scholarly journals Truthmaker Semantics for Relevant Logic

2020 ◽  
Vol 49 (4) ◽  
pp. 681-702
Author(s):  
Mark Jago
Keyword(s):  
Relevant Logic ◽  
Philosophical Idea ◽  
Relevant Implication ◽  
Natural Notion ◽  
Truthmaker Semantics ◽  
In Virtue Of ◽  
Excluded Middle

AbstractI develop and defend a truthmaker semantics for the relevant logic R. The approach begins with a simple philosophical idea and develops it in various directions, so as to build a technically adequate relevant semantics. The central philosophical idea is that truths are true in virtue of specific states. Developing the idea formally results in a semantics on which truthmakers are relevant to what they make true. A very natural notion of conditionality is added, giving us relevant implication. I then investigate ways to add conjunction, disjunction, and negation; and I discuss how to justify contraposition and excluded middle within a truthmaker semantics.

scholarly journals A non-transitive relevant implication corresponding to classical logic consequence

2019 ◽  
Vol 16 (2) ◽  
pp. 10
Author(s):  
Peter Verdée ◽  
Inge De Bal ◽  
Aleksandra Samonek
Keyword(s):  
Classical Logic ◽  
Sequent Calculus ◽  
Modus Ponens ◽  
Relevant Logic ◽  
Object Language ◽  
Cut Rule ◽  
Consequence Relation ◽  
Relevant Implication ◽  
Relevant Logics ◽  
Traditional Sense

In this paper we first develop a logic independent account of relevant implication. We propose a stipulative denition of what it means for a multiset of premises to relevantly L-imply a multiset of conclusions, where L is a Tarskian consequence relation: the premises relevantly imply the conclusions iff there is an abstraction of the pair <premises, conclusions> such that the abstracted premises L-imply the abstracted conclusions and none of the abstracted premises or the abstracted conclusions can be omitted while still maintaining valid L-consequence.          Subsequently we apply this denition to the classical logic (CL) consequence relation to obtain NTR-consequence, i.e. the relevant CL-consequence relation in our sense, and develop a sequent calculus that is sound and complete with regard to relevant CL-consequence. We present a sound and complete sequent calculus for NTR. In a next step we add rules for an object language relevant implication to thesequent calculus. The object language implication reflects exactly the NTR-consequence relation. One can see the resulting logic NTR-> as a relevant logic in the traditional sense of the word.       By means of a translation to the relevant logic R, we show that the presented logic NTR is very close to relevance logics in the Anderson-Belnap-Dunn-Routley-Meyer tradition. However, unlike usual relevant logics, NTR is decidable for the full language, Disjunctive Syllogism (A and ~AvB relevantly imply B) and Adjunction (A and B relevantly imply A&B) are valid, and neither Modus Ponens nor the Cut rule are admissible.

scholarly journals Arithmetic Formulated Relevantly

2021 ◽  
Vol 18 (5) ◽  
pp. 154-288
Author(s):  
Robert Meyer
Keyword(s):  
Intuitionistic Logic ◽  
Natural Deduction ◽  
Relevant Logic ◽  
Peano Arithmetic ◽  
Critical Problem ◽  
First Order ◽  
Order Form ◽  
Relevant Implication ◽  
Relevant Logics ◽  
Natural Way

The purpose of this paper is to formulate first-order Peano arithmetic within the resources of relevant logic, and to demonstrate certain properties of the system thus formulated. Striking among these properties are the facts that (1) it is trivial that relevant arithmetic is absolutely consistent, but (2) classical first-order Peano arithmetic is straightforwardly contained in relevant arithmetic. Under (1), I shall show in particular that 0 = 1 is a non-theorem of relevant arithmetic; this, of course, is exactly the formula whose unprovability was sought in the Hilbert program for proving arithmetic consistent. Under (2), I shall exhibit the requisite translation, drawing some Goedelian conclusions therefrom. Left open, however, is the critical problem whether Ackermann’s rule γ is admissible for theories of relevant arithmetic. The particular system of relevant Peano arithmetic featured in this paper shall be called R♯. Its logical base shall be the system R of relevant implication, taken in its first-order form RQ. Among other Peano arithmetics we shall consider here in particular the systems C♯, J♯, and RM3♯; these are based respectively on the classical logic C, the intuitionistic logic J, and the Sobocinski-Dunn semi-relevant logic RM3. And another feature of the paper will be the presentation of a system of natural deduction for R♯, along lines valid for first-order relevant theories in general. This formulation of R♯ makes it possible to construct relevantly valid arithmetical deductions in an easy and natural way; it is based on, but is in some respects more convenient than, the natural deduction formulations for relevant logics developed by Anderson and Belnap in Entailment.

