Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat (...) the semantic pathology suffered by at least some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

Kuhn's alleged taxonomic interpretation of incommensurability is grounded on an ill defined notion of untranslatability and is hence radically incomplete. To supplement it, I reconstruct Kuhn's taxonomic interpretation on the basis of a logical-semantic theory of taxonomy, a semantic theory of truth-value, and a truth-value conditional theory of cross-language communication. According to the reconstruction, two scientific languages are incommensurable when core sentences of one language, which have truth values when considered within its (...) own context, lack truth values when considered within the context of the other due to the unmatchable taxonomic structures underlying them. So constructed, Kuhn's mature interpretation of incommensurability does not depend upon the notion of truth-preserving translatability, but rather depends on the notion of truth-value-status-preserving cross-language communication. The reconstruction makes Kuhn's notion of incommensurability a well grounded, tenable and integrated notion.Author Keywords: Incommensurability; Thomas Kuhn; Taxonomic structures; Lexicons; Truth-value; Untranslatability; Cross-language communication. (shrink)

A lot has been written on solutions to the semantic paradoxes, but very little on the topic of general theories of paradoxicality. The reason for this, we believe, is that it is not easy to disentangle a solution to the paradoxes from a specific conception of what those paradoxes consist in. This paper goes some way towards remedying this situation. We first address the question of what one should expect from an account of paradoxicality. We then present one conception of (...) paradoxicality that has been offered in the literature: the fixed-point conception. According to this conception, a statement is paradoxical if it cannot obtain a classical truth-value at any fixed-point model. In order to assess this proposal rigorously we provide a non-metalinguistic characterization of paradoxicality and we evaluate whether the resulting account satisfies a number of reasonable desiderata. (shrink)

The aim of this dissertation is to offer and defend a correspondence theory of truth. I begin by critically examining the coherence, pragmatic, simple, redundancy, disquotational, minimal, and prosentential theories of truth. Special attention is paid to several versions of disquotationalism, whose plausibility has led to its fairly constant support since the pioneering work of Alfred Tarski, through that by W. V. Quine, and recently in the work of Paul Horwich. I argue that none of these theories (...) meets the correspondence intuition---that a true sentence or proposition in some way corresponds to reality---despite the explicit claims by each to capture this intuition. I distinguish six versions of the correspondence theory, and defend two against traditional objections, standardly taken as decisive against them, and show, plainly, that these two theories capture the correspondence intuition. Due to the importance of meeting this intuition, only these two theories stands a chance of being a satisfactory theory of truth. I argue that the version of the correspondence theory incorporating a simple semantic representation relation is preferable to its rival, for which the representation relation is complex. I present and argue for a novel version of this correspondence theory according to which truth is a correspondence property sensitive to semantic context. One consequence of this context-sensitivity is that an ungrounded sentence does not express a proposition. In addition to accounting for the similarity between the Liar and Truth-Teller sentences, this theory of truth is immune to the Liar Paradox, including empirical versions. It is argued that the Liar Paradox is devastating to all of the other theories above, and even formal theories of truth designed to solve it, such as the revision and vagueness theories. Customized versions of the Liar Paradox besetting this theory are handled by its context-sensitivity, and by enforcing the distinction between truth and truth value. This same pair of considerations also yields solutions to Lob's Paradox and Grelling's Paradox. Arguments similar to those given to defend this correspondence theory show that with one minor alteration, Kripke's fixed point theory may be used to model this correspondence notion of truth. (shrink)

A theory of truth is introduced for a first--order language L of set theory. Fully interpreted metalanguages which contain their truth predicates are constructed for L. The presented theory is free from infinite regress, whence it provides a proper framework to study the regress problem. Only ZF set theory, concepts definable in L and classical two-valued logic are used.

This paper outlines a new pluralistic theory of normative reasons for belief, welfarist pluralism, which aims to explain how there can be basic alethic/epistemic reasons for belief and basic pragmatic/non-alethic reasons for belief that can combine to determine what one ought to believe. The paper shows how this non-derivative first-order pluralism arises from a purely welfarist account of the foundations of theoretical normativity, thereby combining foundational pragmatism with non-derivative pluralism about normative reasons for belief. In addition, this paper outlines (...) how welfarist pluralism provides a new and potentialy attractive account of the value of truth (or its indicators), namely that the value of truth (or its indicators) is its direct contribution to individuals' personal good or wellbeing. (shrink)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual (...) semantic connection of sentences, above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

Based on a crowdsourced truth value judgment experiment, we provide empirical evidence challenging two classical views in semantics, and we develop a novel account of counterfactuals that combines ideas from inquisitive semantics and causal reasoning. First, we show that two truth-conditionally equivalent clauses can make different semantic contributions when embedded in a counterfactual antecedent. Assuming compositionality, this means that the meaning of these clauses is not fully determined by their truth conditions. This finding has a clear (...) explanation in inquisitive semantics: truth-conditionally equivalent clauses may be associated with different propositional alternatives, each of which counts as a separate counterfactual assumption. Second, we show that our results contradict the common idea that the interpretation of a counterfactual involves minimizing change with respect to the actual state of affairs. We propose to replace the idea of minimal change by a distinction between foreground and background for a given counterfactual assumption: the background is held fixed in the counterfactual situation, while the foreground can be varied without any minimality constraint. (shrink)

ABSTRACT: In its strongest unqualified form, the principle of wholistic reference is that in any given discourse, each proposition refers to the whole universe of that discourse, regardless of how limited the referents of its non-logical or content terms. According to this principle every proposition of number theory, even an equation such as "5 + 7 = 12", refers not only to the individual numbers that it happens to mention but to the whole universe of numbers. This principle, its (...) history, and its relevance to some of Oswaldo Chateaubriand's work are discussed in my 2004 paper "The Principle of Wholistic Reference" in Essays on Chateaubriand's "Logical Forms". In Chateaubriand's réplica (reply), which is printed with my paper, he raised several important additional issues including the three I focus on in this tréplica (reply to his reply): truth-values, universes of discourse, and formal ontology. This paper is self-contained: it is not necessary to have read the above-mentioned works. The principle of wholistic reference (PWR) was first put forth by George Boole in 1847 when he espoused a monistic fixed-universe viewpoint similar to the one Frege and Russell espoused throughout their careers. Later, Boole elaborated PWR in 1854 from the pluralistic multiple-universes perspective. (shrink)

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical (...) two-valued language. Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (shrink)

According to one tradition, uttering an indicative conditional involves performing a special sort of speech act: a conditional assertion. We introduce a formal framework that models this speech act. Using this framework, we show that any theory of conditional assertion validates several inferences in the logic of conditionals, including the False Antecedent inference. Next, we determine the space of truth-conditional semantics for conditionals consistent with conditional assertion. The truth value of any such conditional is settled whenever (...) the antecedent is false, and whenever the antecedent is true and the consequent is false. Then, we consider the space of dynamic meanings consistent with the theory of conditional assertion. We develop a new family of dynamic conditional-assertion operators that combine a traditional test operator with an update operation. (shrink)

This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.

A theory of truth is usually demanded to be consistent, but -consistency is less frequently requested. Recently, Yatabe has argued in favour of -inconsistent first-order theories of truth, minimising their odd consequences. In view of this fact, in this paper, we present five arguments against -inconsistent theories of truth. In order to bring out this point, we will focus on two very well-known -inconsistent theories of truth: the classical theory of symmetric truth FS (...) and the non-classical theory of naïve truth based on ᴌukasiewicz infinitely valued logic: PAᴌT. (shrink)

This paper outlines a quantitative theory of strongly semantic information (TSSI) based on truth-values rather than probability distributions. The main hypothesis supported in the paper is that the classic quantitative theory of weakly semantic information (TWSI), based on probability distributions, assumes that truth-values supervene on factual semantic information, yet this principle is too weak and generates a well-known semantic paradox, whereas TSSI, according to which factual semantic information encapsulates truth, can avoid the paradox and is (...) more in line with the standard conception of what generally counts as semantic information. After a brief introduction, section two outlines the semantic paradox implied by TWSI, analysing it in terms of an initial conflict between two requisites of a quantitative theory of semantic information. In section three, three criteria of semantic information equivalence are used to provide a taxonomy of quantitative approaches to semantic information and introduce TSSI. In section four, some further desiderata that should be fulfilled by a quantitative TSSI are explained. From section five to section seven, TSSI is developed on the basis of a calculus of truth-values and semantic discrepancy with respect to a given situation. In section eight, it is shown how TSSI succeeds in solving the paradox. Section nine summarises the main results of the paper and indicates some future developments. (shrink)

