Jean Buridan developed his theory of consequence within a semantical framework compatible with what we now call token-based semantics. In his Treatise on Consequences and Sophismata, Buridan showed...

Based on historical comparisons among master-pupil chains and other aspects of social networks among philosophers, some prmciples are suggested regarding long-term intellectual change. The higher the eminence ofphilosophers, the more tightly they are connected to mtergenerational chains of other eminent philosophers, and to horizontal circles of the intellectual community. Intellectual creativity proceeds through the contemporaneous development of rival positions, dividing up the available attention space in the intellectual community. Strong thought-communities, those that have strong external support for their institutional base, (...) subdivide to maximize internal distinctiveness; weakly supported thought-communities disappear or amalgamate by syncretism. External conditions thus affect the content of ideas indirectly by affecting the space available in the mternal field of the intellectual community. The content of philosophies, the degree of abstraction and self-conscious reflection upon intellectual operations, depends on how many generations intellectual networks maintain continuity under conditions of creative rivalry. New positions are produced by competitive appropriation of prior ideas and by negation of preexisting positions along the lines of greatest organizational rivalry. (shrink)

History and Philosophy of Logic, Volume 32, Issue 2, Page 187-191, May 2011.

Discrete supposition occurs whenever a discrete term, such as ‘Socrates‘, is the subject of a given proposition. I propose to examine this apparently simple notion. I shall draw attention to the incongruity, within a general theory of the semantic variation of terms in a propositional context, of the notion of discrete supposition, in which a term usually has a single semantic correlate. The incongruity comes to the fore in those treatises that attempt to describe discrete supposition as a sort of (...) personal supposition, although the same term cannot be in simple supposition in another propositional context, because it has no significate distinct from its suppositum. This shows a fundamental link between common signification, simple supposition and predicability, three notions that rely on the existence of a significate distinct and independent from the suppositum of the term. The connection is to be seen especially in William of Sherwood’s Introductiones, the only author of a terminist Summa who recognizes the existence of simple supposition for discrete terms. (shrink)

This paper shows that William Stanley Jevons was not precursor of logical positivism despite his attempt to build up a unified science. His mechanical reductionism was directed towards this project, and Jevons tried to found mathematics on logic through the development of a theory of number. We show that his attempts were unsuccessful, and that his errors remain visible within the totality of his mechanical system, including his economics. We argue that both his logic and his economics are comprehensible only (...) when interpreted in terms of extent of meaning, and that Jevons? system gives rise to difficulties when interpreted in terms of intent of meaning. We argue that Jevons? methodological recommendations were intended to bridge the gap between extent and intent of meaning. Although Jevons did not succeed in establishing a unified science, his flawed methodology resulted in one of the first applications of statistics to the social sciences. (shrink)

Investiga-se a possibilidade de uma abordagem do fenômeno do pluralismo lógico a partir de uma perspectiva inspirada no pensamento de Quine. A matematização da lógica termina por levar à flexibilização da teoria lógica, logo surgindo, não apenas sistemas complementares e alternativos à lógica clássica, mas também a questão da admissibilidade de mais do que um sistema lógico. A tal posição se dá o nome “pluralismo lógico”. Quine foi um destacado defensor da lógica clássica a partir de uma perspectiva monista, ainda (...) que admitisse em princípio a possibilidade de sua revisão. Pode-se, contudo, investigar se as linhas gerais do pensamento quineano são compatíveis com uma perspectiva pluralista. Algumas possibilidades são levantadas tomando em consideração propostas como as teorias pluralistas de Carlo Dalla Pozza e Richard Epstein. Conclui-se que, embora Quine não concebesse a possibilidade de apoiar o pluralismo lógico, a sua filosofia ajuda a enquadrar e avaliar as maneiras de estudar o assunto. (shrink)

If true, this is one the the most important papers in the history of mathematics. the natural numbers are defined and one to one correspondence between the natural numbers is made precise. the paper deals with the very fundamentals of arithmetic and the logical principles differ quite markedly from those used by georg cantor.