scholarly journals Negación dialéctica y lógica transitiva (I)

1983 ◽  
Vol 15 (43) ◽  
pp. 51-78
Author(s):  
Lorenzo Peña
Keyword(s):  
Mathematical Logic ◽  
Fuzzy Sets ◽  
Paraconsistent Logic ◽  
The World ◽  
Recent Developments ◽  
Law Of Excluded Middle ◽  
The Law ◽  
In Virtue Of ◽  
Excluded Middle

In this essay I bring up the issue of how to deal with dialectical views -especialIy with dialectic negation- from the standpoint of a transitive logic, which is a particular paraconsistent logic. After briefly tracing the development of the debate between dialectic thinkers and those who, hewing to entrenched logical theories, did out of hand reject any contradictorial proposal -up to recent developments of paraconsistent systems of mathematical logic- I canvass a variety of grounds shoring up the thesis of the contradictoriality of the world. Chief among them is fuzziness. The paper tries to show that fuzziness has nothing to do with uncertainty, and that accepting fuzzy sets and facts not only does not compel us to waive the law of excluded middle, but -on the base of reasonable presuppositions- entails recognition of that law's relevant instances -the ones that purportedly ought to be dropped as true sentences, should fuzziness be acknowledged. True enough, fuzziness plus excluded middle leads to contradiction, i.e. to negation inconsistency. But then fuzziness is -or can he viewed as being- negation inconsistency, since a fuzzy situation is one wherein something neither is nor fails to be the case: which -in virtue of involutivity of simple negation and De Morgan laws- means that something both ia and yet is not the case. [L.P.]

Exact Truthmakers, Modality, and Essence

2020 ◽  
pp. 124-140
Author(s):  
Bob Hale
Keyword(s):  
Special Interest ◽  
Truthmaker Semantics ◽  
The Right ◽  
In Virtue Of

Non-reductive essentialist explanations of necessities and possibilities in general locate their source in a special, basic or fundamental kind of necessities—those directly arising from the essences of things. All remaining necessities and possibilities can be seen as grounded, more or less indirectly, in these basic necessities. If this idea is on the right lines, it ought to be possible to distinguish clearly between those necessities which are directly grounded in the natures of things, and those which are indirectly so grounded. Special interest is shown in this question, treated within the framework of Fine’s version of truthmaker semantics. We might expect that within this framework, it would be possible to capture the distinction between what is directly true in virtue of essence, and what is only indirectly true.

scholarly journals Starting the Dismantling of Classical Mathematics

2018 ◽  
Vol 15 (2) ◽  
pp. 280
Author(s):  
Ross Brady
Keyword(s):  
Relevant Logic ◽  
Classical Mathematics ◽  
Law Of Excluded Middle ◽  
The Law ◽  
Excluded Middle

This paper uses the relevant logic, MCQ, of meaning containment to explore mathematics without various classical theses, in particular, without the law of excluded middle.

What Is an Institution?

2007 ◽  
pp. 5-27 ◽  
Author(s):  
J. Searle
Keyword(s):  
Physical Structure ◽  
Necessary Condition ◽  
Collective Intentionality ◽  
Institutional Facts ◽  
Institutional Fact ◽  
The Status ◽  
The Creation ◽  
State Of Affairs ◽  
In Virtue Of ◽  
Typical Point

The author claims that an institution is any collectively accepted system of rules (procedures, practices) that enable us to create institutional facts. These rules typically have the form of X counts as Y in C, where an object, person, or state of affairs X is assigned a special status, the Y status, such that the new status enables the person or object to perform functions that it could not perform solely in virtue of its physical structure, but requires as a necessary condition the assignment of the status. The creation of an institutional fact is, thus, the collective assignment of a status function. The typical point of the creation of institutional facts by assigning status functions is to create deontic powers. So typically when we assign a status function Y to some object or person X we have created a situation in which we accept that a person S who stands in the appropriate relation to X is such that (S has power (S does A)). The whole analysis then gives us a systematic set of relationships between collective intentionality, the assignment of function, the assignment of status functions, constitutive rules, institutional facts, and deontic powers.

