In recent years, semantical partiality has emerged as an important explanatory concept in philosophical logic as well as in the study of natural language semantics. Despite the many applications, however, a number of mathematically intriguing questions associated with this concept have received only very limited attention. ;The present dissertation aims to present a systematic study of certain types of partiality in the area of basic model theory. Two types of issues are given special attention: Introducing partially defined models, there are (...) many ways to generalize the classical truth definition for sentences of a simple first order language relative to standard, complete models. Different interpretations of the formal framework motivate conflicting truth definitions between language and partial models: A partial model can be taken to represent a part of the world, or a partial information set. The truth of a sentence can be supported directly by a part of the world, but can also follow indirectly from an information set. These notions are related, and the relation motivates a comparison between various weaker and stronger alternative truth definitions. Results are obtained about the extent to which these truth definitions differ, and a number of characterization results are deduced. ;Among other conditions that are not expressible in the framework of standard, complete model theory, a condition of monotonicity or persistence of truth relative to partial models is argued to follow under both the given interpretations of the formal framework. The final chapter investigates the relation between such conditions and expressibility properties in general. These discussions culminate with a combined Lindstrom and persistence characterization theorem. (shrink)

This article investigates models of axiomatizations related to the semantic conception of truth presented by Kripke (J Philos 72(19):690–716, 1975), the so-called _fixed-point semantics_. Among the various proof systems devised as a proof-theoretic characterization of the fixed-point semantics, in recent years two alternatives have received particular attention: _classical systems_ (i.e., systems based on classical logic) and _nonclassical systems_ (i.e., systems based on some nonclassical logic). The present article, building on Halbach and Nicolai (J Philos Log 47(2):227–257, 2018), shows (...) that there is a sense in which classical and nonclassical theories (in suitable variants) have the same models. (shrink)

This chapter contains sections titled: 6.1 6.2 6.3 6.4 6.5.

Argues that a pluralistic understanding of truth can foster productive conversations about common concerns involving religion, science, ethics, politics, economics, and ecology without falling into relativism. In this book, Donald A. Crosby defends the idea that all claims to truth are at best partial. Recognizing this, he argues, is a necessary safeguard against arrogance, close-mindedness, and potentially violent reactions to differences of outlook and practice. Crosby demonstrates how “partial truths” are inevitably at work in conversations and (...) debates about religion, science, morality, economics, ecology, and social and political progress. He then focuses on the concept in the discipline of philosophy, looking at a number of distinctions that are taken to be strictly binary—those between fact and value, continuity and novelty, rationalism and empiricism, mind and body, and good and evil—and demonstrates how in all of these cases, each on its own can offer only an incomplete picture. Partial Truths and Our Common Future invites ongoing dialogue with others for the sake of mutual enlargements of understanding rather than mere civility, and provides incentive for continuing open-minded and shared inquiries into the important issues of life. “This is a transdisciplinary philosophical work that moves with grace across traditions, time periods, and thinkers. It is a master class in the existential and public relevance of philosophy and a rare example of a book that is both timely and timeless.” — Michael S. Hogue, author of The Promise of Religious Naturalism. (shrink)

The nature of truth has occupied philosophers since the very beginning of the field. Our goal is to clarify the notion of scientific truth, in particular the notion of partial truth of facts. Our strategy consists to brake the problem into smaller, more manageable, questions. Thus, we distinguish the truth of a scientific theory, what we call the "global" truth value of a theory, from the truth of a particular scientific proposition, what we (...) call the "local" truth values of a theory. We will present a new local theory of partial truth and will have few things to say about the global level. Moreover, we will also introduce some purely formal results, the most important being the introduction of a new class of algebraic structures which have some interesting connections with classical logic. (shrink)

Yablo has argued for an alternative form of if-thenism that is more conducive with his figurative fictionalism. This commentary sets out to challenge whether the remainder, ρ, tends to be an inaccurate representation of the conditions that are supposed to complete the enthymeme from φ to Ψ. Whilst by some accounts the inaccuracies shouldn't set off any alarm bells, the truth of ρ is too inexact. The content of ρ, a partial truth, must display a sensitivity to (...) the contextual background conditions for subtraction to work properly in Yablo's view. Using a toy example, I argue that Yablo's subtraction model tends to yield partial truths as remainders that fail to rule out inaccurate expressions that may prove to be problematic for it. (shrink)