There is a fundamental incompatibility between a developmental orientation to education and instrumental and scientistic conceptions of rationality that dominate educational inquiry. An expanded conception of rationality is provided in the critical theory of Jurgen Habermas. This study draws on Habermas' work to present a theory of inquiry that is consistent with a developmental perspective. I distinguish three interdependent realms of experience--the objective world of nature, the intersubjective world of society and the subjective world of each individual. Then, (...) I argue that current conceptions of rationality tend to reduce personal and interpersonal experience to the objective material realm. Under prevailing conceptions, human action is rational when it pursues valued ends guided by knowledge about the world and effective means-ends relationships. Both theories of knowledge and theories of value in these conceptions are inadequate for a developmental orientation. -/- First, knowledge is defined as justified true belief. Theories of truth are based on the correspondence of beliefs with an external world; theories of justification are based on perceptual certainty. These conceptions objectify experience by making experience an object of natural science and instrumental action separate from and external to the person. Such conceptions reduce experience to the objective material dimension and cannot adequately account for the personal and interpersonal dimensions of human experience and understanding. -/- Second, because value claims are not capable of justification by these standards, they are considered ultimately irrational and treated as subjectively held empirical properties of individuals. The only standard of rationality is efficiency and economy in the selection of means. Ethics is reduced to empirical science. But the removal of practical questions from public discourse divests action of ethical significance. With its strict separation of descriptive and normative domains, empirical-analytic inquiry can neither acknowledge its standard of instrumental efficiency nor reach into the practical arena to guide the selection of values and ends that orient and gude human action. Practical questions that cannot be framed in terms of technical problems cannot be taken seriously. -/- Whereas these conceptions of rationality are generally derived from theories of experienced based on individual consciousness, Habermas looks to language for a more adequate account of the intersubjective nature of experience. This account provides an expanded conception of rationality with theories for justifying beliefs and actions that incorporate the personal and interpersonal dimensions of experience so critical to a developmental perspective. Through an analysis of the universal pragmatic structure of language directed to the resolution of problematic truth claims and moral claims, this study presents a consensus theory of truth (for a more adequate theory of knowledge) and a communicative theory of ethics (based on a more adequate theory of human values). -/- The concept of truth refers to a universal pragmatic convention of the unforced agreement of an ideal community of inquirers. Ethical conduct is guided by norms that reflect a rational general will and that regulate genuine human needs. Problematic truth claims and moral claims are discursively justified by the force of the better argument under the conditions of an anticipated "ideal speech situation" inherent in the very structure of communication. Furthermore, a theory of inquiry is developed in which inquiry processes are represented as historically evolved extensions of developmental process in the three realms of experience. Three interrelated forms of inquiry are derived--empirical-analytic, hermeneutic and critical. I derive each from its respective experiential realm, and indicate the logic of inquiry, object domain, and kind of knowledge gained from each. -/- An exploration of the relationship between inquiry and development provides a foundation for a developmental orientation to education. Finally, the theory is contrasted with prevailing inquiry approaches in education and illustrated with an application to a particular educational problem. (shrink)

Abstract: We propose a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this semantic view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that (...) this theory provides a general framework within which we can understand the relation between vague terms and concepts and the corresponding crisp portions of reality. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more familiar approaches. Central to our approach is the idea that judgments about reality involve in every case (1) a separation of reality into foreground and background of attention and (2) the feature of granularity. On this basis we attempt to show that even vague judgments made in naturally occurring contexts are not marked by truth-value indeterminacy. We distinguish, in addition to crisp granular partitions, also vague partitions, and reference partitions, and we explain the role of the latter in the context of judgments that involve vagueness. We conclude by showing how reference partitions provide an effective means by which judging subjects are able to temper the vagueness of their judgments by means of approximations. (shrink)

ABSTRACTRecent debate over the semantics and pragmatics of epistemic modals has focused on intuitions about cross-contextual truth-value assessments. In this paper, we advocate a different approach to evaluating theories of epistemic modals. Our strategy focuses on judgments of the incompatibility of two different epistemic possibility claims, or two different truth value assessments of a single epistemic possibility claim. We subject the predictions of existing theories to empirical scrutiny, and argue that existing contextualist and relativist theories are (...) unable to account for the full pattern of observed judgments. As a way of illustrating the theoretical upshot of these results, we conclude by developing a novel theory of epistemic modals that is able to predict the results. (shrink)

This dissertation argues that we have no good reason to accept any one theory of properties as correct. To show this, I present three possible bases for theory-choice in the properties debate: coherence, explanatory adequacy, and explanatory value. Then I argue that none of these bases resolve the underdetermination of our choice between theories of properties. First, I argue considerations about coherence cannot resolve the underdetermination, because no traditional theory of properties is obviously incoherent. Second, I (...) argue considerations of explanatory adequacy cannot resolve the underdetermination, because every traditional theory of properties lacks the theoretical resources to adequately explain resemblance, causal powers, and predication. However, these inadequacies are easily remedied with theoretical modifications. But this results in an overabundance of modified, but adequate, theories of properties. Third, I argue explanatory virtues cannot resolve the underdetermination, because we have no reason to think explanatory virtues make theories of properties more likely to be true. I reject the common argument that explanatory virtues are truth-conducive in theories of properties because they are truth-conducive in scientific theories. Since none of the three bases for theory choice can resolve the underdetermination, I conclude that we have no good reason to accept any one theory of properties as correct. Finally, I consider the possibility of choosing one theory over the others on pragmatic grounds. But I argue that pragmatic grounds cannot resolve the underdetermination either. Instead, I suggest we accept the view I call 'instrumental pluralism,' which allows practitioners to use whatever theory of properties they find useful. Adviser: Jennifer McKitrick. (shrink)

Abstract In this paper I present a short outline of an Indicativity Theory of Knowledge, for the cases of Perceptual Knowledge and Knowledge by Memory. I explain the main rationale for a token-indicativity approach, and how it is fleshed out precisely in terms of chances. I elaborate on the account of the value of knowledge it provides, and what that value is. I explain why, given the rationale of conceiving Knowledge as token indicativity, separate sub-accounts in terms (...) of chances should be extracted for the different modes of Knowledge, elaborating on the common core of high token-indicativity. In the main section that outlines the account of Perceptual Knowledge, the main Indicativity condition is presented, as are the main condition of in what sense high token indicativity should yields high chance, the important Discriminability condition, and its associated Contrast Class. (shrink)

We propose a logic to reason about data collected by a num- ber of measurement systems. The semantic of this logic is grounded on the epistemic theory of measurement that gives a central role to measure- ment devices and calibration. In this perspective, the lack of evidences (in the available data) for the truth or falsehood of a proposition requires the introduction of a third truth-value (the undetermined). Moreover, the data collected by a given source are (...) here represented by means of a possible world, which provide a contextual view on the objects in the domain. We approach (possibly) conflicting data coming from different sources in a social choice theoretic fashion: we investigate viable opera- tors to aggregate data and we represent them in our logic by means of suitable (minimal) modal operators. (shrink)

This paper presents a conception of corruption informed by epistemic democratic theory. I first explain the view of corruption as a disease of the political body. Following this view, we have to consider the type of actions that debase a political entity of its constitutive principal in order to assess corruption. Accordingly, we need to consider what the constitutive principle of democracy is. This is the task I undertake in the second section where I explicate democratic legitimacy. I present (...) democracy as a procedure of social inquiry about what ought to be done that includes epistemic and practical considerations. In the third section, I argue that the problem of corruption for a procedural conception of democracy is that the epistemic value of the procedure is diminished by corrupted agents’ lack of concern for truth. Corruption, according to this view, consists in two deformities of truth: lying and bullshit. These deformities corrupt since they conceal private interests under the guise of a concern for truth. In the fourth section, I discuss the difficulties a procedural account may face in formulating solutions to the problem of corruption. (shrink)

What do you know when you know what a sentence means? According to some theories, understanding a sentence is, in part, knowing its truth-conditions. Dorit Bar-On, Claire Horisk, and William Lycan have defended such theories on the grounds of an “epistemic determination argument”. That argument turns on the ideas that understanding a sentence, along with knowledge of the non-linguistic facts, suffices to know its truth-value, and that being able to determine a sentence’s truth-value given knowledge (...) of the non-linguistic facts is knowing its truth-conditions. I argue that the EDA withstands the objections recently raised by Daniel Cohnitz and Jaan Kangilaski, but fails for other reasons. It equivocates between a fine-grained and a coarse grained conception of “facts.”. (shrink)

Fregean theories of descriptions as terms have to deal with improper descriptions. To save bivalence various proposals have been made that involve assigning referents to improper descriptions. While bivalence is indeed saved, there is a price to be paid. Instantiations of the same general scheme, viz. the one and only individual that is F and G is G, are not only allowed but even required to have different truth values.