The principles that AN INSTANCE OF A CLASS IS THE CLASS and A CLASS IS AN INSTANCE OF ITSELF allow for the so called LAWS OF THOUGHTIDENTITY - WHAT IS, IS.CONTRADICTION - NOTHING BOTH IS and IS NOT.EXCLUDED MIDDLE - EVERYTHING IS or IS NOT.and allow us to adopt a bivalent system. Everything essential for primary logic is provided.Though this is not the place to discuss it, it should be noted that the development of general logic with its current theories (...) of class, identity and natural numbers could take a very different course from the one it currently pursues.Human thought would have had to evolve to a high level of development before any systematic attempt to analyse it could have been made. It seems it was in the floruit of the Greek civilisation that this attempt was first made. The issues in this paper were of prime concern to those ancient thinkers and their achievements were considerable. Since those times further developments have occurred, many of which they would not have dreamed, but to this day there are still great issues that have not been resolved. The state of the art leaves much to be desired and it is my hope that this paper will contribute to its progress.If the ideas in this paper are true, then it seems we have come across the very origins of human rationality. (shrink)

Además de los indemostrables, la lógica estoica incluye varias reglas de reducción. En este trabajo, analizo la primera de ellas con el fin de comprobar si fue derivada formalmente a partir de los indemostrables o los estoicos pudieron plantearla a partir del uso de sus capacidades naturales de razonamiento. De esta manera, trato de mostrar que tenemos razones para apoyar ambas posibilidades y, basándome en un enfoque semántico como el de la teoría de los modelos mentales, de ofrecer argumentos al (...) respecto. (shrink)

This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is (...) a settled feature of the landscape. His paper opens the first of four sections that examine, in turn, historical philosophical assessments of judgement and reason; their place in early modern philosophy; the notion of judgement and logical theory in Wolff, Kant and Neo-Kantians like Windelband; their development in the Husserlian phenomenological paradigm; and the work of Bolzano, Russell and Frege. The papers, whose authors include Per Martin-Löf, Göran Sundholm, Michael Della Rocca and Robin Rollinger, represent a finely judged editorial selection highlighting work on philosophers exercised by the question of whether or not an epistemic notion of judgement has a role to play in logic. The volume will be of profound interest to students and academicians for its application of historical developments in philosophy to the solution of vexatious contemporary issues in the foundation of logic. ​. (shrink)

Moral reductionist believes that the reality of moral qualities are the same qualities which can be expressed with immoral words. Such an ontological view has an epistemological aspect which states our understanding of moral facts is either our understanding of immoral facts or our deductions of immoral understanding. From moral reductionists and especially the naturalists’ point of view, the ability to explain moral knowledge without resorting to some theories such as moral intuition is considered to be an important advantage and (...) even a strong reason for their view. Therefore, the present paper is going to study the reductionistic explanations about moral knowledge and justifications of moral believes. We have come to the conclusion that among the explanations presented by the naturalists, analytic knowledge has the same problems which have discredited the theory of analytic reductionism. Also, deducing value from non-value is either facing the logical gap of is-must; or if there is a meaningful descriptive-valuable link, we can’t finally come to unconditional moral results. (shrink)

Is it possible to distinguish communities of arguers by tracking the argumentation schemes they employ? There are many ways of relating schemes to communities, but not all are productive. Attention must be paid not only to the admissibility of schemes within a community of argumentational practice, but also to their comparative frequency. Two examples are discussed: informal mathematics, a convenient source of well-documented argumentational practice, and anthropological evidence of nonstandard reasoning.

I defend the compatibility of the classical theistic doctrine of divine providence, which includes infallible foreknowledge of all future events, with a libertarian understanding of creaturely free will. After setting out the argument for theological determinism, which purports to show the inconsistency of foreknowledge and freedom, I reject several responses as inadequate and then defend the ‚Ockhamist‛ response as successful. I further argue that the theory of middle knowledge or ‚Molinism‛ is crucial to the viability of the Ockhamist response, and (...) proceed to defend Molinism against the most pressing objections. Finally, I argue that a proper understanding of the Creator-creature relationship accounts for why no explanation can be given for how God’s middle knowledge comes about. (shrink)

