Chrysippus often talks as if there is a third option when we might expect that two options in response to a question are exhaustive. Things are true, false or neither; equal, unequal, or neither; the same, different, or neither.. and so on. There seems to be a general pattern here that calls for a general explanation. This paper offers a general explanation of this pattern, preserving Stoic commitments to excluded middle and bivalence, arguing that Chrysippus employs this trichotomy move when (...) he wishes to argue that apparent contradictories are only contraries, and wishes to endorse a third option. This general explanation of the pattern of trichotomies sheds light on a number of interpretive puzzles, including on Chrysippus's response to the paradox of the cone. The purpose of these trichotomies is also discussed, and it is suggested that they originate from the dialectical context in which philosophical problems were posed. (shrink)

We prove several trichotomy results for ideals of compact sets. Typically, we show that a "sufficiently rich" universally Baire ideal is either $\Pi _{3}^{0}$-hard, or $\Sigma _{3}^{0}$-hard, or else a σ-ideal.

According to a standard picture, for any two comparable objects and a basis for comparison, either one is greater than the other or they are equal with respect to the basis. This picture has been called the Trichotomy Thesis, and although it is intuitive and plausible, it has been called into question by such philosophers as Derek Parfit, James Griffin, Joseph Raz, and Ruth Chang. Chang’s discussion is particularly rich, for she proposes and provides a detailed account of a possible (...) fourth relation that, she argues, provides a satisfying explanation of hard cases of comparison. In this paper, I will examine a version of the main argument against the Trichotomy Thesis and attempt to show that it is unsound. (shrink)

. The PCF Trichotomy Theorem deals with sequences of ordinal functions on an infinite $\kappa$ modulo some ideal I. If a $<_I$ -increasing sequence of ordinal functions has regular length which is larger than $\kappa^+$ , then by the Trichotomy Theorem the sequence satisfies one of three structural conditions. It was of some interest to find out if the Trichotomy Theorem could hold also for sequences of length $\kappa^+$ . It is shown that this is not the case.

Using a dictionary translating a variety of classical and modern covering properties into combinatorial properties of continuous images, we get a simple way to understand the interrelations between these properties in ZFC and in the realm of the trichotomy axiom for upward closed families of sets of natural numbers. While it is now known that the answer to the Hurewicz 1927 problem is positive, it is shown here that semifilter trichotomy implies a negative answer to a slightly stronger form of (...) this problem. (shrink)

Name der Zeitschrift: Semiotica Jahrgang: 2016 Heft: 213 Seiten: 165-175.

The term “objective” has both a metaphysical and an epistemological meaning, and each of these meanings gives rise to a corresponding objective-subjective dichotomy. A formal definition of objectivity is given, and this clarifies the nature of the epistemological dichotomy. These dichotomies are represented by classes of existents, and a Venn-type diagram is used to illustrate the relationship between them. It is shown that the class of all existents can be partitioned into three mutually exclusive and exhaustive classes, which correspond to (...) Rand's intrinsic-subjective-objective trichotomy. (shrink)

The issue of the ordering of the ten trichotomies is one among the many questions still open regarding Peirce’s extended theory of signs. A proper decision regarding the order of the ten trichotomies demands a discussion of the entire semiotic process. The aim of this paper is to discuss the order of the trichotomies related to the mode of being of the immediate and dynamical objects. Therefore, it addresses only one part of this process, which concerns the (...) relationship between the sign and its objects. When subdividing the object, Peirce begins to consider the immediate and the dynamic objects as trichotomies, that is, aspects to be considered in the definition of the classes of signs. The introduction of these two trichotomies brings in a problem: how to order them in the system of ten trichotomies. Diverging opinions regarding this ordering are found in Peirce’s texts, and in his commentators. We will investigate this problem by seeking a sort of pragmatic clarification of the matter, presenting a reflection about the philosophical and semiotic consequences of the different proposals for the ordering of these trichotomies. Placing the dynamic object after the sign may even help to explain the functioning of fictional signs, but is this coherent with Peirce’s philosophy? On the other hand, would it be possible to talk about lying signs if every object was determined by its own sign? (shrink)

Shelah develops the theory of \\) without the assumption that \\), going so far as to get generators for every \\) under some assumptions on I. Our main theorem is that we can also generalize Shelah’s trichotomy theorem to the same setting. Using this, we present a different proof of the existence of generators for \\) which is more in line with the modern exposition. Finally, we discuss some obstacles to further generalizing the classical theory.