The purpose of this paper is to explore the connection between change and the B-theory of time, sometimes also called the Scientific view of time, according to which reality is a four-dimensional spacetime manifold, where past, present and future things equally exist, and the present time and non-present times are metaphysically the same. I argue in favour of a novel response to the much-vexed question of whether there is change on the B-theory or not. In fact, B-theorists are (...) often said to hold a ‘static’ view of time. But this far from being innocent label: if the B-theory of time presents a model of temporal reality that is static, then there is no change on the B-theory. From this, one can reasonably think as follows: of course, there is change, so the B-theory must be false. What I plan to do in this paper is to argue that in some sense there is change on the B-theory, but in some other sense, there is no change on the B-theory. To do so, I present three instances of change: Existential Change, namely the view that things change with respect to their existence over time; Qualitative Change, the view that things change with respect to how they are over time; Propositional Change, namely the view that things (i.e. propositions) change with respect to truth value over time. I argue that while there is a reading of these three instances of change that is true on the B-theory, and so there is change on the B-theory in this sense, there is a B-theoretical reading of each of them that is not true on the B-theory, and therefore there is no change on the B-theory in this other sense. (shrink)

A key assumption fuelling optimism about the progress of Large Language Models (LLMs) in modelling the world is that the truth is systematic: true statements about the world form a whole that is not just consistent, in that it contains no contradictions, but cohesive, in that the truths are inferentially interlinked. This holds out the prospect that LLMs might rely on that systematicity to fill in gaps and correct inaccuracies in the training data: consistency and cohesiveness promise to facilitate (...) progress towards comprehensiveness in an LLM’s representation of the world. However, philosophers have identified reasons to doubt that the truth is systematic across all domains of thought, arguing that in normative domains, in particular, the truth is not necessarily systematic. I argue that insofar as the truth in normative domains is asystematic, this renders it correspondingly harder for LLMs to make progress, because they cannot rely on the consistency and cohesiveness of the truth to work towards comprehensiveness. And the less LLMs can rely on the systematicity of truth, the less we can rely on them to do our practical deliberation for us, as there is correspondingly more of a role for human agency in navigating asystematic normative domains. (shrink)

