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A '''grounded relation''' over a [[sequence]] of [[set]]s is a mathematical object consisting of two components. The first component is a subset of th * [[Logic of relatives]]

...r as the [[propositional calculus|propositional or sentential]] aspects of logic are concerned. ...1–115 in ''The New Elements of Mathematics by Charles S. Peirce, Volume 4, Mathematical Philosophy'', [[Carolyn Eisele]] (ed.), Mouton, The Hague, 1976.

...">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. ...]] that are subject to logical description. In formal logic, differential logic treats the principles that govern the use of a ''differential logical calcu

...Robert Kilwardby]]. In 1979 he began the study of the history of grammar, logic and rhetoric at Oxford in the period 1220-1320. In 1979 he went to the Pon * 'The Oxford Condemnations of 1277 in Grammar and Logic', in English Logic and Semantics, ed. Braakhuis, Nijmegen 1981.

...">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. .... In all of these uses it is understood that the various terms refer to a mathematical object and not the corresponding sign or syntactic expression.

...">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. ...n of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities'', Macmillan Publishers, 1854. Reprinted with correction

.../search&#63;q&#61;&#34;Original+Logic+Error&#34;+HOLE Humankind's Original Logic Error] (HOLE).

...">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. The '''logic of relatives''', more precisely, the '''logic of relative terms''', is the study of [[relation (mathematics)|relation]]s

[https://oeis.org/wiki/User:Jon_Awbrey/Mathematical_Notes Mathematical Notes] ...s://oeis.org/wiki/User:Jon_Awbrey/Peirce%27s_Logic_Of_Information Peirce's Logic Of Information]

...rsci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives Peirce's Logic Of Relatives] ...i.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction]

* [http://meta.wikimedia.org/wiki/Help:Displaying_a_formula Mathematical formulas] * [http://en.wikipedia.org/wiki/Wikipedia:Mathematical_symbols Mathematical symbols]

...prepare equivocal signs, that are otherwise recalcitrant to being ruled by logic, for the application of logical laws. The example of &#950;&#969;&#959;&#9 ...subject are not yet harvested. I will only say that the subject concerns Logic, but that the divisions so obtained must not be confounded with the differe

...">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. ...that is, up to somorphism, constituted by the structural relationships of mathematical objects called ''propositions''.

{{DISPLAYTITLE:Epitext for Differential Logic and Dynamic Systems}} ===Qualitative Logic and Quantitative Analogy===

...It presents a consummate integration of his ideas on the interrelations of logic, mathematics, and semeiotic, or the theory of signs. <p>Logic is the study of the essential nature of signs.</p>

...">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. ...study from the perspectives of abstract algebra on the one hand and formal logic on the other.

''The Theory of Gambling and Statistical Logic'' ranks as the most popular of Epstein's technical books. He served as a co * Richard A. Epstein, ''The Theory of Gambling and Statistical Logic'' (revised edition), Academic Press, 1995, {{ISBN|0-12-240761-X}}. (Second

* SIL m = ''Studies in Logic by Members of the Johns Hopkins University'', page m. :* ''Volume 2 : Elements of Logic'', 1932.

...originally to honor scientists in the fields of the "physical, biological, mathematical, or engineering sciences." The Committee on the National Medal of Science | "For laying the foundation for today's flourishing study of mathematical [[logic]]."

'''[[Table of mathematical symbols|&#8810; Table of Mathematical Symbols &#8811;]]''' '''[[GetMeta:Mathematical symbols|&#8810;Have Tape Must Loop&#8811;&#8810;HT(ML)*&#8811;]]'''

[[Table of mathematical symbols|'''Table of Mathematical Symbols''']] A '''relation''' is a mathematical object of a very general type, the generality of which is best approached i

...">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. ...e are ''three'' items involved in each row.&nbsp; The relation itself is a mathematical object, defined in terms of concepts from set theory, that carries all the

...">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. This completes the derivation of the mathematical objects that are denoted by the signs <math>{}^{\backprime\backprime} \righ

=Mathematical Philosophy (10 Mar 2003)= > expressive power to limited subsets of logic.