In 1959, Lao Sze-Kwang (1927 – 2012), a well-known Chinese Kantian philosopher and author of the New Edition of the History of Chinese Philosophy, published On Existentialist Philosophy introducing existential philosophers to Chinese readers. This paper argues that Lao misinterpreted Kierkegaard’s ultimate philosophical quest of “how to become a Christian” as a question of ‘virtue completion,’ because he failed to recognize and acknowledge Kierkegaard’s distinction between aesthetic, moral and religious passion. By describing and clarifying Lao’s misinterpretation, the paper then argues (...) that Lao’s trichotomy of the self fails to give due credit to the independence of religiousness from morality and aesthetics in Kierkegaard’s thought. (shrink)

This paper first re-examines Levinson’s notion of activity type, followed by a review of ethnographic, sociopsychological and ecological studies of the same phenomenon under varied names. The activity type is generally treated as a context in pragmatics. This paper departs from this thinking by proposing that it be treated as the primary object and unit of investigation per se. The role the activity type plays should be that of an interface bridging the langue-parole dichotomy, and the individual-society dichotomy. It is (...) further proposed that the activity type be studied as embodied activities at the token level. It is thus re-conceptualized in term of land-borne situated discourse. (shrink)

The drastically increasing availability ofmodern computers coupled with the equally drasticallylower cost of a given amount of computer power inrecent years has resulted in the evolution of thetraditional experimental/theoretical dichotomy inchemistry into anexperimental/theoretical/computational trichotomy. This trichotomy can be schematically represented by atriangle with experimental,theoretical, and computational chemistry at the threevertices. The ET and EC edges of the ETC triangledepict the uses of theoretical and computationalchemistry, respectively, to predict and interpretexperimental results. The TC edge depicts therelationship between theoretical and computationalchemistry. Mathematics (...) plays an increasing role in allaspects of chemistry, particularly theoreticalchemistry, and has led to the evolution of thediscipline of mathematical chemistry. Research inmathematical chemistry can be considered to lie on achemistry-mathematics continuum depending on therelative depths of the underlying chemistry andmathematics. Examples of the author's own researchlying near each end of the chemistry-mathematicscontinuum include his work on applications of graphtheory and topology in inorganic coordination andcluster chemistry lying near the chemistry end and hiswork on chirality algebra lying near the mathematicsend. The general points in this essay are illustratedby an analysis of the roles of computational andtheoretical chemistry in developing an understandingof structure and bonding in deltahedral boranes andrelated carboranes. This work has allowed extensionof the concept of aromaticity from two dimensions asin benzene and other planar hydrocarbons to the thirddimension in deltahedral boranes. (shrink)

This article explores the main similarities and differences between Derek Parfit’s notion of imprecise comparability and a related notion I have proposed of parity. I argue that the main difference between imprecise comparability and parity can be understood by reference to ‘the standard view’. The standard view claims that 1) differences between cardinally ranked items can always be measured by a scale of units of the relevant value, and 2) all rankings proceed in terms of the trichotomy of ‘better than’, (...) ‘worse than’, and ‘equally good’. Imprecise comparability, which can be understood in terms of the more familiar notions of cardinality and incommensurability, rejects only the first claim while parity rejects both claims of the standard view. -/- I then argue that insofar as those attracted to imprecise comparability assume that all rankings are trichotomous, as Parfit appears to, the view should be rejected. This is because imprecise equality is not a form of equality but is a sui generis ‘fourth’ basic way in which items can be ranked. We should, I argue, understand imprecise equality as parity, and imprecise comparability as entailing ‘tetrachotomy’ – that if two items are comparable, one must better than, worse than, equal to, or on a par with the other. Thus those attracted to the idea that cardinality can be imprecise should abandon trichotomy and accept parity and tetrachotomy instead. -/- Finally, I illustrate the difference between Parfit’s trichotomous notion of imprecise comparability and parity by examining how each notion might be employed in different solutions to the problem posed by the Repugnant Conclusion in population ethics. I suggest that parity provides the arguably more ecumenical solution to the problem. (shrink)

In this paper we study some statements similar to the Partition Principle and the Trichotomy. We prove some relationships between these statements, the Axiom of Choice, and the Generalized Continuum Hypothesis. We also prove some independence results. MSC: 03E25, 03E50, 04A25, 04A50.