Two stages of the creative writing process were characterized through mobile scalp electroencephalography in a 16-week creative writing workshop. Portable dry EEG systems with synchronized head acceleration, video recordings, and journal entries, recorded mobile brain-body activity of Spanish heritage students. Each student's brain-body activity was recorded as they experienced spaces in Houston, Texas, and while they worked on their creative texts. We used Generalized Partial Directed Coherence to compare the functional connectivity among both stages. There was a trend of (...) higher gPDC in the Preparation stage from right temporo-parietal to left anterior-frontal brain scalp areas within 1–50 Hz, not reaching statistical significance. The opposite directionality was found for the Generation stage, with statistical significant differences restricted to the delta band. There was statistically higher gPDC observed for the inter-hemispheric connections AF07–AF08 in the delta and theta bands, and AF08 to TP09 in the alpha and beta bands. The left anterior-frontal recordings showed higher power localized to the gamma band for the Generation stage. An ancillary analysis of Sample Entropy did not show significant difference. The information transfer from anterior-frontal to temporal-parietal areas of the scalp may reflect multisensory interpretation during the Preparation stage, while brain signals originating at temporal-parietal toward frontal locations during the Generation stage may reflect the final decision making process to translate the multisensory experience into a creative text. (shrink)

Formalization of reasoning which accepts rules of inference leading to conclusions whose logical values are not smaller than the logical value of the “weakest” premise leads to the concept of consequence operation preserving degrees of truth. Several examples of such consequence operation have already been considered . In the present paper we give a general notion of the consequence operation preserving degrees of truth and its characterization in terms of projective generation and selfextensionality.

Firstly I characterize Simple Partial Logic (SPL) as the generalization and extension of a certain two-valued logic. Based on the characterization I present two definitions of validity in SPL. Finally I show that given my characterization these two definitions are more appropriate than other definitions that have been prevalent, since both have some desirable semantic properties that the others lack.

This is part two of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show (...) that our theory is a proof-theoretically conservative extension of the ramified theory of positive truth up to. (shrink)

A logic for classical conditional events was investigated by Dubois and Prade. In their approach, the truth value of a conditional event may be undetermined. In this paper we extend the treatment to many-valued events. Then we support the thesis that probability over partially undetermined events is a conditional probability, and we interpret it in terms of bets in the style of de Finetti. Finally, we show that the whole investigation can be carried out in a logical and algebraic (...) setting, and we find a logical characterization of coherence for assessments of partially undetermined events. (shrink)

In the paper we investigate Birkhoff’s conditions and. We prove that a discrete lattice L satisfies the condition ) if and only if L is a 4-cell lattice not containing a cover-preserving sublattice isomorphic to the lattice S*7. As a corollary we obtain a well known result of J. Jakub´ık from [6]. Furthermore, lattices S7 and S*7 are considered as so-called partially cover-preserving sublattices of a given lattice L, S7 ≪ L and S7 ≪ L, in symbols. It is shown (...) that an upper continuous lattice L satisfies if and only if L is a 4-cell lattice such that S7 ≪/ L. The final corollary is a generalization of Jakubík’s theorem for upper continuous and strongly atomic lattices. Keywords: Birkhoff’s conditions, semimodularity conditions, modular lattice, discrete lattices, upper continuous lattice, strongly atomic lattice, cover-preserving sublattice, cell, 4-cell lattice. (shrink)

Based on da Costa's and French's notions of partial structures and pragmatic truth, this paper examines two possible characterizations of the concept of empirical adequacy, one depending on the notion of partial isomorphism, the other on the hierarchy of partial models of phenomena, and both compatible with an empiricist view. These formulations can then be employed to illuminate certain aspects of scientific practice.An empirical theory must single out a specific part of the world, establish reference to (...) that part, and say—by way of contingent, substantial claim about the world—that its models fit that. Now, how exactly can this be done? Bas C. van Fraassen. (shrink)

I consider the well-known criticism of Quine's characterization of first-order logical truth that it expands the class of logical truths beyond what is sanctioned by the model-theoretic account. Briefly, I argue that at best the criticism is shallow and can be answered with slight alterations in Quine's account. At worse the criticism is defective because, in part, it is based on a misrepresentation of Quine. This serves not only to clarify Quine's position, but also to crystallize what is (...) and what is not at issue in choosing the model-theoretic account of first-order logical truth over one in terms of substitutions. I conclude by highlighting the need for justifying the belief that the definition of first-order logical truth in terms of models is superior to its definition in terms of substitutions. (shrink)