A comprehensive survey of Martin-Löf's constructive type theory, considerable parts of which have only been presented by Martin-Löf in lecture form or as part of conference talks. Sommaruga surveys the prehistory of type theory and its highly complex development through eight different stages from 1970 to 1995. He also provides a systematic presentation of the latest version of the theory, as offered by Martin-Löf at Leiden University in Fall 1993. This presentation gives a fuller and updated account of the system. (...) Earlier, brief presentations took no account of the issues related to the type-theoretical approach to logic and the foundations of mathematics, while here they are accorded an entire part of the book. Readership: Comprehensive accounts of the history and philosophy of constructive type theory and a considerable amount of related material. Readers need a solid background in standard logic and a first, basic acquaintance with type theory. (shrink)

Is formal logic a failure? It may be, if we accept the context-independent limits imposed by Russell, Frege, and others. In response to difficulties arising from such limitations I present a Toulmin-esque social recontextualization of formal logic. The results of my project provide a positive view of formal logic as a success while simultaneously reaffirming the social and contextual concerns of argumentation theorists, critical thinking scholars, and rhetoricians.

I characterize the deductivist ideal of justification and, following to a great extent Toulmin’s work The Uses of Argument, I try to explain why this ideal is erroneous. Then I offer an alternative model of justification capable of making our claims to knowledge about substantial matters sound and reasonable. This model of justification will be based on a conception of justification as the result of good argumentation, and on a model of argumentation which is a pragmatic linguistic reconstruction of Toulmin’s (...) model of argument. (shrink)

Certain distributivity results for Lukasiewicz’s infinite-valued logic Lℵ0..

The paper emphasizes significant resemblances between the Informal Logic Initiative and the Lvov-Warsaw School – the Polish philosophical movement, the rise of which is associated with “the Golden Age of Science and Letters”. The correspondence between informal logic and the logical studies of the LWS will be explored by discussing their subject-matter, goals, and methods. The project focused on applying logical studies of the LWS in analyzing and assessing arguments will be proposed.

Da bi ocenil Fregejev prispevek k utemeljitvi moderne logike se je avtor v svojem prispevku vrnil v preteklost, do Leibnizove lingua characteristica. Vzporednic ni težko najti: odprava dvoumja v govorici in zgradba enoznačnega jezika na tej osnovi, možnost razrešitve spoznavne moči s kalkulom, kar ločuje leibnizoviko tradicijo od kartezijanske. Srž obeh teorij je en in isti boj znanstvenega govora z govorico, razlika pa je v načinu, kako prehod k zapisu udejani ideal calculus ratiocinator. Različni načini, kako so elementi tega boja (...) med seboj povezani, lahko nudijo tudi osnove za premero specifike družbene razsežnosti obeh pristopov. (shrink)

In the analysis of syllogistic reasoning, a type of inference patternbased on the chaining of terms through quantified statements, two interpretationsabout them can be found in the literature. One is the so-called set-based interpretation,which assumes that quantified statements and syllogisms talk aboutquantity-relationships between sets. The other one, the so-called conditionalinterpretation, assumes that they talk about conditional propositions and howstrong are the links between the antecedent and the consequent. In this paper,we expose both models and formulate three relevant questions to be (...) taken intoaccount for a further development of this type of reasoning. (shrink)

Some authors have talken about the problem of the future contingents Aristotle exposed in De Interpretatione IX. But most of them do not explain the role of that chapter in his own work. Last analysis always try to find a formal solution. And this is very significative because De Interpretatione is a treatise that belongs to the semantic of the Organon. In this article we show that: 1. The aim of the problem of future contigents is not only formal and (...) the frame of the Aristotle’s solution. 2. Its implication with others important concepts in his philosophy like “substance”, “truth” and “dialectics”. (shrink)

The nominalist attitude in medieval logic supported a fully extensional conception of the sense of expressions. Many arguments against this approach were raised at that time. I would like to show in this article that there is a extensional conception of notions in current logic, namely in the interpretation of formal theories and the creation models of them and that, and how, traditional arguments against the extensional conception are relevant also for logic today.