In their paper Nothing but the Truth Andreas Pietz and Umberto Rivieccio present Exactly True Logic, an interesting variation upon the four-valued logic for first-degree entailment FDE that was given by Belnap and Dunn in the 1970s. Pietz & Rivieccio provide this logic with a Hilbert-style axiomatisation and write that finding a nice sequent calculus for the logic will presumably not be easy. But a sequent calculus can be given and in this paper we will show that a calculus for (...) the Belnap-Dunn logic we have defined earlier can in fact be reused for the purpose of characterising ETL, provided a small alteration is made—initial assignments of signs to the sentences of a sequent to be proved must be different from those used for characterising FDE. While Pietz & Rivieccio define ETL on the language of classical propositional logic we also study its consequence relation on an extension of this language that is functionally complete for the underlying four truth values. On this extension the calculus gets a multiple-tree character—two proof trees may be needed to establish one proof. (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. (...) Much of Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices for (1) can (...) be computed from the calculus. (shrink)

How can humanist principles of respect, dignity, and care inform and improve design for non-human lifeforms? This paper uses ageing and dying urban trees to understand how architectural, urban, and landscape design respond to nonhuman concerns. It draws on research in plant sciences, environmental history, ethics, environmental management, and urban design to ask: how can more-than-human ethics improve multispecies cohabitation in urban forests? The paper hypothesises that concepts of dignity and respect can underline the capabilities of nonhuman lifeforms and lead (...) to improved designs for multispecies cohabitation. To investigate the implications of this ethical framework, we 1) indicate injustices of current management in relation to natural and cultural histories of trees; 2) outline a conceptual framework that includes large old trees as stakeholders in urban communities; and 3) use this framework in a thought experiment with urban trees in Melbourne, outlining comparative design outcomes. Our findings show that the expansion of dignity to include nonhuman life is possible and plausible. Such an extension can justify and encourage design innovation for multiple species and sites. The resulting design practices will lead to improvements by supporting communities of trees at all stages of their life-cycles, including old age, death, and rebirth. This approach requires substantial shifts in accepted thinking and practices including history, ethics, aesthetics, regulation, and education. Design can play a significant role in the necessary transitions by demonstrating tangible and positive outcomes. In this context, history emerges as an essential tool that can extend societal imagination by situating possible future places in the context of ancient and ongoing geological, evolutionary, ecological, and cultural processes. (shrink)

In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic, or multiple-conclusion calculi for classical logic). -/- The sequent derivations and proofnets are both simple extensions of sequents and proofnets for classical propositional logic, in which the new machinery—to take account of the modal vocabulary—is directly motivated (...) in terms of the simple, universal Kripke semantics for S5. The sequent system is cut-free and the circuit proofs are normalising. (shrink)

In a recent paper we have defined an analytic tableau calculus PL_16 for a functionally complete extension of Shramko and Wansing's logic based on the trilattice SIXTEEN_3. This calculus makes it possible to define syntactic entailment relations that capture central semantic relations of the logic---such as the relations |=_t, |=_f, and |=_i that each correspond to a lattice order in SIXTEEN_3; and |=, the intersection of |=_t and |=_f,. -/- It turns out that our method of characterising these semantic relations---as (...) intersections of auxiliary relations that can be captured with the help of a single calculus---lends itself well to proving interpolation. All entailment relations just mentioned have the interpolation property, not only when they are defined with respect to a functionally complete language, but also in a range of cases where less expressive languages are considered. For example, we will show that |=, when restricted to L_{tf}, the language originally considered by Shramko and Wansing, enjoys interpolation. This answers a question that was recently posed by M. Takano. (shrink)