=Mathematical Philosophy (10 Mar 2003)= > expressive power to limited subsets of logic.

...the Nature of Mathematics), in: Mancosu, P.: Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, Oxford University Press: Oxford-New Yo ...the Liar: The Modern Relevance of Medieval Solutions to the Liar Paradox, Logic, Epistemology and the Unity of Science, Springer Publishing Company

...tle as an authorities for his opinions. He derived the idea of music as a mathematical science from Aristotle’s position in the Posterior Analytics that music i ...Erfordensis (= Roberti Kilwardby ?) Sophisma TANTUM UNUM EST. [[Directory:Logic Museum/CIMAGL#1997|CIMAGL 1997]]

...igh level [[programming language]] which has become a model of clarity and mathematical rigor. He is one of the principal exponents of the science and art of [[pro |''For his pioneering effort in programming languages and mathematical notation resulting in what the computing field now knows as APL, for his co

...">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. ...er of relations. Relations and their combinations may be described in the logic of relative terms, in set theories of various kinds, and through a broadeni

{{DISPLAYTITLE:Functional Logic : Quantification Theory}} ==Toward a Functional Conception of Quantificational Logic==

...ale, William]], and [[Martha Kneale|Kneale, Martha]], ''The Development of Logic'', Oxford University Press, London, UK, 1962. ..., Jean]] (ed. 1967), ''From Frege To Gödel: A Source Book in Mathematical Logic, 1879–1931'', Harvard University Press, Cambridge, MA.

...ale, William]], and [[Martha Kneale|Kneale, Martha]], ''The Development of Logic'', Oxford University Press, London, UK, 1962. ..., Jean]] (ed. 1967), ''From Frege To Gödel: A Source Book in Mathematical Logic, 1879–1931'', Harvard University Press, Cambridge, MA.

...rt systems, dynamical systems, information theory, learning organizations, mathematical systems theory, operations research, simulation, and systems engineering. ...ecting the fields of [[control system]]s, [[electrical network]] theory, [[logic modeling]], and [[neuroscience]] in the 1940s. The name ''cybernetics'' w

And here is a classical logic proof of the type proposition: Here are three references on combinatory logic and lambda calculus, given in order of difficulty from introductory to adva

...were he utilized the will to believe doctrine to justify the [[axioms]] of logic, mathematics, and [[Kant|Kant's]] [[synthetic a priori]]. Later he would pu ...ogic." What he offers is something philosophers would recognize today as a logic covering the [[context of discovery]] and the [[hypothetico-deductive metho

A '''relation''' is a mathematical object of a very general type, the generality of which is best approached i A '''relation''' <math>L</math> is defined by specifying two mathematical objects as its constituent parts:

...henomena]]. As a form of philosophical inquiry, it examines the record of mathematical inquiry and poses questions regarding its aims, its conduct, and its result # What are the sources of mathematical subject matter?

...henomena]]. As a form of philosophical inquiry, it examines the record of mathematical inquiry and poses questions regarding its aims, its conduct, and its result # What are the sources of mathematical subject matter?

...ions of mathematics, among other applications. Boolean algebra has a rich mathematical theory, though unlike group theory which exhibits complex diversity in its ...exist. This suggests that it is impossible to have an infinitary Boolean logic for lack of terms.

Here, we describe the [[mathematics|mathematical]] meaning of '''transfinite ordinal numbers'''. They were introduced by [[ ...order]]ing with transfinite induction, where transfinite induction extends mathematical induction beyond the finite. Ordinals represent equivalence classes of wel

<font size=4>'''Differential Logic : Series A'''</font><br> ...e you have a really decent calculus for boolean functions or propositional logic, whatever you want to call it, is to compute the differentials of these fun

{{DISPLAYTITLE:Change In Logic}} logic, namely, to distinguish whatever things satisfy a description.

...">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. ...the systems of graphical syntax that Charles Sanders Peirce developed for logic.

...ize="3">☞</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. ...wikibiz.com/Charles_Sanders_Peirce Charles Sanders Peirce] developed for [[logic]].