Predication is a lingual relation. We have this relation when a term is said (λέγεται) of another term. This simple definition, however, is not Aristotle’s own definition. In fact, he does not define predication but attaches his almost in a new field used word κατηγορεῖσθαι to λέγεται. In a predication, something is said of another thing, or, more simply, we have ‘something of something’ (ἓν καθ᾿ ἑνὸς). (PsA. , A, 22, 83b17-18) Therefore, a relation in which two terms are posited (...) to each other in a way that one is said (predicated) of the other is a predication. The term of which the other term is said is called a subject (ὑποκειμένον) and the other, which is said about the subject, is called the predicate. Thus, in a predication the predicate is predicated of the subject; given that being predicated is almost as the same as being said. The relation between being said and being predicated is so close that ‘if something is said of a subject both its name and its definition are necessarily predicated of the subject.’ (Cat., 5, 2a19-26) This, however, is true only about the second genera and not the accidents. a) Nature of relation in predication What is Aristotle’s theory about the nature of the relation in a predication? How does he fundamentally understand this relation? Phil Corkum distinguishes between predication logic and traditional term logic and argues that the relation between subject and predicate in Aristotle is of the latter kind. While in predicate logic, subjects and predicates have distinct roles, they have the same role in traditional term logic. In predication logic, subjects refer, but predicates characterize. Thereupon, a sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. In traditional term logic, both subjects and predicates refer and a sentences expresses a truth if both name one and the same thing. He concludes that Aristotle ‘problematically conflates prediction and identity claims’ because while he thinks both subjects and predicates refer, he would deny that a sentence is true just in case the subject and the predicate name one and the same thing. Based on this, Corkum believes that Aristotle’s core semantic is not identity but the weaker relation of constitution, which is a mereological interpretation: ‘All men are mortal’ is true just in case the mereological sum of humans is part of the mereological sum of mortals. b) Aristotle’s theory of predication: one or two theories? Frank Lewis finds an inconsistent gap between the theory of predication in the Categories and that in the later books of the Metaphysics VII, 6. So too Joan Kung, Terry Irwin, Daniel Graham. c) Distinction of ‘being said of’ and ‘being in’ Owen enumerates the texts in which Aristotle’s distinction between ‘being said of’ and ‘being in’ is asserted: OI. 11b38-12a17; To., 127b1-4; Cat. 1a20-b9; 2a11-14; 2a27-b6; 2b15-17; 3a7-32; 9b22-24 d) Predication in Aristotle and the standard ‘S is P’ Marie De Rijk Lambertus thinks that the ‘S is P’ pattern is misleading when it comes to express predication in Aristotle. In his view, ‘The Aristotelian procedure should be described in terms of appositively assigning an attribute (κατηγορούμενον) to a substrate (ὑποκείμενον), rather than ascribing a predicate to a subject by means of a copula…. The comment should be considered an attribute which is said to fall to a substrate, without understanding this procedure in terms of sentence predication.’ e) Aristotle’s predication: bipartite or tripartite? It is a difficulty to make Aristotle’s theories of name-verb predication and tripartite predication consistent. The reason is that tripartite is not consistant with his name-verb structure based on which he says that the predicate term is the ‘verb.’ (20a31; 20b1-2; 16a13-5) The problem is that in a tripartite form like ‘Socrates is white’ we cannot take ‘is white’ as the verb because, based on Aristotle himself, no part of a verb can be significant itself. (16b6-7) However, his assertions about the equivalences between the two structures (OI. 12, 21b9-10; PrA. 51b13-16; Met., 1017b22-30) must mean that they are not inconsistent in his own view. Thus, as Allen Bāck points, ‘Aristotle seems to think that he has a single, consistent theory.’ The sense of saying or speaking as the root sense of rhema makes the relation between predication (saying something of something) and verb more interesting. The use of rhema in the sense of a long expression approves this. In Plato’s work (399ac) where Socrates claims that the name anthropos derives from anthron ha opopen (‘he who examines what he has seen’) we have an onoma from, or in place of, a rhema. 1) Subject The subject (ὑποκειμένον) is that of which another term is said or predicated. Aristotle’s own definition is of a much more philosophical value: ‘By subject I mean that which is expressed by an affirmative term (λέγω δὲ ὑποκείμενον τὸ κάταφάσει δηλούμενον).’ (Met., K, 1067b18) Throughout Aristotle’s work, three kinds of subjects can be found: possible, prime and absolute subject. a) Possible subject Those things that can take the position of a subject in a predication we call possible subjects, no matter they can or cannot take the position of predicate in any predication. All terms except the ultimate predicates are possible subjects because they can take the position of subject. b) Prime subject Those that in any predication can only take the position of a subject and not the position of a predicate are prime subjects. (Cat., 5, 3a36-b2; Met., Z, 1028b36-1029a1) This is the truest sense of subject and belongs only to substances. (Met., Z, 1029a1-2) In fact, ‘that which is not predicated of a subject, but of which all else is predicated’ is a substance. (Met., Z, 1029a7-9) In Categories, besides primary substances (Cat., 2, 1b3-6), individual qualities are also said not to be able to be said of anything else. (Cat., 2, 1a23-29) Aristotle’s examples are a certain ‘knowledge-of-grammar’ (τὶς γράμματικὴ) and ‘an individual white’ (τὸ τὶ λευκὸν). Thus, although substances are indeed in the truest sense individuals and, thereby, in the truest sense primary subjects, other individuals can take the position of subject as well. c) Absolute subject While substances are prime subjects of all other things, there is still something of which substances can be predicated and this predication is not an accidental predication: matter. (Met., Z, 1029a21-24) This predication is, indeed, the predication of a ‘form or this’ on matter and material substance. (Met., Θ, 1049a34-36) The only thing that is absolutely a subject, therefore, and can be a predicate is prime matter (πρώτη ὓλη). (Met., Θ, 1049a24-27) d) Subject and substance The most important thing in being a substance is being a subject: ‘It is because the primary substances are subjects for all the other things and all the other things are predicated of them or are in them, that they are called substances most of all.’ (Cat., 5, 2b15-17) And what is nearer to this position is more a substance as a species is more a substance than a genus.’ (Cat., 5, 2b7-8) e) Primary versus accidental subject A subject is a primary subject in a predication when the predicate is predicated of it as itself. In such a case, the subject is the subject of the predicate qua itself and not qua something else. A subject, on the one hand, is an accidental subject when it is not the primary subject of the predicate that is predicated on it. It means that a subject is an accidental subject when the predicate is predicated of it not qua itself but qua something else. An accidental subject is, therefore, anything other than a substance. 2) Predicate as universal It is evident from our discussion of kinds of subjects that except matter, primary substances (if we ignore both accidental predication and cases of absolute subjects) and other individuals, everything else can take the position of a predicate. Since primary substances are individuals, it results that everything except matter and individuals are capable to take the position of predicate. The immediate consequence of this is that the predicate must be a universal. When individuals cannot take the position of predicate, this position cannot be taken by any particular. Therefore, only universals can be predicated of others. Moreover, albeit universals can be a simple subject (for another universal), they are not prime subjects. The closeness of universal and predicate is to the extent that Aristotle differentiates universal from subject. (Met., Θ, 1049a27-30) 3) Categories or classes of predicates Aristotle distinguishes ten highest classes into one of which each predicate must necessarily fall: substance (or what a thing is), quality, quantity, relation, place, time, position, state, activity and passivity. (Cat., 4, 1b25-27; To., I, 9, 103b20- ; PsA., A, 22, 83b13-23) The substance counted among predicates must refer to secondary and not primary substances not only because Aristotle insists that primary substances cannot be predicated but also from his own examples of the category of substance: man and animal. (To., I, 9, 103b25) However, if a predicate be asserted of itself or its genus be asserted of it, the predicate signifies substance or what is; but if ‘one kind of predicate is asserted of another kind,’ it signifies one of the other nines. (To., I, 9, 103b30) These categories are so comprehensive that no predicate can remain outside them so that even non-being has as many senses as categories. (Met., M, 1089a26-30) a) That whether Aristotle’s categories are merely linguistic or fundamentally ontological is a so much controversial dispute. Some like G. E. R. Lloyd believe that ‘categories are primarily intended as a classification of reality … rather than of the signifying terms themselves.’ b) Although Aristotle’s categories have been historically regarded as a classification of predications, there are some recent commentators like Jonathan Barnes that think it is classifying predicates and not predications. 4) Kinds of predicates In his introduction of Categories, as J. W. Thorp truly points out , Aristotle distinguishes between the category of substance and the other categories using μὲν ... δὲ construction. This construction illustrates that beside tenfold classification of categories, there is an even more crucial differentiation between two kinds of predicates: substance or what is on the one hand and the other nine ones on the other hand: the distinction between what is predicated of the subject as what it is and what is predicated of it as an accident. Therefore, we have three kinds of classification - a twofold, a fourfold and a tenfold-complicatedly classifying the same thing, viz. the predicate. Predicates can be divided also to four kinds: property, definition, genus and accident. (To., I, 4, 101b11-20) A property is that predicate that is convertible with its subject and does not signify its essence. A definition is that predicate that is convertible with its subject and signifies its essence. It is a genus if it is not predicated convertibly and is contained in the definition of its subject. And it is an accident if it is neither convertible nor contained in the definition of its subject. (To., I, 8, ^103b3) All of these four kinds are among categories. (To., I, 9, 103b20) It seems that there might be some kind of relation between the twofold and the fourfold distinction: whereas genus and definition are predicated as what it is, accidents are not so predicated. There seems to be some rules that determine to each of these four kinds each predicate belongs. At To., IV, 123b30ff. Aristotle asserts: ‘If B has a contrary and A does not, then B does not belong to A as its genus.’ There is a dispute around per se accidents (τὰ καθ’ αὑτὰ συμβεβηκότα) (Topics., 102a18) whether they must be regarded as either of the four kinds or as a fifth kind. Barnes (1970) argued that they ‘do not fit at all neatly into the fourfold classification.’ He argues that based on the definition of accidents at A, 5, 102b4-5, they must be accidents but based on another definition, A, 5, 102b6-7, they cannot be accidents. He also defends the view that they are not properties. Barnes concludes: ‘This shows that the two definitions are not equivalent, and hence that the ‘predicables’ are not well-defined.’ Demetris J. Hadgopoulos defends the view that the two definitions of accidents are equivalent and per se accidents are properties. 5) Five types of predications We have five kinds of predications based on our division of subjects and our discussion of predicates: simple, primary (itself divided to substantial and accident), accidental (itself divided to primary and secondary), aoincidental and absolute predication. a) Simple predication. This is a predication in which a universal is predicated of either a particular or a universal subject. This sense of predication includes all other senses except the first kind of accidental predication. b) Primary predication. This is a predication in which a universal is predicated of a primary subject, namely a substance. A primary predication is of two kinds: i) Substantial predication. A primary predication in which the predicate is part of, or is included in, the definition of the subject. The universal that is the predicate here is the definition or the genus or the species or the diferentia of the subject. It is this predication that Aristotle calls a unity: ‘A statement may be called a unity … because it exhibits a single predicate as inhering not accidentally in a single subject.’ (PsA., B, 10, 93b35-37) It is only substantial predicates that can be predicated of each other: ‘Predicates which are not substantial are not predicated of one another.’ (PsA., A, 22, 83b18-19) Aristotle defines a substantial predication also in another way. A predication in which a higher genus is predicated on a lower genus, species, a substance or an individual, (or a species is predicated on an individual) is a substantial predication. Therefore, a substantial predication is a predication in a series that has individuals on one of its ends and a general category on its other end. In fact, only substantial predicates can be predicated of one another. (PsA., A, 22, 83b17-19) This series cannot be an infinite series because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) -/- ii) Accident predication. A primary predication in which the predicate is not part of, or is not included in, the definition of its subject. The universal that is the predicate here is the property or the accident of the subject. c) Accidental predication. This is a predication in which the subject is not a primary subject and its predicate is a substance. This predication is of two kinds: i) Primary accidental predication. This is a predication in which an accident is predicated of substance. Such a predication can go ad infinitum, which is inferable from Aristotle’s assertion that the secondary accidental predication cannot go ad infinitum. ii) Secondary accidental predication. It is a predication in which an accident is predicated of another accident. Such a predication, Aristotle asserts, cannot go ad infinitum because even more than two accidents cannot be combined. Now what is the meaning of Aristotle’s assertion that we cannot continue this ad infinitum? Does it mean that we cannot continue the predication ‘The musician is white’ and say ‘The white is Athenian?’ But why not? Or maybe he means that by adding any predication, we are still in a condition of predicating two accidents of a substance on each other. -/- As primary subjects, substances can also take the position of predicate though not essentially but accidentally. In propositions like ‘the white is a log’ or ‘That big thing is a log’ we observe substance taking the position of predicate but this is only accidentally: ‘When I affirm ‘the white is a log,’ I mean that something which happens to be white is a log- not that white is the subject in which log inheres (οὐχ ὡς τὸ ὑποκείμενον τῷ ξύλῳ τὸ λευκόν ἐστι), for it was not qua white or qua a species of white that the white (thing) came to be a log (οὔτε λευκὸν ὄν οὔθ᾿ ὃπερ λευκόν τι ἐγἐνετο ξύλον), and the white (thing) is consequently not a log except incidentally.’ (PsA., 22, 83a3-9) Aristotle compares this accidental use of substance in the position of predicate with the substantial use of it in the place of a subject: ‘On the other hand, when I affirm ‘the log is white,’ I do not mean that something else, which happens to be a log, is white (οὐχ ὃτι ἓτερόν τί ἐστι λευκόν, ἐκείνῳ δὲ συμβέβηκε ξύλῳ εἶναι), (as I should if I said ‘the musician is white,’ which would mean ‘The man who happens also to be a musician is white’); on the contrary, log is here the subject- the subject which actually came to be white, and did so qua wood or qua a species of wood and qua nothing else.’ (PsA., 22, 83a8-14) Aristotle asks us not to call propositions like ‘The white is a log’ a predication at all or at least call them accidental predication instead of simple (ἁπλως) predication. (PsA., A, 22, 83a14-17) An accidental predication, in which we have a substance in the place of predicate, is different from an essential predication in that while the subject of an accidental predication is said to be the predicate not by itself but as something different with which it coincides, the subject of an essential predicate is said to be the predicate by itself and not because it is something else: ‘Since there are attributes which are predicated of a subject essentially and not accidentally- not, that is, in the sense in which we say ‘That white (thing) is a man,’ which is not the same mode of predication as when we say ‘The man is white’: the man is white not because he is something else but because he is man, but the white is man because ‘being white’ coincides with ‘humanity’ within one subject. Therefore, there are terms such as are essentially subjects of predicates. (PsA., A, 19, 81a24-29) This capability of ‘non-essentially and only accidentally’ being a subject does belong, in fact, to all sensible things. (PsA., A, 27a32-36) d) Coincidental predication. this is a predication in which none of the subject and predicate are a substance or an individual. In this predication, one of the accidents of a substance or individual is predicated of one of the other accidentals of the same substance or individual. For example, when it is said that ‘The white is musical,’ there is an individual, say Socrates, for which both of white and musical are accidents. e) Absolute predication. This is a predication in which a form or a substance is predicated of a matter or a material substance. Some commentators like Loux and Lewis regarded this predication as close to accident predication, both based on inherence. As R.M. Dancy points out, these predications make Aristotle’s theory of predication immanentist: not only accident predications are explained by the immanence of accidents in substances, some of the substantial predications, which were not explained in Categories, are also explained by the immanence of form in matter. It is interesting that in this kind of predication, it is the predicate and not the subject, which is in the strictest sense substance. As the central books of Metaphysics claim, the form is the substance. Thus, in this predication, substance gets away from the sense of ὑποκείμενον. Corkum mentiones 68a19 as the only instance where Aristotle explicitly claims that a term may be predicated of itself, a passage that is, in Corkum’s view, problematic. 6) Demonstrable predicates Those predicates are demonstrable that are so related to their subjects that there are other predicates prior to them predicable of their subjects (ἔτι δ᾿ ἄλλος, εἰ ὧν πρότερα ἄττα κατηγορεῖται). (PsA., A, 22, 83b32-34) 7) Series of predications Since it is possible for a predicate to be itself the subject of another predication, we can have a series of predications in which the predicate of a predication is the subject of the next predication. This series has the following features: a) It has a limit (in number) (PsA., A, 22, 83b14-16) on the side of subjects: there are subjects that cannot themselves be predicated (PsA., A, 27, 43a39-41), which are, as we noted, prime subjects: particulars, i.e. prime substances and other individuals. (PsA., A, 19-22) Aristotle calls them ultimate (ὓστατον). (PsA., 21, 82a36-b1) b) It has a limit (in number of kinds) (PsA., A, 22, 83b14-16) also on the side of predicates: there must be predicates that cannot be subjects. (PsA., A, 19-22; PsA., A, 27, 43a36-39) Aristotle calls them primary (πρῶτον). (PsA., A, 21, 82b1-4) These are the highest categories or the highest genera of categories. (PsA., A, 22, 83b14-16) c) The series has an escalating shape from mere subjects at its downside to mere predicates at its upside. It is Aristotle himself whos uses the words up and down in this sense. (e.g. PsA., A, 22, 83b2-3) d) The predications that lie between lowest and highest ones must be finite in number. (PsA., A, 19-22 especially: 20, 82a21-35) These have subjects and predicates, each capable of both of the roles of being subject and being predicated. A result of this fitness is that neither demonstration can go to infinity nor everything is demonstrable, the two points Aristotle always insist on. e) The upward side includes the more universal ones and the downward the more particular ones. (PsA., 20, 82a21-23) f) It follows from the above features that ‘neither the ascending nor the descending series of predications … are infinite.’ (PsA., A, 22, 83b24-25) g) Reciprocation and convertibility. Except in case of terms (i.e. subjects and predicates) that are at each of the ends of series of predications, namely ultimates and primaries, it is possible to reciprocate (ἀντιστρέφειν) terms and convert the predication. (PsA., A, 19, 82a15-20) h) Antipredication. Antipredication means that in a predication (S is P), the subject becomes the predicate of its predicate (P is S) in the same category its predicate was predicated on it. For example, if P is in the category of quality, antipredication means that S be predicated of P in the category of quality. In other words, P is a quality of S and S is a quality of P. Aristotle rejects this. (PsA., A, 22, 83a36-b3) i) Self-predication versus other-predication. Aristotle distinguishes between a predication in which a term is said of itself and a predication in which a term is said of another. (Phy., Δ, 2, 209a31-33) j) Predicablity (Cat., 5, 3a36-b2): 1) Primary substances and individuals are not predicable. 2) Secondary substances are of two kinds: genus and species i) Genus is predicable able both of the species and of the individuals. ii) Species is predicable of the individual. 3) Differentiae are predicable both of the species and of the individuals. 8) Predication as classification a) Richard Patterson believes that Aristotle’s so repeated construction using hoper (estin A hoper B) in Topics (120a23 sq., 122b19, 26sq., 123a, 124a18, 125a29, 126a21, 128a35. Also in Posterior Analytics (83a24-30) (Brunschwig’s list. ‘expresses the fact that A is a kind of B (esti A B tis), that A is a species of the genus B.’ 9) Universal predication Aristotle defines universal predication (κατὰ παντὸς κατηγορεῖσθαι) as such: ‘wherever no instance of the subject (τῶν τοῦ ὑποκειμέμνου) can be found of which the other term cannot be asserted.’ (PrA., A, 24b27-29) In this predication, the subject is included in another as in a whole (ἐν ὃλῳ εἶναι) and the predicate is predicated of all of the subject (κατὰ παντὸς κατηγορεῖσθαι). (PrA., A, 24b26-27) Attach another discussion we had about ἐν ὃλῳ here. 10) Quantity of predication A predication, truly stated, has a quantity, which is the number of objects under the name of the subject of which the predicate is predicated. The quantity of subject can be stated in four ways: a. Indefinite: when the predicate belongs or does not belong to the subject without any mark to show to haw many of the particulars under the name of the subject it does or does not belong. E.g. ‘Man is white’; ‘Man is not white.’ (PrA., A, 24a20; OI., I, 7, 17b8-12) b. Universal quantity: When the predicate belongs to all or none of the subject. E.g. ‘Every man is animal’; ‘No man is animal.’ (PrA., A, 24a18-19; OI., I, 7, 17b5-6) The contrary of a predication of a universal quality is a predication of a universal quality. E.g. the contrary of ‘Every man is white’ is ‘No man is white.’ (OI., I, 7, 17b20-23) c. Particular quantity: When the predicate belongs (or does not belong) to some of the subject. E.g. ‘Some men are white’; ‘Some men are not white.’ (PrA., A, 24a19-20) d. Single quantity: when the subject is a proper name of only one object. E.g. ‘Socrates is white’; ‘Socrates is not white.’ The contrary of this predication is of a single quantity: ‘Socrates is not white.’ (OI., I, 7, 17b38-18a4) 11) Convertibility of predication. Some predications are convertible, that is, it is possible to change the place of subject and predicate in a true proposition so that the converted proposition remains true. This is supposed to mean that given the truth of a predication, the truth of the converted predication is inferable. The convert form of a predication depends on its quantity. a. Indefinite quantity: This predication has no strictly true convert because its quantity is not stated. b. Universal quantity: It can be converted in two ways: i) A negative universal can be converted to a negative universal in which the terms are changed. E.g. ‘No pleasure is good’ can be converted to ‘No good is pleasure.’ (PrA., A, 2, 25a5-8 and a14-19) ii) An affirmative universal can be converted to an affirmative particular in which the terms are changed. E.g. ‘Every pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a7-9) c. Particular quantity: If it is negative, it cannot be converted but if it is affirmative, it can be converted to an affirmative predication with particular quantity. E.g. ‘Some pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a10-13 and a20-24) d. Single quantity: It cannot be converted. 12) Characteristics of relations between subject and predicate 1. A predicate is of a wider range than its subject. It is based on this fact that Aristotle: a) Prevents individuals to be predicate because there is nothing of which an individual be of a wider range. In other words, it is due to the fact that since an individual is only ‘one particular’ thing and, thus, cannot be of a wider extent than anything that Aristotle prevents them of being a predicate. Matthews, however, thinks we cannot use Socrates, a substance and an individual, in the place of predicate and say it of Socrates because ‘Socrates does not classify Socrates: it names him.’ b) Prevents differentia, species and things under species to be predicated of genus. (To., Z, 6, 144a27-) c) Prevents the species and the things under it to be predicated of the differentia. (To., Z, 6, 144b1-4) d) Also about the effect because it is wider than its subject. (PsA., B, 17, 99a) e) Each attribute is wider than every individual it is predicated on, though several attributes, collectively considered, might not be wider but exactly the substance of a thing. (PsA., B, 13, 96a32-b1) 2. The predicate of a predicate of a subject will be predicated of the subject too: ‘whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject too.’ (Cat., 3, 1b10-15) In fact, it is due to its predication of the subject that it is predicated of its predicate. (Cat., 5, 2a36-b1) Moreover, what is not predicated of the predicate of a subject cannot be predicated of it as well. (PrA., A, 27, 43b22-27) Thus, what, for example, is not predicated of animal, cannot be predicated of man. 3. The predicate of a subject can be predicated of its predicates as well. (Cat., 5, 3a1-6) For example, you call the individual man grammatical and, thence, you call both a man and an animal grammatical. Nonetheless, the predicate of a subject belongs to it more properly than to its higher predicates. (PrA., A, 27, 43a27-32) 4. It is only the subject that can be distributed and not the predicate. (PrA., A, 27, 43b16-22; OI, I, 7, 17b12-16) Therefore, we can say e.g. ‘Every man is animal’ but we cannot say ‘Every man is every animal.’ 5. It is the reason of the relation between subjects and predicates, that is the reason of predication, which is the subject of inquiry. (Met., Z, 1041a20-24) In other words, since it is a meaningless inquiry to ask why a thing is itself (Met., Z, 1041a14-15), the only remaining meaningful inquiry is to ask why something is something else, i.e. to ask about the reason of predication. 6. A subject cannot categorize its predicate in the same category in which it is categorized by it. If e.g. A is a quality of B, B cannot be a quality of A. Therefore, there is no reciprocation in the same category. (PsA., A, 22, 83a36-39) 13) Characteristics of series of predications 1. A series of secondary accidental predication cannot go ad infinitum for not even more than two terms can be comnbined. For an accident is not an accident of an accident, unless it be because both are accidents of the same subject. (Met., Γ, 1007b1-4) 2. Infinite series cannot be traversed in thought. (PsA., A, 22, 83b6-7) 3. The predications of genera on each other must be ended and cannot go to infinity because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) Therefore, a series of predication of genera on each other must be limited on both sides. There must be an upward limit in general categories as well as a downward limit in individual because they cannot be predicated of others. Whatever lies between these limits can both be predicated of others and others be predicated of them. (PrA., A, 27, 43a36-43) 4. The order of predicates matters: it makes a difference whether the series be ABC or BAC. (PsA., B, 13, 96b25-32) . (shrink)