This paper argues for the existence of a fourth positive generic value relation that can hold between two items beyond ‘better than’, ‘worse than’, and ‘equally good’: namely ‘on a par’.

This unpublished paper, which readers should feel free to cite, is posted primarily for the historical record. In recent work that has, deservedly, received some attention, Paul R. Daniels presents and defends a non-standard theory of persistence that he dubs transdurantism, according to which persisting objects are temporally extended simples. This is exactly what I do in work dating back to 2004. (This work began with an earlier draft of this paper, which was presented to the University of Rochester's Philosophy (...) Department in 2005, and culminated in this version, which I believe dates from 2010.) While this might be a total coincidence, I doubt that it is, especially given that 'transdurantism' appears as a name for a theory of persistence associated with me in at least two places in the literature, one of which includes a citation of this paper. The paper begins with a discussion of what I call 'locative relations' (the relations borne by material objects to the regions of space and time they occupy), which draws relevant distinctions that others have failed to draw. The results of this discussion are then used in constructing spatial analogues for the three established theories of persistence--endurantism, perdurantism, and exdurantism--as well as for transdurantism. Next, these four views concerning persistence are explicitly formulated and a defense of their formulation is offered. Finally, transdurantism's advantages and disadvantages relative to the other theories are discussed. The main goal of the paper is to challenge the trichotomy between the established theories by arguing that transdurantism is also a viable view concerning persistence through time. [Note: Befitting its status as a historical document, with the exception of some light editing to fix typos that might impede understanding, no changes have been made to the paper.]. (shrink)

The semeiotic of Charles Sanders Peirce is irreducibly triadic, positing that a sign mediates between the object that determines it and the interpretant that it determines. He eventually holds that each sign has two objects and three interpretants, standardizing quickly on immediate and dynamical for the objects but experimenting with a variety of names for the interpretants. The two most prominent terminologies are immediate/dynamical/final and emotional/energetic/logical, and scholars have long debated how they are related to each other. This paper seeks (...) to shed new light on the matter by reviewing the numerous manuscript drafts where Peirce develops the latter nomenclature while attempting to introduce his pragmatism to a general audience. It then goes on to examine an additional set of interpretants, intentional/effectual/communicational, and shows that the three different trichotomies can be understood as complementary, rather than redundant or conflicting. (shrink)

In theMetaphysics, Aristotle pointed out that some activities are engaged in for their own sake, while others are directed at some end. The test for distinguishing between them is to ask, ‘At any time during a period in which someone is Xing, is it also true that they have Xed?’ If both are true, the activity is being done for its own sake. If not, it is being done for the sake of some end other than itself. For example, if (...) I am thinking, it is true that I have thought. But if I’m making a blouse, it is not true that I have made a blouse, at least not this particular blouse. That’s not true until I have completed the project.There have been a number of attempts to deepen our understanding of this distinction. Anthony Kenny devoted a chapter of Action, Emotion, and Will to this issue, exploring the effect tense has on implication relations, and using that as a basis for dividing verbs of action into state-verbs, activity-verbs and performance-verbs. In more recent years the trend has been to generalize these categories so as to include occurrences other than actions, i.e., occurrences which do not involve intentions. While interest in this area tends to focus primarily on linguistic issues, such as the categorization of verbs, or on the logical analysis of sentences, there has been some interest in related metaphysical issues. In 1978 Alexander Mourelatos published ‘Events, Processes, and States,’ a paper which has turned out to be quite influential, in which he proposes an ontological trichotomy of occurrences. In his view, processes and events form distinct categories within the general category of occurrences. In this paper I will examine the reasoning underlying Mourelatos’s claim, arguing that the differences between processes and events cannot provide the basis for an ontological subcategorization of occurrences. (shrink)