Elgin has argued that scientific models that are, strictly speaking, inaccurate representations of the world, are epistemically valuable because the “falsehoods” they contain are “felicitous”. Many, including Elgin herself, have interpreted this claim as offering an alternative to scientific realism and “veritism”. In this paper, I will argue that there is a more felicitous interpretation of Elgin’s work: “felicitous falsehoods” do play a role in the epistemic value of inaccurate models, but that role is of instrumental value. Elgin’s view is (...) not best understood as claiming that falsehoods provide scientific understanding in and of themselves, only that they facilitate epistemic access to the fundamental, even if partial, truths that are contained within models. While falsehoods may be felicitous in that they facilitate exemplification, the epistemic value of inaccurate models ultimately relies on their partial accuracy. (shrink)

This paper presents the first purely algebraic characterization of classes of partial algebras definable by a set of strong equations. This result was posible due to new tools such as invariant congruences, i.e. a generalization of the notion of a fully invariant congruence, and extension of algebras, specific for strong equations.

This paper discusses a common contemporary characterization of skepticism and skeptical arguments-that their real importance is instrumental, that they “drive progress in philosophy.“ I explore two possible contrasts to the idea that skepticism's significance is thus wholly methodological. First, I recall for the reader a range of views that can be understood as `truth in skepticism' views. These concessive views are those most clearly at odds with the idea that skepticism is false, but instrumentally valuable. Considering the contributions (...) of such `truth in skepticism' theorists, I argue, shows that the good of furthering philosophical progress is partly achieved by the work of those who would reject the `merely methodological' view of skepticism's import. While this shows such a view of skepticism's import to be partially self-effacing, it is not therefore incoherent. Rather, the characterization is revealed to be wedded to particular diagnoses of skepticism, and not independently innocuous or neutral. Second, I discuss the idea that the `merely methodological' characterization of skepticism's import draws a contrast with philosophical positions or theses that are supposed to have practical teeth. Here, I think the danger of acquiescing too readily to this view is that the normative import of skeptical arguments is obscured. At a time when discussions of the value of knowledge are in ascendency, this in particular seems a loss-a route from consideration of skeptical arguments to broader normative questions worth keeping open is rather more obscured than opened up. Any radically revisionary outcome of an encounter with skepticism is less likely, led by such an understanding, just when there is opportunity instead to connect up with broad questions of epistemic value. For these reasons I argue the characterization is not one to too readily, unthinkingly, endorse. (shrink)

The article is a commentary to Susan Haack’s The Whole Truth and Nothing but the Truth. It consists of two parts. In the first one some doubts about Haack’s conception of partiality of truth are formulated. However, Haack’s concept of truth is treated as one of the assumptions and not brought up for discussion. In the second part of the article a simple typology of possible sources of truth’s partiality in science is presented. The list (...) includes deliberate and unintentional omissions, misleading, lack of scientific interest, unattainability, and epistemological problems with truth and realism. (shrink)

Newton da Costa and Steven French have argued that the concept of partial truth plays an important role in our understanding of significant aspects of scientific practice: from the status of scientific theories through the understanding of inconsistency in science to the nature of induction (see da Costa and French 2003). In this paper, I use the concept of partial truth and the associated framework of partial structures to offer a formulation of the concept of (...) visual evidence, and I examine some of the roles that this notion plays in scientific activity. DOI:10.5007/1808-1711.2011v15n2p249. (shrink)

Da Costa and French explore the consequences of adopting a 'pragmatic' notion of truth in the philosophy of science. Their framework sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate, as well as the nature of scientific models and their heuristic development.