...name="antikythera">{{cite web | author=Phillips, Tony | publisher=American Mathematical Society | year=2000 | title=The Antikythera Mechanism I | url=http://www.ma ...tch circuit, [[Nikola Tesla]] who filed for patents of devices containing logic gate circuits in 1898 (see [[List of Tesla patents]]), and [[Lee De Forest]

<font size=4>'''Differential Logic : Series B'''</font><br> logic, namely, to distinguish whatever things satisfy a description.

...">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. ...a sign is one that he gives in the context of providing a definition for ''logic'', and so it is informative to view it in that setting.

...''[[Acta Mathematica]]'', a century later still one of the world's leading mathematical journals. Through his influence in [[Stockholm]] he persuaded [[King Oscar ...o, beginning in 2004, the Nobel-like [[Shaw Prize]] included an award in [[mathematical science]]s. The [[Fields Medal]] is often described as the "Nobel Prize of

...and diversity. There are several different introductions to differential logic that I have written and distributed across the Internet. You might start w ...//stderr.org/pipermail/inquiry/2004-February/thread.html#1132 Differential Logic A]

...">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. ...rlies a particular conception of truth, such as those used in art, ethics, logic, mathematics, philosophy, the sciences, or any discussion that either menti

{{DISPLAYTITLE:Differential Logic : Introduction}} ...tes any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation that pervad

==Differential Logic 2002== or propositional logic, whatever you want to call it,

...ular conception of [[truth]], such as those used in [[art]], [[ethics]], [[logic]], [[mathematics]], [[philosophy]], the [[science]]s, or any discussion tha ...een truth and ''[[logical validity]]'', "because the fundamental notion of logic is validity and this is definable in terms of truth and falsehood" (Kneale

...ular conception of [[truth]], such as those used in [[art]], [[ethics]], [[logic]], [[mathematics]], [[philosophy]], the [[science]]s, or any discussion tha ...een truth and ''[[logical validity]]'', "because the fundamental notion of logic is validity and this is definable in terms of truth and falsehood" (Kneale

{{DISPLAYTITLE:Dynamics And Logic}} I am going to excerpt some of my previous explorations on differential logic and dynamic systems and bring them to bear on the sorts of discrete dynamic

==Logic As Semiotic== #[http://suo.ieee.org/ontology/thrd48.html#03070 Jon Awbrey (Aug 2001), "Logic As Semiotic", Ontology List].

...xt{Table 5.} ~~ \text{Syntax and Semantics of a Calculus for Propositional Logic}\!</math> ...alculus, see the entries on [[minimal negation operator]]s, [[zeroth order logic]], and [[Differential Propositional Calculus#Table A1. Propositional Forms

...or universals. Now by proving logic ''fictional'', Peirce believes he does logic a favor, that is, by saving it from the psychologists. This suggests that ...of the symbol itself which it cannot ''as a symbol'' transgress. ("On the Logic of Science" (1865), CE 1, 173.)

{{DISPLAYTITLE:Differential Logic}} ...ersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Sketch_2 Differential Logic : Sketch 2]. &#9734;'''

...t and employed as a scientist for 30 years, it is for his contributions to logic, mathematics, philosophy, and the theory of signs, or ''[[semeiotic]]'', th ...ed under the philosophies of knowledge, language, and science. Peirce saw logic as the formal branch of the theory of signs, or ''[[semiotics]]'', here usi

...een truth and ''[[logical validity]]'', "because the fundamental notion of logic is validity and this is definable in terms of truth and falsehood" (Kneale ...nevertheless said to be true or false of various objects. For example, in logic there are ''terms'' such as "man" or "woman" that are true of some things a

...een truth and ''[[logical validity]]'', "because the fundamental notion of logic is validity and this is definable in terms of truth and falsehood" (Kneale ...nevertheless said to be true or false of various objects. For example, in logic there are ''terms'' such as "man" or "woman" that are true of some things a

{{DISPLAYTITLE:Functional Logic : Inquiry and Analogy}} ...he three fundamental types of reasoning that Peirce adopted from classical logic. In Peirce's analysis both inquiry and analogy are complex programs of rea

.../math> respectively. The early CSP, as in his essay on &ldquo;Qualitative Logic&rdquo;, and also GSB, emphasized the <math>\mathrm{En}\!</math> interpretat ...of the ''weed and seed theorem'' (WAST). The proof is just an exercise in mathematical induction, once a suitable basis is laid down, and it will be left as an ex

...iconicity are worth buying, at least when it comes to graphical systems of logic, it will useful to introduce one more distinction that affects the types of ...w.math.uic.edu/~kauffman/Arithmetic.htm Box Algebra, Boundary Mathematics, Logic, and Laws of Form].