This Element examines Kant's innovative account of labour in his political philosophy and develops an intersectional analysis of Kant. By demonstrating that Kant's analysis of slavery, citizenship, and sex developed in inter-linked ways over several decades, culminating in his development of a 'trichotomy' of Right, the author shows that Kant's normative account of independence is configured through his theory of labour, and is continuous with his anthropological accounts of race and gender, providing a systemic justification for the dependency of women (...) and non-whites embedded in his philosophy of right. By examining Kant's arguments about slavery as intertwined with his account of domestic labour, the author argues that his ultimate rejection of slavery may owe more to his changing conceptualization of labour than to his theory of race, and that his final arguments against slavery rehearse strategies for embedding intersectional patterns of domestic dependence in his account of the rightful state. (shrink)

A linear space is a system of points and lines such that any two distinct points determine a unique line; a Steiner k-system is a linear space such that each line has size exactly k. Clearly, as a two-sorted structure, no linear space can be strongly minimal. We formulate linear spaces in a vocabulary $\tau $ with a single ternary relation R. We prove that for every integer k there exist $2^{\aleph _0}$ -many integer valued functions $\mu $ such that (...) each $\mu $ determines a distinct strongly minimal Steiner k-system $\mathcal {G}_\mu $, whose algebraic closure geometry has all the properties of the ab initio Hrushovski construction. Thus each is a counterexample to the Zilber Trichotomy Conjecture. (shrink)

The familiar Vendler-Kenny scheme of verb-types, viz., performances (further differentiated by Vedler into accomplishments and achievements), activities, and states, is too narrow in two important respects. First, it is narrow linguistically. It fails to take into account the phenomenon of verb aspect. The trichotomy is not one of verbs as lexical types but of predications. Second, the trichotomy is narrow ontologically. It is a specification in the context of human agency of the more fundamental, topic-neutral trichotomy, event-process-state.The central component in (...) this ontological trichotomy, event, can be sharply differentiated from its two flanking components by adapting a suggestion by Geoffrey N. Leech and others that the contrast between perfective and imperfective aspect in verbs corresponds to the count/mass distinction in the domain of nouns. With the help of two distinctions, of cardinal count adverbials versus frequency adverbials, and of occurrence versus associated occasion, two interrelated criteria for event predication are developed. Accordingly, Mary capsized the boat is an event predication because (a) it is equivalent to There was at least one capsizing of the boat by Mary, or (b) because it admits cardinal count adverbials, e.g., at least once, twice, three times. Ontologically speaking, events are defined as those occurrences that are inherently countable. (shrink)