ABSTRACT: Recently a bold and admirable interpretation of Chrysippus’ position on the Sorites has been presented, suggesting that Chrysippus offered a solution to the Sorites by (i) taking an epistemicist position1 which (ii) made allowances for higher-order vagueness. In this paper I argue (i) that Chrysippus did not take an epistemicist position, but − if any − a non-epistemic one which denies truth-values to some cases in a Sorites-series, and (ii) that it is uncertain whether and how he made (...) allowances for higher-order vagueness, but if he did, this was not grounded on an epistemicist position. (shrink)

Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and (...) complete, and allows cut-elimination. A question by Takano regarding the eliminability of the Takeuti-Titani density rule is answered affirmatively. (shrink)

Easy to understand philosophy papers in all areas. Table of contents: Three Short Philosophy Papers on Human Freedom The Paradox of Religions Institutions Different Perspectives on Religious Belief: O’Reilly v. Dawkins. v. James v. Clifford Schopenhauer on Suicide Schopenhauer’s Fractal Conception of Reality Theodore Roszak’s Views on Bicameral Consciousness Philosophy Exam Questions and Answers Locke, Aristotle and Kant on Virtue Logic Lecture for Erika Kant’s Ethics Van Cleve on Epistemic Circularity Plato’s Theory of Forms Can we trust our senses? (...) Yes we can Descartes on What He Believes Himself to Be The Role of Values in Science Modern Science Kant’s Moral Philosophy Plato’s Republic as Pol Potist Bureaucracy Schopenhauer on Human Suffering Bertrand Russell on the Value of Philosophy The Philosophical Value of Uncertainty Logic Homework: Theorems and Models Searle vs. Turing on the Imitation Game Hume, Frankfurt, and Holbach on Personal Freedom Manifesto of the University of Wisconsin, Madison Secular Society Michael’s Analysis of the Limits of Civil Protections Bentham and Mill on Different Types of Pleasure Set Theory Homework Aristotle on Virtue Nagel On the Hard Problem Wittgenstein on Language and Thought Camus and Schopenhauer on the Meaning of Life Camus’ Hero as Rebel without a Cause My Little Finger: Camus’ Absurdism Illustrated Are Late-term Abortions Ethical? Does Mathematics Assume the Truth of Platonism? The Self-defeating Nature of Utilitarianism and Consequentialism Generally What is The Good Life? Bentham and Mill regarding types of pleasures Kant’s Moral Philosophy Five Short Papers on Mind-body Dualism Tracy Latimer’s Father had the Right to Kill Her: Towards a doctrine of generalized self-defense Arguments Concerning God and Morality Goldman, Rousseau and von Hayek on the Ideal State J.S Mill on Liberty and Personal Freedom A Kantian Analysis of a Borderline Date-rape Situation Living Well as Flourishing: Aristotle’s Conception of the Good Life Three Essays on Medical Ethics: Answers to Exam Questions on Elective Amputation, Vaccination, and Informed Consent Hobbes, Marx, Rousseau, Nietzsche: Their Central Themes De Tocqueville on Egoism Mill vs. Hobbes on Liberty Exam-Essays on the Moral Systems of Mill, Bentham, and Kant Kant’s Moral System Aristotle on Virtue Plato’s Cave Allegory An Ethical Quandary Superorganisms The Tuskegee Experiment A Rawlsian Analysis Why Moore’s Proof of an External World Fails A Defense of Nagel’s Argument Against Materialism A Utilitarian Analysis of a Case of Theft The Paradox of the Self-aware Wretch: An Analysis of Pascal’s Moral Philosophy Jean-Paul Sartre: Decline and Fall of a Marxist Sell-out A One Page Proof of Plato’s Theory of Forms Plato’s Republic as Pol Potist Bureaucracy The problem of the one and the many Four Short Essays on Truth and Knowledge What is ‘the Good Life?’ The Ontological Argument Different Political Philosophies: Plato, Locke, Madison, Rousseau, Hayek, and Mill on the State What do I know with certainty? Skepticism about skepticism Neuroscience and Freewill Operant Conditioning What makes us special? Are Late-term Abortions Ethical? No Two Papers on Epistemology: Gettier and Bostrom Examination Nietzsche on Punishment God’s Foreknowledge and Moral Responsibility . (shrink)

In his article “Why Philosophical Theories of Evidence Are (and Ought to Be) Ignored by Scientists,” Peter Achinstein argues that philosophical theories of evidence are ignored by scientists because they rest on assumptions which make their concepts of evidence too weak for scientists to work with, or which entail that the truth or falsity of evidential statements can be determined a priori. Given that, as Achinstein argues, the truth of many evidential statements can only be determined empirically, this (...) “a priorist” assumption makes scientists consider philosophical accounts of evidence irrelevant to their work. -/- In this article I examine the value of evidence, its nature, and its relation to science. I try to show that, while Achinstein’s conclusions are mostly right, the arguments and examples he gives to support them are flawed in some of their details. Specifically, I propose an account of evidence according to which, though evidential claims are objective to a large extent, something counts as evidence only if, ultimately, it has a relation to beings for whom it counts as evidence. On this view something’s status as evidence does not derive merely from people’s beliefs, but from shared practices that are embodied in what I call contexts of inquiry. I also propose that this concept of evidence is one according to which evidential claims, though defeasible, are in one respect a priori. I argue that this account of evidence is one that should be of interest to scientists. (shrink)

These days the two most popular approaches to belief ascription are Millianism and Contextualism. The former approach is inconsistent with the existence of ordinary Frege cases, such as Lois believing that Superman flies while failing to believe that Clark Kent flies. The Millian holds that the only truth-conditionally relevant aspect of a proper name is its referent or extension. Contextualism, as I will define it for the purposes of this essay, includes all theories according to which ascriptions of the (...) form ‘S believes that a is F’ and ‘S believes that b is F’, where ‘a’ and ‘b’ are coreferential proper names, may, depending on the context, differ in truth-value even though in those very contexts each ascription relates the same believer to the very same proposition. What the two theories have in common is the claim that names are Millian. What separates the two theories is what they say about belief contexts. In this essay I prove that Millianism is true, Contextualism is true, or our intuitions regarding belief ascriptions are hopelessly inaccurate. As a consequence, my argument is a proof that either names and many general terms are Millian or our intuitions regarding belief ascriptions are hopelessly inaccurate. (shrink)