This paper explores the status of partial truths, i.e., statements that are partially true and partially false, in Aristotle’s Metaphysics. Contrary to what some scholars have suggested, it argues that partial truths are not confined to reputable opinions (endoxa) that have not yet been clarified and disambiguated. Rather, they have a more central role in Aristotle’s investigation. First, I propose that the fundamental question of being, namely, “What is substance?” is such that even our best attempts to answer (...) it may never yield a full or complete truth. Second, at least in some instances, Aristotle does not seem interested in disambiguating the assertions of previous thinkers to attain propositions that are fully true or fully false. This is the case because our capacity to gain insights into the nature of things is mediated by our reflections on previous theories and on the problems that they incur. It may thus be desirable to retain some partial truths that, owing to their very ambiguity, force us to interrogate the nature of things more deeply. (shrink)

This paper explores the status of partial truths, i.e., statements that are partially true and partially false, in Aristotle’s Metaphysics. Contrary to what some scholars have suggested, it argues that partial truths are not confined to reputable opinions that have not yet been clarified and disambiguated. Rather, they have a more central role in Aristotle’s investigation. First, I propose that the fundamental question of being, namely, “What is substance?” is such that even our best attempts to answer it (...) may never yield a full or complete truth. Second, at least in some instances, Aristotle does not seem interested in disambiguating the assertions of previous thinkers to attain propositions that are fully true or fully false. This is the case because our capacity to gain insights into the nature of things is mediated by our reflections on previous theories and on the problems that they incur. It may thus be desirable to retain some partial truths that, owing to their very ambiguity, force us to interrogate the nature of things more deeply. (shrink)

In the past thirty years, two fundamental issues have emerged in the philosophy of science. One concerns the appropriate attitude we should take towards scientific theories--whether we should regard them as true or merely empirically adequate, for example. The other concerns the nature of scientific theories and models and how these might best be represented. In this ambitious book, da Costa and French bring these two issues together by arguing that theories and models should be regarded as partially rather than (...) wholly true. They adopt a framework that sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate. The new machinery of "partial structures" that they develop offers a new perspective from which to view the nature of scientific models and their heuristic development. Their conclusions will be of wide interest to philosophers and historians of science. (shrink)

Newton da Costa and Steven French have argued that the concept of partial truth plays an important role in our understanding of significant aspects of scientific practice: from the status of scientific theories through the understanding of inconsistency in science to the nature of induction. In this paper, I use the concept of partial truth and the associated framework of partial structures to offer a formulation of the concept of visual evidence, and I examine some (...) of the roles that this notion plays in scientific activity. (shrink)