...atabase searches, through dynamic simulation and statistical reasoning, to mathematical theorem proving. Insofar as these tasks constitute specialized efforts, ea * Next, I will select mathematical systems theory as an indispensable tool, both for the analysis of inquiry i

{{DISPLAYTITLE:Peirce's 1870 Logic Of Relatives}} ...-context. Current style sheets for mathematical texts specify italics for mathematical variables, with upper case letters for sets and lower case letters for indi

...atabase searches, through dynamic simulation and statistical reasoning, to mathematical theorem proving. Insofar as these tasks constitute specialized efforts, ea ...of intelligent software systems that support inquiry. Then, I will select mathematical systems theory as an indispensable tool, both for the analysis of inquiry i

of propositional models, sentential logic, or zeroth order logic. starting about a decade ago, to begin to develop a "differential logic",

methods of differential geometry with the techniques of logic logic and dynamics in the study of intelligent systems can be seen in relation

===Differential Logic : First Approach=== ...re us, we have come to the verge of seeing how the word "model" is used in logic, namely, to distinguish whatever things satisfy a description.

{{DISPLAYTITLE:Differential Logic and Dynamic Systems 3.0}} ...Working Draft. The current version of this document is '''[[Differential Logic and Dynamic Systems 2.0]].'''''

; Mathematical Notes : [[User:Jon Awbrey/Mathematical Notes#CAT. Category Theory|CAT. Category Theory]]

...an, and scarcely at all as a philosopher. Even his work in philosophy and logic will not be understood until this fact becomes a standing premise of Peirci ...Boole, and other mathematicians of that era who had emphasized the role of mathematical symbolism. The rest of the section was written in response to a reader who

{{DISPLAYTITLE:Differential Logic and Dynamic Systems}} ...:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0|Differential Logic and Dynamic Systems 2.0]].'''''

...f the Disadvantage to Players of Multiple Decks in the Game of 21.” ''The Mathematical Scientist'', '''32''', 2, p. 57-69</ref><ref>http://www.appliedprobability Despite the logic of this suggestion, the park district continues to waste trees and taxpayer

...f the Disadvantage to Players of Multiple Decks in the Game of 21.” ''The Mathematical Scientist'', '''32''', 2, p. 57-69</ref><ref>http://www.appliedprobability Despite the logic of this suggestion, the park district continues to waste trees and taxpayer

...f the Disadvantage to Players of Multiple Decks in the Game of 21.” ''The Mathematical Scientist'', '''32''', 2, p. 57-69</ref><ref>http://www.appliedprobability Despite the logic of this suggestion, the park district continues to waste trees and taxpayer

...on integrating the methods of differential geometry with the techniques of logic programming. I will attempt to embody this project in the form of computer One of the chief theoretical difficulties that obstructs the unification of logic and dynamics in the study of intelligent systems can be seen in relation to

{{DISPLAYTITLE:Differential Logic and Dynamic Systems 2.0}} ...previous discussion on the problem of dealing with change and diversity in logic-based intelligent systems. It is useful to begin by summarizing essential

...onal logic'', ''sentential calculus'', or more inclusively, ''zeroth order logic'' (ZOL). ...ngth of the augmented string available as a parameter that can figure into mathematical inductions and motivate recursive proofs, and this handle on the generative

...previous discussion on the problem of dealing with change and diversity in logic-based intelligent systems. It is useful to begin by summarizing essential ...e development in his graphical systems of predicate, relational, and modal logic [Rob]. More recently, these ideas were revived and supplemented in an alte