Ludwig Wittgenstein, in the "Remarks on the Foundation of Mathematics", often refers to contradictions as deserving special study. He is said to have predicted that there will be mathematical investigations of calculi containing contradictions and that people will pride themselves on having emancipated themselves from consistency. This paper examines a way of taking this prediction seriously. It starts by demonstrating that the easy way of understanding the role of contradictions in a discourse, namely in terms of pure convention within (...) a specific linguistic community, is naive and therefore to be avoided. A number of steps will then be taken to formulate and justify what will be called a ‘containment-account’ of contradiction. This term refers to a way of understanding how a contradiction in a discourse can be contained without allowing it to infect the entire discourse with inconsistency. The account builds on work done by N. Rescher and involves complex ontologies that are either over-determined or under-determined at some points. These worlds are such that, for some P, they allow us to deny simultaneously both that P and that -P. They likewise allow us to hold both that P and that -P. The ontological status of P and that of -P are considered independent issues, so as to block the inference from P and -P to the conjunction (P & -P). In this way, the task of containment is carried out by the complexity of the ontology determining the possible worlds under consideration. The paper proceeds by countering the objection that such possible worlds are useless fictions. This is carried out by highlighting three significant areas of application, one in philosophy of science, one in philosophy of religion, and one in the area of epistemology. In general, one may say that, in some language-games, a contradiction can be a useful instrument to attest that rationality goes beyond ratiocination, in other words to indicate that there is more to discourse and practice than what can be expressed in precise algorithmic trees. The upshot of the entire argument is that the proposed ‘containment-account’ of contradiction can be an adequate illustration of how Wittgenstein’s prediction is not sterile, but a possible source of inspiration. (shrink)

We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on trees are sound and complete for (...) the basic positive distributive substructural logic $\mathsf {B}^+$, that collection frames on multisets are sound and complete for $\mathsf {RW}^+$ (the relevant logic $\mathsf {R}^+$, without contraction, or equivalently, positive multiplicative and additive linear logic with distribution for the additive connectives), and that collection frames on sets are sound for the positive relevant logic $\mathsf {R}^+$. The completeness of set frames for $\mathsf {R}^+$ is, currently, an open question. (shrink)

A wide family of many-valued logics—for instance, those based on the weak Kleene algebra—includes a non-classical truth-value that is ‘contaminating’ in the sense that whenever the value is assigned to a formula φ⁠, any complex formula in which φ appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with multiple (...) contaminating values. In this paper, we consider the countably infinite family of multiple-conclusion consequence relations in which classical logic is enriched with one or more contaminating values whose behavior is determined by a linear ordering between them. We consider some motivations and applications for such systems and provide general characterizations for all consequence relations in this family. Finally, we provide sequent calculi for a pair of four-valued logics including two linearly ordered contaminating values before defining two-sided sequent calculi corresponding to each of the infinite family of many-valued logics studied in this paper. (shrink)

The problem of algorithmic structuring of proofs in the sequent calculi LK and LKB ( LK where blocks of quantifiers can be introduced in one step) is investigated, where a distinction is made between linear proofs and proofs in tree form. In this framework, structuring coincides with the introduction of cuts into a proof. The algorithmic solvability of this problem can be reduced to the question of k-l-compressibility: "Given a proof of length k , and l ≤ k (...) : Is there is a proof of length ≤ l ?" When restricted to proofs with universal or existential cuts, this problem is shown to be (1) undecidable for linear or tree-like LK-proofs (corresponds to the undecidability of second order unification), (2) undecidable for linear LKB-proofs (corresponds to the undecidability of semi-unification), and (3) decidable for tree-like LKB -proofs (corresponds to a decidable subprob- lem of semi-unification). (shrink)

Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than forcing their unification. In this paper, we introduce nested sequent calculi for propositional standpoint logics---proof systems that manipulate trees whose nodes are multisets of formulae---and show how to automate standpoint reasoning by means of non-deterministic proof-search algorithms. To obtain worst-case complexity-optimal proof-search, we introduce a novel technique in the (...) context of nested sequents, referred to as "coloring," which consists of taking a formula as input, guessing a certain coloring of its subformulae, and then running proof-search in a nested sequent calculus on the colored input. Our technique lets us decide the validity of standpoint formulae in CoNP since proof-search only produces a partial proof relative to each permitted coloring of the input. We show how all partial proofs can be fused together to construct a complete proof when the input is valid, and how certain partial proofs can be transformed into a counter-model when the input is invalid. These "certificates" (i.e. proofs and counter-models) serve as explanations of the (in)validity of the input. (shrink)

Phylogenetic models traditionally represent the history of life as having a strictly-branching tree structure. However, it is becoming increasingly clear that the history of life is often not strictly-branching; lateral gene transfer, endosymbiosis, and hybridization, for example, can all produce lateral branching events. There is thus motivation to allow phylogenetic models to have a reticulate structure. One proposal involves the reconciliation of genealogical discordance. Briefly, this method uses patterns of disagreement – discordance – between trees of different genes to (...) add lateral branching events to phylogenetic trees of taxa, and to estimate the most likely cause of these events. I use this practice to argue for: (1) a need for expanded accounts of multiple-models idealization, (2) a distinction between automatic and manual de-idealization, and (3) recognition that idealization may serve the meso-level aims of science in a different way than hitherto acknowledged. (shrink)

Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences of a (...) flaw. However, since different programs and machines can interact with (or be nested into) one another, we need to account for different kind of errors, and this calls for an evaluation of systems with multiple contaminating values. In this paper, we make steps toward these evaluation systems by considering two logics, HYB1 and HYB2, whose semantic interpretations account for two contaminating values beside classical values 0 and 1. In particular, we provide two main formal contributions. First, we give a characterization of their relations of (multiple-conclusion) logical consequence—that is, necessary and sufficient conditions for a set Δ of formulas to logically follow from a set Γ of formulas in HYB1 or HYB2 . Second, we provide sound and complete sequent calculi for the two logics. (shrink)

Bilateralism is the view that the speech act of denial is as primitive as that of assertion. Bilateralism has proved helpful in providing an intuitive interpretation of formalisms that, prima facie, look counterintuitive, namely, multiple-conclusion sequent calculi. Under this interpretation, a sequent of the form $\Gamma \vdash \Delta$ is regarded as the statement that it is incoherent, according to our conversational norms, to occupy the position of asserting all the sentences in $\Gamma$ and denying all the sentences in (...) $\Delta$. Some have argued, based on this interpretation, that the notion of invalidity is as conceptually primitive and important as the notion of validity: whereas the latter is couched in terms of what positions are incoherent and hence untenable, the former is couched in terms of what positions are coherent and hence tenable. My ultimate goal in this paper is to contest this view. Based on a novel technical account of the two notions—one that I find more accurate than the existing accounts in the literature—I shall argue that the notion of incoherence takes conceptual priority over the notion of coherence. (shrink)

The future is different from the past. What is past is fixed and set in stone. The future, on the other hand, is open insofar as it holds numerous possibilities. Branching-tree models of time account for this asymmetry by positing an ontological difference between the past and the future. Given a time t, a unique unified past lies behind t, whereas multiple alternative existing futures lie ahead of t. My goal in this paper is to show that there (...) is an incompatibility between the way branching-tree models account for the open future and the possibility of time travel. That is, I argue that once time travel enters the picture, branching time fails to model the openness of the future by means of alternative future branches. I show how this holds independently of whether branching-time models are cashed out in A-theoretic or B-theoretic terms. (shrink)

In Plato’s dialogues, Socrates calls things like justice, piety, and largeness “forms.” In several of these dialogues, he makes clear that forms are very different from familiar objects like tables and trees. Why, exactly, does he think that they differ and how are they supposed to do so? This chapter argues that in the Phaedo Socrates does not assume that they are different, but rather, over five stages of the dialogue, provides an account of how and why they do so. (...) To fully understand the claims made in the first stage, one must look to the next stage, and so on until the final stage. Socrates' ultimate reason for distinguishing forms from ordinary objects does not depend on our intuitions about things like justice and largeness, nor on the distinction between universals and particulars. Ultimately, forms cannot be ordinary objects because the form of f-ness must cause every f-thing to be f, but no ordinary object could serve as such a cause. They cannot do so because they have multiple parts and are receptive of opposites; by contrast, the form of f-ness must be simple and unchanging, since it causes every f-thing to be f. (shrink)

As Francis Bacon put it on the frontispiece of his Novum Organum, grafting an apocalyptic vision on a research program, multi pertransibunt et multiplex erit scientia. The development of science becomes steadily associated with the end of earthly life, a theme that would resound deeply in Western thought up until Goethe’s Faust. What grounds then the multiplicity of knowledge? What is the common trunk out of which all realms of knowledge unfold, like the burgeoning branches of the celebrated tree? (...) After the Augustinian imprint of the first Christian centuries and after the admirable effort of the high scholastics’ Aristotelian and Christian synthesis, the seventeenth century undertakes new scientific work with the need of a new steady ground. All the big names of the modern era, Francis Bacon, Galileo, Descartes, Robert Boyle, Spinoza or Leibniz, found themselves engaged in the search for a common trunk of wisdom, each of them nourishing the intimate conviction that they possessed the philosophical core which would satisfy the learned men’s newly found appetite for indefinitely extending knowledge. In doing this, all of these masters needed to confront the philosophical tradition that they received, reworking and merging together the old structures of science through this epistemological prism of the search for the unity of knowledge. (Vlad Alexandrescu). (shrink)