How should we understand validity? A standard way to characterize validity is in terms of the preservation of truth (or truth in a model). But there are several problems facing such characterizations. An alternative approach is to characterize validity epistemically, for instance in terms of the preservation of an epistemic status. In this paper, I raise a problem for such views. First, I argue that if the relevant epistemic status is factive, such as being in a position to (...) know or having conclusive evidence for, then the account runs into trouble if we endorse certain familiar logical principles. Second, I argue that if the relevant epistemic status is non-factive, such as is rationally committed to or has justification for believing, then a similar problem arises if we endorse the logical principles as well as a sufficiently strong epistemic “level-bridging” principle. Finally, I argue that an analogous problem arises for the most natural characterization of validity in terms of rational credence. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:A Partial Truth (Poems 2015–19) by Christopher NorrisNiall GildeaNorris, Christopher. A Partial Truth (Poems 2015–19). The Seventh Quarry Press, 2019. 133pp.“No interval but some event takes place.”(Norris, “Freeze-Frame,” A Partial Truth)A Partial Truth, a collection of thirty-seven pieces, is the seventh volume of poetry by philosopher and literary theorist Christopher Norris. Nobody familiar with Norris’s distinguished career will be surprised (...) to learn that his recent turn to versification is not a repudiation of intellectual and rhetorical seriousness, but a re-emphasis of the same using resources not typically found in academic prose. Norris, an interdisciplinarian long before that term became a slogan, has in his work clocked up considerable epistemological mileage across diverse terrain, his critical friendship with deconstruction leading him to important interventions in analytic and Continental philosophy, institutional critique, philosophy of science and mathematics, legal studies, music, politics and, after all, creative criticism.Creative criticism is a relatively embryonic genre, until recently typified generally by a prose that owes a debt to Jacques Derrida’s Cir-confession, Glas and La carte postale. This is a style that foregrounds the philosophical unsaid – the repressed autobiographical, desirous, and otherwise messy constituents of that canon. It does so in part by jettisoning the academic politesse, and let’s say timidity, which help maintain such statutes of limitation. In a more specific way, creative criticism may be understood as a Romantic development set in train by the “Yale School” of deconstruction and its fellow travelers, straining in their own ways against the subordinate role of the reader and critic instituted by the likes of Matthew Arnold and T. S. Eliot.In the foreword to his 2017 volume The Winnowing Fan, Norris at once compliments this “strong” critical rebelliousness (xii), and critiques its ecstatic, quasi-apocalyptic hubris, provisionally aligning his own creative criticism with the “poetic diction” (xxi) of eighteenth-century figures such as Dryden and Pope. It is an analogy with caveats – not least Norris’s stated allergy to the “air of arrogance” (Tempus-Fugitives ix) of [End Page 122] their heavily end-stopped tendentiousness – but one which schematizes a poetics that both carries a definite argument and could not make this argument otherwise than in a manner reliant on verse’s formal properties.Note, however, the fact that Norris takes his distance from both strong criticism and those eighteenth-century essayists on the grounds of their shared self-assurance. A steadier presiding influence is William Empson, whose enmity towards Eliotic New Criticism, which “fixes a prescriptive gulf between poetry and other kinds of discourse,” makes him a political forebear, dissenting from modern forms of literary historical doctrinalism, specifically “that whole anti-rationalist complex of ideas that made the discontinuity between poetic and non-poetic language into a shibboleth of aesthetic, ethical, and (though rarely advertised as such) socio-political principle” (Tempus-Fugitives xix–xx). Norris is no straightforward disciple of Empson – who regarded Derrida, and the other “horrible Frenchmen” Norris used to invite him to read, as “so very disgusting, in a simple moral or social way, that I cannot stomach them” (qtd. in Haffenden 52). And yet, one constant quality of both Norris’s verse and prose criticism is a welcome sobriety of explication when it comes to the more recondite or outright flamboyant enclaves of modern European thought.A Partial Truth, and Norris’s books of verse generally, are explicit in outlining the ways in which his poetry functions as a reaction to the diaristic, mumbling slackness of much contemporary poetry; but does his turn to verse also indicate some reaction to contemporary theory? A Partial Truth’s “Foreword,” with modesty, states that “[i]f these poems have any distinctive merit then it lies in the treatment of interesting ideas in a way that deploys certain formal means to draw out complexities and further implications that would lie beyond the reach of a prose rendition” (14). We will specify some of the relations between form and discursive complexity presently, but for now, it is worth suggesting that Norris’s commitment to verse forms of historically recognizable kinds forecloses from him the mealy-mouthed, argumentatively fugitive character of... (shrink)

Kripke’s theory of truth is arguably the most influential approach to self-referential truth and the semantic paradoxes. The use of a partial evaluation scheme is crucial to the theory and the most prominent schemes that are adopted are the strong Kleene and the supervaluation scheme. The strong Kleene scheme is attractive because it ensures the compositionality of the notion of truth. But under the strong Kleene scheme classical tautologies do not, in general, turn out to be (...) true and, as a consequence, classical reasoning is no longer admissible once the notion of truth is involved. The supervaluation scheme adheres to classical reasoning but violates compositionality. Moreover, it turns Kripke’s theory into a rather complicated affair: to check whether a sentence is true we have to look at all admissible precisification of the interpretation of the truth predicate we are presented with. One consequence of this complicated evaluation condition is that under the supervaluation scheme a more proof-theoretic characterization of Kripke’s theory becomes inherently difficult, if not impossible. In this paper we explore the middle ground between the strong Kleene and the supervaluation scheme and provide an evaluation scheme that adheres to classical reasoning but retains many of the attractive features of the strong Kleene scheme. We supplement our semantic investigation with a novel axiomatic theory of truth that matches the semantic theory we have put forth. (shrink)

The present study reiterates one of the main ideas that we exposed in 1983, in the paper “Din fals rezultă orice” (“From False Follows Anything”), published in the volume Întemeieri raţionale în filosofia ştiinţei (Rational Foundations in the Philosophy of Science) when we referred to the notion of semi-truth, as a third alethic value, placed between „truth” and „falsehood”, thus contributing to the functionality of the trivalent logic. Now we analyze the conceptions of Petre Botezatu, Mario Bunge, Karl (...) R. Popper and Nicholas Rescher, in order to argue that it is important not to identify the epistemological term „probable” (= uncertain) with the semantic term „partial” or „approximate”, when we speak about the concept of truth. (shrink)