...sort of hypothesis over a wider subject area can act to prime the pump of mathematical induction all the more generously, and actually increase the power of the r ...easoning built into it, and this disposition to a particular conception of logic may be lodged in such a way that it makes it nearly impossible to reflect o

...f the Disadvantage to Players of Multiple Decks in the Game of 21.” ''The Mathematical Scientist'', '''32''', 2, p. 57-69</ref><ref>http://www.appliedprobability Despite the logic of this suggestion, the park district continues to waste trees and taxpayer

...information that he developed from the time of his lectures on the &ldquo;Logic of Science&rdquo; at Harvard University (1865) and the Lowell Institute (18 ==Selections from Peirce's “Logic of Science” (1865&ndash;1866)==

...Jon Awbrey/Philosophical Notes#JITL. Just In Time Logic|JITL. Just In Time Logic]] | signifying facts of logic being very few in comparison with those which

...n deliberately ignored the "extraordinary claims" test for evidence when a mathematical climate model suggested that a substantial nuclear exchange could upset the ...Appelle]] notes that Sagan "wrote frequently on what he perceived as the [[logic|logical]] and [[empiricism|empirical]] [[fallacy|fallacies]] regarding UFOs

==Differential Logic 2003&ndash;2004== DLOG A. Differential Logic -- Series A

...amming'' in computer science (Wirth 1976, 49, 303) have a long ancestry in logic and philosophy, going back to a strategy for establishing or discharging co ...ficial intelligence (the prospective study of how we might think), and the logic of operations research (the normative study of how we ought to think in ord

The graph itself is a mathematical object and does not inhabit [[Category:Logic]]

Group theory, as a methodological subject, is used to illustrate the ''mathematical language'' (ML) approach, which ordinarily takes it for granted that signs ...us ignored as a factor of theoretical concern. This is appropriate to the mathematical level, which abstracts away from pragmatic factors and is intended precisel

.../www.logicmuseum.com/authors/aquinas/summa/Summa-I-7-10.htm Now at the new Logic Museum]

...'' discrete maths, it merely expresses banalities as formalisms (predicate logic, automata theory, syntax diagrams, set theory) borrowed from discrete maths ...temological theory embedded even in everyday experience (eg. the inductive logic we employ when we say "lemons are sour"). Saying "NLP is an epistemology" i

(Wirth 1976, 49, 303) have a long ancestry in logic and philosophy, going back logic (the normative study of how we ought to think in order to accomplish

...www.logicmuseum.com/authors/aquinas/summa/Summa-I-65-69.htm Now at the new Logic Museum]

...a] has quit [Quit: You cannot logic someone out of an opinion they did not logic themselves into] 08:19 < Isarra> And I ain't lunatic enough to say anything mathematical about it.

...a] has quit [Quit: You cannot logic someone out of an opinion they did not logic themselves into] 19:04 < pion> Oskr220: I can't find anything in that image that makes any mathematical sense.

...www.logicmuseum.com/authors/aquinas/summa/Summa-I-84-86.htm Now at the new Logic Museum]

...//www.logicmuseum.com/authors/aquinas/summa/Summa-I-1-6.htm Now at the new Logic Museum]

15:51 < Isarra> By the same logic files should also be protected, as they are similarly used in other pages, ...limits the money supply. Here the supply is being set by some rather dodgy mathematical assumptions.

18:57 < TParis> dekiss: It doesn't matter what the mathematical labels we use, you could use spanish if you chose. But two objects added w 19:01 < ToAruShiroiNeko> its sci-fi level logic but its cute to think about :p

May 02 14:21:40 <Headbomb|Laptop> you can just have find/replace logic and everything gets happy May 05 18:17:25 <Dragonfly6-7> I remember seeing that there's a mathematical proof of all possible electoral systems being broken

[23:07] <Matthew_> Heh, my logic is single-handedly deleting the entire Global Titleblacklist, ARG! [11:01] <mareklug> Dcoetzee btw, I ended up replacing the logic board on the 2005 iMac and never ended up getting the (replacement) mini se