In this paper, we investigated multiple machine learning classifiers which are, Multinomial Naive Bayes, Support Vector Machine, Decision Tree, K Nearest Neighbors, and Random Forest in a text classification problem. The data we used contains real and fake job posts. We cleaned and pre-processed our data, then we applied TF-IDF for feature extraction. After we implemented the classifiers, we trained and evaluated them. Evaluation metrics used are precision, recall, f-measure, and accuracy. For each classifier, results were summarized and (...) compared with others. (shrink)

A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems.

This paper challenges the negative attitudes towards labelled proof systems, usually referred to as semantic pollution, by arguing that such critiques overlook the full potential of labelled calculi. The overarching objective is to develop a practice-based philosophical analysis of labelled calculi to provide insightful considerations regarding their proof-theoretic and philosophical value. To achieve this, successful applications of labelled calculi and related results will be showcased, and comparisons with other relevant works will be discussed. The paper ends by (...) advocating for a more practice-based approach towards the philosophical understanding of proof systems and their role in structural proof theory. (shrink)

This paper focuses on the framework for the compositional relations of properties in the sciences, or "realization relations", offered by Ken Aizawa and Carl Gillett (A&G) in a series of papers, and in particular on the analysis of "multiple realizations" they build upon it. I argue that A&G's analysis of multiple realization requires an account of levels and I try to show, then, that the A&G framework is not successful under any of the extant accounts of levels. There (...) is consequently a real concern tha thte A&G framework for realization may not be viable. (shrink)

This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In (...) the single-agent case, we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate. (shrink)

We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm , Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3Tstit are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also Xstit can be characterized through relational frames, omitting the use of BT+AC (...) frames. (shrink)

Descriptive accounts of the nature of explanation in neuroscience and the global goals of such explanation have recently proliferated in the philosophy of neuroscience and with them new understandings of the experimental practices of neuroscientists have emerged. In this paper, I consider two models of such practices; one that takes them to be reductive; another that takes them to be integrative. I investigate those areas of the neuroscience of learning and memory from which the examples used to substantiate these models (...) are culled, and argue that the multiplicity of experimental protocols used in these research areas presents specific challenges for both models. In my view, these challenges have been overlooked largely because philosophers have hitherto failed to pay sufficient attention to fundamental features of experimental practice. I demonstrate that when we do pay attention to such features, evidence for reduction and integrative unity in neuroscience is simply not borne out. I end by suggesting some new directions for the philosophy of neuroscience that pertain to taking a closer look at the nature of neuroscientific experiments. (shrink)

We study the first-order theories of some natural and important classes of coloured trees, including the four classes of trees whose paths have the order type respectively of the natural numbers, the integers, the rationals, and the reals. We develop a technique for approximating a tree as a suitably coloured linear order. We then present the first-order theories of certain classes of coloured linear orders and use them, along with the approximating technique, to establish complete axiomatisations of the four (...) classes of trees mentioned above. (shrink)

Dwork, Hardt, Pitassi, Reingold, & Zemel [6] introduced two notions of fairness, each of which is meant to formalize the notion of similar treatment for similarly qualified individuals. The first of these notions, which we call additive metric fairness, has received much attention in subsequent work studying the fairness of a system composed of classifiers which are fair when considered in isolation [3, 4, 7, 8, 12] and in work studying the relationship between fair treatment of individuals and fair treatment (...) of groups [6, 7, 13]. Here, we extend these lines of research to the second, less-studied notion, which we call multiplicative metric fairness. In particular, we exactly characterize the fairness of conjunctions and disjunctions of multiplicative metric fair classifiers, and the extent to which a classifier which satisfies multiplicative metric fairness also treats groups fairly. This characterization reveals that whereas additive metric fairness becomes easier to satisfy when probabilities of acceptance are small, leading to unfairness under functional and group compositions, multiplicative metric fairness is better-behaved, due to its scale-invariance. (shrink)