There are numerous interpretations of Plato's theory of justice as it relates to the ideal state, deeply intertwined with his political philosophy. This complexity makes understanding his interlocking ideas challenging, as he seeks to construct a theory of the ideal state. Plato's philosophy of justice, particularly in its political dimension, emphasizes integration as a fundamental factor in grasping his theory. This paper aims to elucidate the original concept of justice in Plato's state by delving into the roots (...) of the Republic, analyzing its historical context. Plato's predictions reflect values and truths connected to politics and philosophy, emphasizing integration as essential to understanding his theory of justice, which lies at the core of his philosophy. This essay compares the relationship between the functions and class structure of the state. Plato classifies human nature into three components: reason, courage, and appetite, which correspond to three major classes in the state. The ruling class, educated in philosophy, governs the state. The military class, characterized by courage and strength, defends the state, while the professional class manages the everyday affairs of governance. Plato's theory posits functional specialization across all classes as fundamental to his ideal state. In essence, while Plato's imagined city may lack historical existence, it holds significant relevance in the realm of speculative human thought. Keywords: Justice. State. Function. Class. Rulers. Guardians. Producers. (shrink)

One of the most common criticisms one hears of the idea of granting a legitimate role for social values in theory choice in science is that it just doesn’t make sense to regard social preferences as relevant to the truth or to the way things are. “What is at issue,” wrote Susan Haack, is “whether it is possible to derive an ‘is’ from an ‘ought.’ ” One can see that this is not possible, she concludes, “as soon as (...) one expresses it plainly: that propositions about what states of affairs are desirable or deplorable could be evidence that things are, or are not, so” (Haack 1993a, 35, emphasis in original). The purpose of this chapter is not to determine whether this widespread view is correct, but rather to show that even if we grant it (which I do), we may still consistently believe that social values have a legitimate role in theory choice in science. I will defend this conclusion by outlining a view about social values and theory choice that is available to a Constructive Empiricist anti-realist, but not to a realist. (shrink)

Philosopher’s judgements on the philosophical value of Tarski’s contributions to the theory of truth have varied. For example Karl Popper, Rudolf Carnap, and Donald Davidson have, in their different ways, celebrated Tarski’s achievements and have been enthusiastic about their philosophical relevance. Hilary Putnam, on the other hand, pronounces that “[a]s a philosophical account of truth, Tarski’s theory fails as badly as it is possible for an account to fail.” Putnam has several alleged reasons for his (...) dissatisfaction,1 but one of them, the one I call the modal objection (cf. Raatikainen 2003), has been particularly influential. In fact, very similar objections have been presented over and over again in the literature. Already in 1954, Arthur Pap had criticized Tarski’s account with a similar argument (Pap 1954). Moreover, both Scott Soames (1984) and John Etchemendy (1988) use, with an explicit reference to Putnam, similar modal arguments in relation to Tarski. Richard Heck (1997), too, shows some sympathy for such considerations. Simon Blackburn (1984, Ch. 8) has put forward a related argument against Tarski. Recently, Marian David has criticized Tarski’s truth definition with an analogous argument as well (David 2004, p. 389-390).2 This line of argument is thus apparently one of the most influential critiques of Tarski. It is certainly worthy of serious attention. Nevertheless, I shall argue that, given closer scrutiny, it does not present such an acute problem for the Tarskian approach to truth as many philosophers think. But I also believe that it is important to understand clearly why this is so. Moreover, I think that a careful consideration of the issue illuminates certain important but somewhat neglected aspects of the Tarskian approach. (shrink)

Recent experimental work has shown that the truth-value judgments of color predications, i.e. utterances of the form “the leaves on my tree are green” or “these walls are brown,” are influenced by slight changes in the context of utterance (Hansen and Chemla 2013, Ziółkowski, 2021). Most explanations of this phenomenon focus on the semantics of color adjectives. However, it is not clear if these explanations do justice to the nuances of the empirical data on context-sensitivity of color predications (...) (Ziółkowski, 2021). In contrast to the adjectival explanations, Agustin Vicente (2015) has recently proposed that the context-sensitivity of color predications can be explained by invoking the polysemy of the noun. In this paper, we present the results of three studies designed to empirically test this hypothesis: a traditional survey experiment (Study 1), an exploratory correlational study inspired by the semantic integration paradigm (Study 2a), and a follow-up experiment (Study 2b) that was designed to mitigate possible shortcomings of Study 2a. The results of our studies present preliminary evidence against Vicente’s theory. (shrink)

The problem of value disagreement and contextualist, relativist and metalinguistic attempts of solving it are laid out. Although the metalinguistic account seems to be on the right track, it is argued that it does not sufficiently explain why and how disagreements about the meaning of evaluative terms are based on and can be decided by appeal to existing social practices. As a remedy, it is argued that original suggestions from Putnam's 'The Meaning of "Meaning"' ought to be taken seriously. (...) The resulting dual aspect theory of meaning can explain value disagreement in much the same way as it deals with disagreement about general terms. However, the account goes beyond Putnam's by not just defending a version of social externalism, but also defending the thesis that the truth conditional meaning of many evaluative terms is not fixed by experts either and instead constantly contested as part of a normal function of language. (shrink)

You can be convinced that something is true but still desire to see it for yourself. A trusted critic makes some observations about a movie, now you want to watch it with them in mind. A proof demonstrates the validity of a formula, but you are not satisfied until you see how the formula works. In these cases, we place special value on knowing by what Sosa (2021) calls “firsthand insight” a truth that we might already know in (...) some other way such as by testimony, the balance of evidence, or proof. This phenomenon raises two questions. First, what is the nature of firsthand insight? Second, what value motivates us to pursue firsthand insight when other kinds of knowledge are readily available? In the two central parts of this paper, I develop answers to these questions. I argue that firsthand insight that a proposition is true is knowledge based on experience of what makes that proposition true, and I argue that desires for firsthand insight are motivated by concerns with alienation. In a concluding section, I briefly illustrate how the resulting view of the nature and value of firsthand insight might bear on broader topics in the theory of value. (shrink)

“Slingshot Arguments” are a family of arguments underlying the Fregean view that if sentences have reference at all, their references are their truth-values. Usually seen as a kind of collapsing argument, the slingshot consists in proving that, once you suppose that there are some items that are references of sentences (as facts or situations, for example), these items collapse into just two items: The True and The False. This dissertation treats of the slingshot dubbed “Gödel’s slingshot”. Gödel argued that (...) there is a deep connection between these arguments and definite descriptions. More precisely, according to Gödel, if one adopts Russell’s interpretation of definite descriptions (which clashes with Frege’s view that definite descriptions are singular terms), it is possible to evade the slingshot. We challenge Gödel’s view in two manners, first by presenting a slingshot even with a Russellian interpretation of definite descriptions and second by presenting a slingshot even when we change from singular terms to plural terms in the light of new developments of the so-called Plural Logic. The text is divided in three chapters, in the first, we present the discussion between Russell and Frege regarding definite descriptions, in the second, we present Gödel’s position and reconstructions of Gödel’s argument and in the third we prove our slingshot argument for Plural Logic. In light of these results we conclude that we can maintain the validity of slingshot arguments even within a Russellian interpretation of definite descriptions or in the context of Plural Logic. (shrink)

The aim of this paper is twofold: first, I provide a cluster of theories of truth in classical logic that is (internally) consistent with global reflection principles: the theories of positive truth (and falsity). After that, I analyse the _epistemic value_ of such theories. I do so employing the framework of cognitive projects introduced by Wright (Proc Aristot Soc 78:167–245, 2004), and employed—in the context of theories of truth—by Fischer et al. (Noûs 2019. https://doi.org/10.1111/nous.12292 ). In particular, (...) I will argue that theories of positive truth are _trustworthy_, analogously to the theories of full disquotational truth. Moreover, I argue that, for a given cognitive project, _if_ the acceptance of trustworthy theories is taken to be an _epistemic norm_ of cognitive project, then one has good reasons to accept theories of positive truth over other rival theories of truth in classical logic. On the other hand, the latter theories are deemed epistemically unacceptable. (shrink)

Cardinal Bessarion (1408–1472), in the second chapter of the first book of his influential work In calumniatorem Platonis, attempted to reply to Georgios Trapezuntios’ (1396–1474) criticism against Plato in the Comparatio Philosophorum Platonis et Aristotelis. Bessarion investigates why the Athenian philosopher maintained, in several dialogues, that the sacred truths should not be communicated to the general public and argued in favor of the value of oral transmission of knowledge, largely based on his theory about the cognitive processes. Recently, (...) Fr. Bessarion Kouotsis has argued that Cardinal Bessarion’s reasoning draws primarily on the “Disciplina Arcani”, i.e., the rule of secrecy, which was an established practice of the Early Christian Church, aimed at protecting and preserving the core elements of the religion from outsiders. While I find Kouotsis’ approach interesting and thought-provoking—for instance, the idea that Bessarion’s argumentation was likely influenced by Eastern Christian views on the rule of secrecy—I intend, first of all, to discuss why Bessarion did not explicitly mention it. Moreover, I would like to argue that Bessarion’s good knowledge of the long Platonic tradition and Eastern mysticism, encompassing both pagan and Christian elements, should also be considered a significant source. Furthermore, I would like to question Kouotsis’ implicit argument that Bessarion’s views were dominated by his training in Orthodox theology and discuss the possibility that Pletho’s (1355–1454) teaching was the obvious influence for Bessarion’s defense of secrecy. After all, we should bear in mind that Anastos has already pointed out Pletho’s reverence for the rule of secrecy. Finally, I would like to support that Bessarion, in the specific text, focused predominantly on the epistemological and cognitive aspects of oral teaching, resorting to the rule of secrecy only to enhance his views. (shrink)