According to a defense of scientific realism known as the “divide et impera move”, mature scientific theories enjoying predictive success are partially true. This paper investigates a paradigmatic historical case: the prediction, based on Fresnel’s wave theory of light, that a bright spot should figure in the shadow of a disc. Two different derivations of this prediction have been given by both Poisson and Fresnel. I argue that the details of these derivations highlight two problems of indispensability arguments, which state (...) that only the indispensable constituents of this success are worthy of belief and retained through theory-change. The first problem is that, contrary to a common claim, Fresnel’s integrals are not needed to predict the bright spot phenomenon. The second problem is that the hypotheses shared by to these two derivations include problematic idealizations. I claim that this example leads us to be skeptical about which aspects of our current theories are worthy of belief. (shrink)

Clausal complements of different kinds of attitude verbs such as believe, doubt, be surprised, wonder, say, and whisper behave differently semantically in a number of respects. For example, they differ in the inference patterns they display. This paper develops a semantic account of clausal complements using partial logic which accounts for such semantic differences on the basis of a uniform meaning of clauses. It focuses on explaining the heterogeneous inference patterns associated with different kinds of attitude verbs, but it (...) contributes also to explaining differences among clausal complements of attitude verbs regarding the possibility of de re reference, anaphora support, presupposition satisfaction, and the distribution of subjunctive in certain languages. Moreover, it gives a new account of factivity. The point of departure of this paper is the general observation that the failure of inferences from attitude reports is relative in that it depends both on the general type of attitude and on the particular instance of the attitude described. Thus, from John is surprised that P and Q one cannot infer John is surprised that P and John is surprised that Q, though this is possible with believe. Conversely, one can infer from John believes that P and John believes that Q, to John believes that P and Q, but only as long as the same belief state of John is involved. In order to capture this dependency of inferences from attitude reports on a particular mental state or act, I propose an account on which clausal complements of attitude verbs (as well as independent sentences) characterize the intentional state or act described by the attitude verb in question, rather than referring to independent propositions. The semantic account of attitude reports of this paper can hence be called an 'event-based account' of clauses. Formally, the denotation of any sentence, both independent and embedded, is construed as a function mapping an intentional state or act to a function from situations (which form the content of the state or act) to truth values.. (shrink)

We show that the representability of cylindric algebras by relativized set algebras depends on the scope of the operation transposition which can be defined on the algebra. The existence of “partial transposition” assures this kind of representability of the cylindric algebra . Further we characterize those cylindric algebras in which the operator transposition can be introduced.

We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and selection functions, independently of any strictness assumption.

In Hard Truths, Elijah Millgram maintains that analytic philosophy rests on a mistake. 1 It is committed to bivalence – the contention that every truth bearer is either true or false. As a result of this commitment, its views about logic and metaphysics are profoundly misguided. He believes that rather than restricting ourselves to two truth values, we should recognize a plethora of partial truths – sentences, beliefs and opinions that are partly true or true in a (...) way. These are located on a multidimensional continuum between truth and falsity. Millgram never says exactly what partial truth is. The closest he comes is ‘Partial truth is the not fully articulated standard, or family of standards to which we hold [utterances, inscriptions and thoughts] in partial truth inferences’ , where partial truth inferences are those used in cases where ‘there is a recognized mismatch between representation and world – but not in any way that requires changing the representations’ . A critical issue then is what constitutes such a mismatch. I will argue that Millgram’s reasons for recognizing partial truths rest on untenable conceptions of logic, truth and language. Perhaps there are partial truths; perhaps recognizing them would enhance our logic or metaphysics. But Millgram’s arguments fail to show it. 1. Logic Recognizing that there can be some truth in sentences that as a whole are false is not unprecedented. Analyses by Ullian and Goodman 2 and, more recently, Yablo 3 reveal how a false sentence or proposition can be true about a particular item. ‘The dog barks and the cat speaks French’ is true about the dog, even though the conjunction as a whole is false. This does not undermine classical logic. Rather, such analyses reveal that truth about a particular subject matter is more fine grained than truth simpliciter. ‘True …. (shrink)

This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of (...) arithmetic and show that the theory is a proof-theoretically conservative extension of the theory PT of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground. (shrink)