Abstract: There has recently been controversy over the existence of 'multiple realization' in addition to some confusion between different conceptions of its nature. To resolve these problems, we focus on concrete examples from the sciences to provide precise accounts of the scientific concepts of 'realization' and 'multiple realization' that have played key roles in recent debates in the philosophy of science and philosophy of psychology. We illustrate the advantages of our view over a prominent rival account ( Shapiro, (...) 2000 and 2004 ) and use our work to rebut recent objections to the long-standing claim that psychological properties are multiply realized. For we use scientific evidence, in combination with our more precise theoretical framework, to show that we have strong reason to believe that psychological properties are indeed multiply realized both at the biochemical and neuronal levels. (shrink)

A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in (...) the number of truth values, and it is shown that this bound is tight. (shrink)

The aim of this paper is to introduce and explain display calculi for a variety of logics. We provide a survey of key results concerning such calculi, though we focus mainly on the global cut elimination theorem. Propositional, first-order, and modal display calculi are considered and their properties detailed.

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable (...) proof-theoretic properties from its associated labelled calculus. (shrink)

In the literature on multiple realizability and the identity theory, cases of neural plasticity have enjoyed a very limited role. The present article attempts to remedy this small influence by arguing that clinical and experimental evidence of quite extensive neural reorganization offers compelling support for the claim that psychological kinds are multiply realized in neurological kinds, thus undermining the identity theory. In particular, cases are presented where subjects with no measurable psychological deficits also have vast, though gradually received, neurological (...) damage. Common objections and concerns are also discussed and rejected. 1 Introduction2 The GRP, Serial Lesion Effect, and Multiple Realizability2.1 A case study of the serial lesion effect2.2 Evaluating the case study’s evidence for multiple realizability3 The GRP More Generally4 Objections to the GRP as Evidence for Multiple Realizability4.1 Small plastic effects and neurological taxonomies4.2 But do neural regions and locations even matter at all?4.3 But are there not other options besides location?5 Conclusion. (shrink)

Our aim here is to lay the groundwork for formal tree-ring analysis combining data from dendrochronology with formal techniques from semantics. We will present the basic syntax of, and basic compositional semantics of tree-ring structures.

During multiple testing, researchers often adjust their alpha level to control the familywise error rate for a statistical inference about a joint union alternative hypothesis (e.g., “H1,1 or H1,2”). However, in some cases, they do not make this inference. Instead, they make separate inferences about each of the individual hypotheses that comprise the joint hypothesis (e.g., H1,1 and H1,2). For example, a researcher might use a Bonferroni correction to adjust their alpha level from the conventional level of 0.050 to (...) 0.025 when testing H1,1 and H1,2, find a significant result for H1,1 (p < 0.025) and not for H1,2 (p > .0.025), and so claim support for H1,1 and not for H1,2. However, these separate individual inferences do not require an alpha adjustment. Only a statistical inference about the union alternative hypothesis “H1,1 or H1,2” requires an alpha adjustment because it is based on “at least one” significant result among the two tests, and so it refers to the familywise error rate. Hence, an inconsistent correction occurs when a researcher corrects their alpha level during multiple testing but does not make an inference about a union alternative hypothesis. In the present article, I discuss this inconsistent correction problem, including its reduction in statistical power for tests of individual hypotheses and its potential causes vis-à-vis error rate confusions and the alpha adjustment ritual. I also provide three illustrations of inconsistent corrections from recent psychology studies. I conclude that inconsistent corrections represent a symptom of statisticism, and I call for a more nuanced inference-based approach to multiple testing corrections. (shrink)

Multiple realisation prompts the question: how is it that multiple systems all exhibit the same phenomena despite their different underlying properties? In this paper I develop a framework for addressing that question and argue that multiple realisation can be reductively explained. I illustrate this position by applying the framework to a simple example – the multiple realisation of electrical conductivity. I defend my account by addressing potential objections:contra Polger and Shapiro, Batterman, and Sober, I claim that (...) multiple realisation is commonplace, that it can be reductively explained, but that it requires asui generisreductive explanatory strategy. (shrink)

Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms of (...) the first-order theory of the generating class C, and indicate the problems obstructing such general results for the other classes. These problems arise from the possible existence of nondefinable paths in trees, that need not satisfy the first-order theory of C, so we have started analysing first order definable and undefinable paths in trees. (shrink)

The notion of multiple location plays an important role in the characterization of endurantism. Several authors have recently offered cases intended to demonstrate the incoherence of multiple location. I argue that these cases do not succeed in making multiple location problematic. Along the way, several crucial issues about multiple location and its use by endurantists are clarified.