Many response-dependence theorists equate moral truth with the generation of some affective psychological response: what makes this action wrong, as opposed to right, is that it would cause (or merit) affective response of type R (perhaps under ideal conditions). Since our affective nature is purely contingent, and not necessarily shared by all rational creatures (or even by all humans), response-dependence threatens to lead to relativism. In this paper, I will argue that emotional responses and moral features do not align (...) in the way predicted by the response-dependence theorist who wishes to tie morality to emotional affect. I further argue that since response-dependence accounts that tie morality to any sort of affect (be it an emotion, a desire, a desire to desire, or so on) cannot explain the objectivity and universality of morality; and since we do not need a psychological response to play a truth-constituting role in morality in order to explain the normativity or content of morality, we should reject such response-dependence accounts. (shrink)

Hilary Putnam spent much of his career criticizing the fact/value dichotomy, and this became apparent already during the phase when he defended internal realism. He later changed his epistemological and metaphysical view by endorsing natural realism, with the consequence of embracing alethic pluralism, the idea that truth works differently in various discourse domains. Despite these changes of mind in epistemology and in theory of truth, Putnam went on criticizing the fact/value dichotomy. However, alethic pluralism entails (...) drawing distinctions among discourse domains, especially between factual and nonfactual domains, and these distinctions are in tension with the rejection of the fact/value dichotomy, as this would in principle hinder factual domains as genuine. This issue raises, prima facie, some doubts about the effective compatibility of these views. (shrink)

Notions such as śūnyatā, catuṣkoṭi, and Indra's net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nāgārjuna considered two levels of reality: one called conventional reality, and the other ultimate reality. Within this framework, śūnyatā refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuṣkoṭi refers to the claim (...) that four truth values, including contradiction, are admissible in reasoning. Indra's net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions that are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of śūnyatā. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of catuṣkoṭi. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

Arguments pro and contra convergent realism - underdetermination of theory by observational evidence and pessimistic meta-induction from past falsity- are considered. It is argued that, to meet the counter-arguments challenge, convergent realism should be considerably changed with a help of modification of the propositions from this meta-programme’s “hard core” and “protecting belt”. Maybe one of the ways out is to turn to the coherent theory of truth. Some of the works of Hegel (as interpreted by Merab Mamardashvili (...) and Alexandre Kojev), Husserl and Heidegger can help to dig still deeper into the background of this theory. Key words: Husserl, Heidegger, Hegel, convergent realism, internal realism, coherent theory of truth. -/- . (shrink)

Many scholars claimed that, according to Immanuel Kant, some judgements lack a truth-value: analytic judgements, judgements about items of which humans cannot have experience, judgements of perception, and non-assertoric judgements. However, no one has undertaken an extensive examination of the textual evidence for those claims. Based on an analysis of Kant's texts, I argue that: (1) according to Kant, only judgements of perception are not truth-apt. All other judgements are truth-apt, including analytic judgements and judgements about (...) items of which humans cannot have experience. (2) Kant sometimes states that truth-apt judgements are actual bearers of truth or falsity only when they are taken to state what is actually the case. Kant calls these judgements assertoric. Other texts ascribe truth and falsity to judgements, regardless of whether they are assertoric. Kant's views on truth-aptness raise challenges for correspondentist and coherentist interpretations of Kant's theory of truth; they rule out the identification of Kant's crucial notion of objective validity with truth-aptness; and they imply that Kant was not a verificationist about truth or meaning. (shrink)

The concept of truth is a fundamental philosophical inquiry that transcends time and cultural boundaries. This paper is aimed at illuminating the nature of truth and its intricate connection to the fabric of reality through an extensive bibliography. The reader will have at his disposal the most important references on the subject with a short abstract. The references are under the various theories of truth, even knowing the difficulties in classifying the authors under a label as those (...) proposed by the various theories of truth such as the correspondence, pragmatic, deflationary, constructivist, ontological, and semantic. (shrink)

Contents: Danuta Ługowska, Incommensurability of Paradigms Exemplified by the Differences Between the Western and Eastern European Image of the Human Person ; Maria-Magdalena Weker, Light, Body and Soul – the Issues Fundamental for Theories of Vision. A Historical Survey ; Dariusz Kucharski, The Conception of Sensory Perception and Scientific Research. (The Theory of Sign within Philosophy of G. Berkeley and T. Reid) ; Grzegorz Bugajak, Causality and Determinism in Physics ; Anna Lemańska, Truth in Mathematics ; Anna Latawiec, (...) Troubles with the Philosophy of Medicine ; Adam Świeżyński, Values, Axiological Experience, and Scientific Research ; Grzegorz Bugajak, Fears of Science. Nature and Human Actions ; Adam Świeżyński, Some Remarks on the Human Search for Sense in the Context of Human Actions. (shrink)

According to Cantor (Mathematische Annalen 21:545–586, 1883 ; Cantor’s letter to Dedekind, 1899 ) a set is any multitude which can be thought of as one (“jedes Viele, welches sich als Eines denken läßt”) without contradiction—a consistent multitude. Other multitudes are inconsistent or paradoxical. Set theoretical paradoxes have common root—lack of understanding why some multitudes are not sets. Why some multitudes of objects of thought cannot themselves be objects of thought? Moreover, it is a logical truth that such multitudes (...) do exist. However we do not understand this logical truth so well as we understand, for example, the logical truth $${\forall x \, x = x}$$ . In this paper we formulate a logical truth which we call the productivity principle. Rusell (Proc Lond Math Soc 4(2):29–53, 1906 ) was the first one to formulate this principle, but in a restricted form and with a different purpose. The principle explicates a logical mechanism that lies behind paradoxical multitudes, and is understandable as well as any simple logical truth. However, it does not explain the concept of set. It only sets logical bounds of the concept within the framework of the classical two valued $${\in}$$ -language. The principle behaves as a logical regulator of any theory we formulate to explain and describe sets. It provides tools to identify paradoxical classes inside the theory. We show how the known paradoxical classes follow from the productivity principle and how the principle gives us a uniform way to generate new paradoxical classes. In the case of ZFC set theory the productivity principle shows that the limitation of size principles are of a restrictive nature and that they do not explain which classes are sets. The productivity principle, as a logical regulator, can have a definite heuristic role in the development of a consistent set theory. We sketch such a theory—the cumulative cardinal theory of sets. The theory is based on the idea of cardinality of collecting objects into sets. Its development is guided by means of the productivity principle in such a way that its consistency seems plausible. Moreover, the theory inherits good properties from cardinal conception and from cumulative conception of sets. Because of the cardinality principle it can easily justify the replacement axiom, and because of the cumulative property it can easily justify the power set axiom and the union axiom. It would be possible to prove that the cumulative cardinal theory of sets is equivalent to the Morse–Kelley set theory. In this way we provide a natural and plausibly consistent axiomatization for the Morse–Kelley set theory. (shrink)

Epistemic theories of truth, such as those presumed to be typical for anti-realism, can be characterised as saying that what is true can be known in principle: p → ◊Kp. However, with statements of the form “p & ¬Kp”, a contradiction arises if they are both true and known. Analysis of the nature of the paradox shows that such statements refute epistemic theories of truth only if the the anti-realist motivation for epistemic theories of truth is not (...) taken into account. The motivation in a link of understandability ans meaningful- ness suggests to change the above principle and to restrict the theory to logically simple sentences, in which case the paradox does not arise. This suggestion also allows to see the deep philosophical problems for anti-realism those counterexamples are pointing at. (shrink)

In this paper, I argue that the cleavage between the theory of reference and the theory of meaning, which under the influence of Quine has dominated a large part of the philosophy of language of the last fifty years, is based on a misrepresentation of Tarski's achievement and on an overestimation of the scope and value of disquotation. In particular, I show that, if we accept Davidson's critique of disquotation, the same kind of reasons that Quine offered (...) in opposition to the Carnapian theory of meaning also apply, mutatis mutandis, to the Tarskian theory of reference. (shrink)