".. Logic investigates the relation of consequence that holds between the premises and the conclusion of a sound argument... By an argument we mean a system of declarative sentences(of a single language) one of which is designated as the conclusion and the other as premises...Sentences are usually classified as declarative, interrogative, imperative etc. Characteristic of declarative sentences is that they are true or false, and it is these that are of primary interest to the logician."
• Jennifer Fisher, The Philosophy of Logic, 2008, p 6: "An argument ..is a set of sentences in which one or sentences are supposed to give some sort of support to another sentence." and p 24 14 "a set of sentences in which one sentence (sentences) is (are) supposed to give some sort of support to another sentence."
• Anthony Harrison-Barbet, Mastering Philosophy, p 13: "In an argument we pass from one or more propositions called premises to another proposition called the conclusion"
• LTF Gamit, Logic Language and Meaning, 1991, p 1 "For our purposes it is convenient to see an argument as a sequence of sentences, with the premises at the beginning and the conclusion at the end of the argument." p 6 "An argument is composed of indicative sentences. It does not contain any questions, for example."
• Barwise & Ethcmendy, Language Proof and Logic, 1999, page 42: "..an arguments is any series of statement in which one (called the concusion) is meant to follow from, or be supported by the others (called the premises)"
• Sybil Wolfram, Philosophical Logic, 1989: p 10 "An argument is generally said to be valid if the conclusion follows from the premises" p 276 "Sentence: (varied usage) here used of series of words bounded by full stops etc"; p 33 "A meaningful declarative sentence is, as a first approximation, one which could express a truth (convey information)
• Ian Hacking, A concise Introduction to Logic, Random House, NY; 1972, pp 5,6: "We can divide an argument into two parts. There is the part that states the conclusion and the part that gives the reasons. Statements giving reasons are called (27) PREMISES/CONCLUSION. The (28)_______________ give reasons for the (29)______________"
• Ralph Johnson's Manifest Rationality: A pragmatic theory of argument (2000) "One view of argument sees it as a set of statements, (propositions, assertions, beliefs, and judgments), one of which, the conclusion, is supported by the others — the premises. A definition of this sort can be found in every kind of logic text, whether deductive or inductive, formal or informal. }}
• The Oxford Companion to Philosophy (Honderich, 1995)p 47 : "In the most important sense for philosophy an argument is a complex consisting of a set of propositions (called its premises) and a proposition (called its conclusion). You can use an argument by asserting its premises and drawing or inferring its conclusion"

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