Do trees of life have roots? What do these roots look like? In this contribution, I argue that research on the origins of life might offer glimpses on the topology of these very roots. More specifically, I argue (1) that the roots of the tree of life go well below the level of the commonly mentioned ‘ancestral organisms’ down into the level of much simpler, minimally living entities that might be referred to as ‘protoliving systems’, and (2) that further (...) below, a system of roots gradually dissolves into non-living matter along several functional dimensions. In between non-living and living matter, one finds physico-chemical systems that I propose to characterize by a ‘lifeness signature’. In turn, this ‘lifeness signature’ might also account for a diverse range of biochemical entities that are found to be ‘less-than-living’ yet ‘more-than-non-living’. (shrink)

The Tree of Life has traditionally been understood to represent the history of species lineages. However, recently researchers have suggested that it might be better interpreted as representing the history of cellular lineages, sometimes called the Tree of Cells. This paper examines and evaluates reasons offered against this cellular interpretation of the Tree of Life. It argues that some such reasons are bad reasons, based either on a false attribution of essentialism, on a misunderstanding of the problem (...) of lineage identity, or on a limited view of scientific representation. I suggest that debate about the Tree of Cells and other successors to the traditional Tree of Life should be formulated in terms of the purposes these representations may serve. In pursuing this strategy, we see that the Tree of Cells cannot serve one purpose suggested for it: as an explanation for the hierarchical nature of taxonomy. We then explore whether, instead, the tree may play an important role in the dynamic modeling of evolution. As highly-integrated complex systems, cells may influence which lineage components can successfully transfer into them and how they change once integrated. Only if they do in fact have a substantial role to play in this process might the Tree of Cells have some claim to be the Tree of Life. (shrink)

The paper aims at critical reconsideration of a motif popular in Indian literary, ritual, and pictorial traditions – a tree goddess (yakṣī, vṛkṣakā) or a woman embracing a tree (śālabhañjīkā, dohada), which points to a close and intimate bond between women and trees. At the outset, I present the most important phases of the evolution of this popular motif from the ancient times to present days. Then two essential characteristics of nature recognized in Indian visual arts, literature, religions (...) and philosophy will be distinguished: (1) a dynamic, creative, self-sufficient and inexhaustible power, and (2) a passive, merely reproductive or vegetative, and dependent field of potentiality. The paper is to demonstrate the interdependence of the popular concepts of nature identified with femininity, and their iconic representations circulating for centuries in Indian culture, with a specific line of argument repeatedly used in social practices and public debates. While doing so, I consider the semiotic function of a cultural topos which proves to be an effective instrument for construing and supporting the gender roles and gender identities. As a modern example illustrating vitality and persuasive power of the motif of yakṣī and śālabhañjīkā, I refer to the Chipko Movement, a group of rural women based in the Garhwal Himalayas (state Uttarakhand), who fought against the mass cut of trees in the 1970s. They were involved in the wide-spread environmental campaign which significantly affected the ecological policy of the local and state authorities. Thus, a traditional motif of the visual arts has been revived and re-elaborated by the activists of this ecofeminist movement through converting the symbolic potential of yakṣī/śālabhañjīkā into social and political power. (shrink)

The multifaceted importance of old forests and large ancient trees is evident in both their ecological and cultural significance. A recent article underscores the urgency of preserving ancient and rare trees due to their crucial role in forest ecosystems. By providing a global perspective on tree biodiversity and analyzing the age distribution and biodiversity of tree species worldwide, the article highlights the critical need to protect these trees to prevent species extinction and foster biodiversity. Furthermore, studies emphasize the (...) importance of rare trees, some of which remain undiscovered, in maintaining the overall health and resilience of forest ecosystems. (shrink)

This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated (...) labelled calculi, such as completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics. (shrink)