Acerca del supuesto fundamentalismo de Wittgenstein en Sobre la certez

2007 ◽  
Vol 13 ◽  
Author(s):  
José M. Ariso Salgado
Keyword(s):  
Ludwig Wittgenstein ◽  
On Certainty ◽  
In Virtue Of ◽  
Basic Beliefs

RESUMENAl analizar si Ludwig Wittgenstein mantiene una posición fundamentalista en Sobre la certeza, suele discutirse si la citada obra se adapta al modelo de fundamentalismo propuesto por Avrum Stroll. Tras exponer las líneas básicas de dicho modelo, en esta nota se mantiene que Sobre la certeza no se adapta al modelo de Stroll debido al importante papel que Wittgenstein concede al contextualismo. Además, se añade que Wittgenstein no puede ser calificado de fundamentalista porque no reconoce ninguna propiedad que, sin tener en cuenta la diversidad de casos particulares, permita justificar de forma conjunta todas nuestras creencias básicas.PALABRAS CLAVEWITTGENSTEIN, FUNDAMENTALISMO, CONTEXTUALISMO, CERTEZAABSTRACTDid Wittgenstein hold a foundationalist position in On Certainty? When this question is tackled, it is often discussed, whether On Certainty fits in the foundationalist model devised by Avrum Stroll. After expounding the main lines of this model, I hold that On Certainty does not fit in Stroll’s model, because of the important role Wittgenstein attaches to contextualism. Furthermore, I add that Wittgenstein cannot be seen as a foundationalist –or a coherentist–, because he does not admit any feature in virtue of which the whole of our basic beliefs are justified without considering circumstances at all.KEYWORDSWITTGENSTEIN, CERTAINTY, FOUNDATIONALISM, CONTEXTUALISM

The Uniqueness of God in Anselm’s Monologion

2014 ◽  
Vol 17 (1) ◽  
pp. 72-93 ◽  
Author(s):  
Christian Tapp
Keyword(s):  
Successful Attempt ◽  
Central Case ◽  
In Virtue Of

In this paper, Anselm’s argument for the uniqueness of God or, more precisely, something through which everything that exists has its being (Monologion 3) is reconstructed. A first reading of the argument leads to a preliminary reconstruens with one major weakness, namely the incompleteness of a central case distinction. In the successful attempt to construct a more tenable reconstruens some additional premises which are deeply rooted in an Anselmian metaphysics are identified. Anselm’s argument seems to depend on premises such as that if two things have the same nature, then there is one common thing from which they have this nature and in virtue of which they exist. Furthermore it appears that infinite regresses are excluded by the premise that if everything that exists is through something, then there is something through which it is “most truly”.

The Green New Deal

2019 ◽  
Author(s):  
Robert C. Hockett
Keyword(s):  
New Deal ◽  
Large Scale ◽  
Public Investment ◽  
Climate Science ◽  
Time Frame ◽  
White Paper ◽  
Good News ◽  
Carbon Neutrality ◽  
The One ◽  
In Virtue Of

This white paper lays out the guiding vision behind the Green New Deal Resolution proposed to the U.S. Congress by Representative Alexandria Ocasio-Cortez and Senator Bill Markey in February of 2019. It explains the senses in which the Green New Deal is 'green' on the one hand, and a new 'New Deal' on the other hand. It also 'makes the case' for a shamelessly ambitious, not a low-ball or slow-walked, Green New Deal agenda. At the core of the paper's argument lies the observation that only a true national mobilization on the scale of those associated with the original New Deal and the Second World War will be up to the task of comprehensively revitalizing the nation's economy, justly growing our middle class, and expeditiously achieving carbon-neutrality within the twelve-year time-frame that climate science tells us we have before reaching an environmental 'tipping point.' But this is actually good news, the paper argues. For, paradoxically, an ambitious Green New Deal also will be the most 'affordable' Green New Deal, in virtue of the enormous productivity, widespread prosperity, and attendant public revenue benefits that large-scale public investment will bring. In effect, the Green New Deal will amount to that very transformative stimulus which the nation has awaited since the crash of 2008 and its debt-deflationary sequel.

Aesthetic and Historical Values - Their Difference and Why It Matters

2020 ◽  
Vol 29 (5) ◽  
pp. 519-535
Author(s):  
Levi Tenen
Keyword(s):  
Natural Environments ◽  
Aesthetic Value ◽  
Environmental Preservation ◽  
Historical Significance ◽  
Recent Scholarship ◽  
In Virtue Of

Aesthetic and historical values are commonly distinguished from each other. Yet there has not been sustained discussion of what, precisely, differs between them. In fact, recent scholarship has focused on various ways in which the two are related. I argue, though, that historical value can differ in an interesting way from aesthetic value and that this difference may have significant implications for environmental preservation. In valuing something for its historical significance, it need not always be the case that there is a reason to want people to experience the entity. Valuing something for its aesthetic merit, by contrast, does imply a reason to want people to experience the entity. I suggest that in virtue of this difference, some historical values may offer better justification for preserving natural environments than do aesthetic considerations.

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