Are the conclusions reached by mature sciences merely “likely stories” or are they “really true”? Questions of this sort have been live issues from Étienne Tempier’s March 1277 condemnation of theses of the Radical Aristotelians of Paris to the May 2005 Kansas State Board of Education deliberations on Darwinism. One major difficulty with the view that scientific findings are “really true” is that, from the historical record, all such statements are recognized as being revisable, even replaceable. Several attempts to formalize (...) a notion of “approximate truth” have addressed this difficulty—without notable success. This book proposes a new solution to the problem—a resolution that stands in the tradition of the American Pragmatists: Peirce, James, and Dewey. (shrink)

This paper develops some ideas from previous work (coauthored, mostly with C.J.Isham). In that work, the main proposal is to assign as the value of a physical quantity in quantum theory (or classical physics), not a real number, but a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; in part mathematical---the valuations arise naturally in the theory of presheaves; and in part (...) conceptual---the valuations arise from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition. In this paper, I give another conceptual motivation for the proposal. I develop (in Sections 2 and 3) the notion of a topos (of which presheaves give just one kind of example); and explain how this notion gives a satisfactory general framework for making sense of the idea of partial truth. Then I review (in Section 4) how our proposal applies this framework to the case of physical theories. (shrink)

The main purpose of this note is to characterize consistency of logic theories in propositional logic by means of topological concept. Based on the concepts of truth degree of formulas and similarity degree between formulas the concept of logic metric space has been proposed by the first author. It is proved in this note that a closed logic theory Γ is consistent if and only if it contains no interior point in the logic metric space. Moreover the relationship between (...) logic closedness and topological closedness of a logic theory Γ is discussed. Finally, the concept of full divergency is also characterized by means of the topological concept of density. (shrink)

In the present work, the microstructure of the melt-spun Al 90 Ce 10 alloy has been characterized using X-ray diffraction and transmission electron microscopy together with energy-dispersive spectrometry. It has been found that the microstructure of the melt-spun Al 90 Ce 10 alloy is composed of the amorphous phase, f -Al, f -Al 11 Ce 3 , Al 3 Ce and unidentified phases, quite different from that of the ingot-like alloy consisting of coarse primary f -Al- f -Al 11 Ce (...) 3 dendrites embedded in the f -Al- f -Al 11 Ce 3 eutectic matrix. Moreover, the amorphous phase is dominant in the melt-spun Al 90 Ce 10 alloy according to the XRD and TEM results. Al 3 Ce particles, less than 100 nm in size, are dispersed in the partial amorphous phase. Polygonal f -Al 11 Ce 3 crystals embedded in the f -Al matrix are also observed. The presence of the hexagonal, kite-like and petal-like intermetallic particles surrounded by the amorphous phase indicates that there exist micro-inhomogeneous structures in the Al 90 Ce 10 melt. These results demonstrate that the overheating of the melt has a significant effect on the amorphization of the Al 90 Ce 10 alloy. (shrink)

We present a theory VF of partial truth over Peano arithmetic and we prove that VF and ID 1 have the same arithmetical content. The semantics of VF is inspired by van Fraassen's notion of supervaluation.

This paper elaborates on the following correspondence theorem (which has been defended and formally proved elsewhere): if theory T has been empirically successful in a domain of applications A, but was superseded later on by a different theory T* which was likewise successful in A, then under natural conditions T contains theoretical expressions which were responsible for T’s success and correspond (in A) to certain theoretical expressions of T*. I illustrate this theorem at hand of the phlogiston versus oxygen theories (...) of combustion, and the classical versus relativistic theories of mass. The ontological consequences of the theorem are worked out in terms of the indirect reference and partial truth. The final section explains how the correspondence theorem may justify a weak version of scientific realism without presupposing the no-miracles argument. (shrink)

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic (...) class='Hi'>truth can be accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed. (shrink)

While the earlier work of Philip Kitcher, in particular The Advancement of Science (1993), continues to inform his more recent studies, such as Science, Truth, and Democracy (2001), there are significant "changes of opinion" from those articulated in the 1990s. One may even speak of two different stages in the configuration of epistemological proposals. An analysis, from an empiricist standpoint, of the shifts between one and the other indicates further evolution towards realist positions but much more modest ones than (...) those previously endorsed. Kitcher qualifies former individualism with an ensuing defence of pluralism, vital to his effort to develop a social epistemology. The present centrality of the achievement of a well-ordered science , one that promotes the common good within the context of democracies, encapsulates recent variation in the work of Kitcher and may be considered one of the author's most defendable proposals, even including its classically empiricist resonance. (shrink)