Multiple Realizability (MR) must still be regarded as one of the principal arguments against type reductionist accounts of higher-order properties and their special laws. Against this I argue that there is no unique MR but rather a multitude of MR categories. In a slogan: MR is itself “multi-realized”. If this is true then we cannot expect one unique reductionist strategy against MR as an anti-reductionist argument. The main task is rather to develop a taxonomy of the wide variety of (...) MR cases and to sketch possible reductionist answers for each class of cases. The paper outlines some first steps in this direction. (shrink)

Although the Evans argument against vague identity has been much discussed, proposah for blocking it have not so far satisfied general conditions which any solution ought to meet. Moreover, the relation between ontically vague identity and ontic vagueness more generally has not yet been satisfactorily addressed. I advocate a way of resisting the Evans argument which satisfies the conditions. To show how this approach can vindicate particular cases of ontically vague identity, I develop a framework for describing ontic vagueness in (...) general in terms of multiple actualities. This provides aprìncipled approach to ontically vague identity which is unaffected by the Evans argument. (shrink)

We survey main developments, results, and open problems on interval temporal logics and duration calculi. We present various formal systems studied in the literature and discuss their distinctive features, emphasizing on expressiveness, axiomatic systems, and (un)decidability results.

Kilimanjaro is an example of what some philosophers would call a ‘vague object’: it is only roughly 5895 m tall, its weight is not precise and its boundaries are fuzzy because some particles are neither determinately part of it nor determinately not part of it. It has been suggested that this vagueness arises as a result of semantic indecision: it is because we didn’t make up our mind what the expression “Kilimanjaro” applies to that we can truthfully say such things (...) as “It is indeterminate whether this particle is part of Kilimanjaro”. After reviewing some of the limitations of this approach, I will propose an alternative account, based on a new semantic relation—multiple reference—capable of holding in a one-many pattern between a term and several objects in the domain. I will explain how multiple reference works, what differentiates it from plural reference and how it might be used to accommodate at least some aspects of our ordinary discourse about vague objects. (shrink)

Gathering the attitudes of the examined respondents would be very significant in some evaluation models. Therefore, a multiple criteria approach based on the use of the neutrosophic set is considered in this paper. An example of the evaluation of restaurants is considered at the end of this paper with the aim to present in detail the proposed approach.

In this article, we perform a detailed proof theoretic investigation of a wide number of relevant logics by employing the well-established methodology of labelled sequent calculi to build our intended systems. At the semantic level, we will characterise relevant logics by employing reduced Routley-Meyer models, namely, relational structures with a ternary relation between worlds along with a unique distinct element considered as the real (or actual) world. This paper realizes the idea of building a variety of modular labelled (...) class='Hi'>calculi by reflecting, at the syntactic level, semantic informations taken from reduced Routley-Meyer models. Central results include proofs of soundness and completeness, as well as a proof of cut- admissibility. (shrink)

This paper will present two contributions to teaching introductory logic. The first contribution is an alternative tree proof method that differs from the traditional one-sided tree method. The second contribution combines this tree system with an index system to produce a user-friendly tree method for sentential modal logic.

This paper develops co-ordinated multiple-domain supervenience relations to model determination and dependence relations between complex entities and their constituents by appealing to R-related pairs and by making use of associated isomorphisms. Supervenience relations are devised for order-sensitive and repetition-sensitive mereologies, for mereological systems that make room for many-many composition relations, as well as for hierarchical mereologies that incorporate compositional and hylomorphic structure. Finally, mappings are provided for theories that consider wholes to be prior to their parts.

This paper explores the ethical insights provided by Anne Truitt's minimalist sculptures, as viewed through the phenomenological lenses of Hannah Arendt's investigations into the co-constitution of reality and Maurice Merleau-Ponty's investigations into perception. Artworks in their material presence can lay out new ways of relating and perceiving. Truitt's works accomplish this task by revealing the interactive motion of our embodied relations and how material objects can actually help to ground our reality and hence human potentiality. Merleau-Ponty shows how our prereflective (...) bodies allow incompossible perceptions to coexist. Yet this same capacity of bodies to gather multiple perceptions together also lends itself to the illusion that we see from only one perspective. If an ethical perspective becomes reified into one position, it then becomes detached from reality, and the ethical potential is actually lost. At the same time, phenomenologically understood, the real world does not exist in terms of static matter, but is instead a web of contextual relations and meanings. An ethics that does not take embodied relations into account—that allows for only one perspective—ultimately loses its capacity for flexibility, and for being part of a common and shared reality. (shrink)