Talk of “essences” has, since Saul Kripke and Hilary Putnam, gained significant currency in contemporary philosophy. It is no longer unfashionable to talk about the essence of this or that (natural) kind, and as such we now find a variety of brands of essentialism on the market including B.D. Ellis’s scientific essentialism, David Oderberg’s real Essentialism, Alexander Bird’s dispositional essentialism, and the contemporary essentialism of Kripke and Putnam. -/- Almost all these brands of essentialism share a particular gloss on Locke’s (...) famous objection to Aristotle that natural kinds are demarcated by nominal essences not real essences. Thus Oderberg claims that ‘Empiricists take [real] essences to be paradigmatically unobservable’ and that this ‘objection goes back at least to John Locke’ (Oderberg 2007: 21). Bird, presenting his dispositional essentialism, defines a notion of “being” as ‘the reverse of Locke’s definition of essence’ which he takes to be ‘the being of any thing, whereby it is what it is’ (Bird 2007: 100). Joseph LaPorte, discussing nominal and real essences, claims that ‘Kripke and Putnam seem to affirm something more substantive: that biological kinds have “real essences” in Locke’s terminology’ (LaPorte 2004: 49). Even avowed anti-essentialists such as John Dupré sanction the standard criticism of Locke that his scepticism about the knowability of real essences was ‘premature’, and claim that ‘genuine natural kinds provide the extensions of many terms of natural language, where these natural kinds are determined by true Lockean real essences’ (Dupré 1993: 22). -/- All of these essentialisms (even Dupré’s anti-essentialism) are wrong about Locke. Oderberg is wrong to claim that Locke thought that real essences were paradigmatically unobservable; Bird is wrong to think that Locke’s notion of essence is the being of anything whereby it is what it is; LaPorte is wrong to think that Kripke and Putnam are talking about Lockean real essences (although so are Kripke and Putnam); and Dupré is wrong to think that genuine natural kinds (if by genuine he means objective or mind-independent) are determined but true Lockean real essences . -/- The mistake stems from a standard, but ultimately incorrect, interpretation of Locke’s discussion of essences in An Essay Concerning Human Understanding . This mistaken interpretation (Lowe 1995, 2006, Von Leyden 1973, Wiggins 1974) takes Locke to mean, by “real essence”, the Aristotelian notion i.e. ‘the very being of anything, whereby it is what it is’ (Essay III.iii.15), and interprets his objection as epistemological: we cannot come to know what real essences are, and therefore they cannot figure in our classifications of things into kinds. -/- This paper will present and defend the following two claims: i) that Locke’s notion of “real essence” is not the Aristotelian notion, and ii) that Locke’s objection to the Aristotelian notion was not merely epistemological. The first claim can be defended by presenting and applying Vienne’s (1993) terminological revision. Vienne argues that Locke did not introduce a dichotomy between real and nominal essence, but a trichotomy between real essence, nominal essence and real constitution. This terminological revision will be employed to highlight where ambiguous uses of the phrase “real essence” have caused some serious misunderstandings of Locke’s philosophy. The second claim (steering Locke around what is the classic objection to his thesis) can be defended by presenting a novel way of splitting up Locke’s objections to the Aristotelian notion of essence. The analysis will show that Locke’s anti-essentialism is still in good shape, and of contemporary significance. (shrink)

Charles S. Peirce’s second trichotomy, which introduces the concepts of iconicity, indexicality, and symbolicity, is probably the only piece of his semiotic that is familiar to visual artists and designers. Although the concepts have found their way into the academy, their utility in the field has been reduced for a couple of reasons. First, as with all of Peirce’s philosophy, his second trichotomy is a concept that is subtle, fluid, and difficult to fully grasp in a sound bite. Second, there (...) has simply been no bridge concept that would form a working connection between that philosophy in its logical guise and the studio practice in the visual arts. The purpose of this article is to remedy that situation by investigating the subtle ways the second trichotomy functions within the visual sphere, and to then suggest a model that can serve to bridge the divide between pure theory and practice. The article makes four main points: first, using examples from visual identity and the graphic arts, it demonstrates how the modes of icon, index, and symbol tend to be blended; second, examples from fine art are used to illustrate how the concept of abstraction, as used in the art world, can only be partially accounted for within the second trichotomy, but can be modeled by supplying a syntactical supplement; third, it expands on and elaborates a previously sketched model, the visual gamut, which makes it possible to classify visual entities according to their position within a map of semantic and syntactic space; finally, it concludes by suggesting ways this enhanced version of the visual gamut model might be used in the analysis of, or creation of, art and design, presenting suggestions for further study. (shrink)

This article aims to examine the relationship between image and narrative by means of Peirce’s first trichotomy of qualisign-sinsign-legisign or, for the purposes of the current argument, image-diagram-metaphor. It is argued that narrative, as an extended metaphor, can be examined in three modes: in the image; schematically, in the imagination; and allegorically or in a thought experiment, through hypothetic interpretation. The article outlines two kinds of diagrammatic reasoning emphasized by Peirce: corollarial deduction in which the image is ‘literally seen’ and (...) the reasoning steps are manifest in its conclusion; and theorematic deduction where the conclusion in a diagram is subject to a hypothesis which transforms the image into something new. Demonstrating the breadth of diagrammatic reasoning with reference to the 2018 film, The Shape of Water, the article seeks to explore how allegory and diagram are mutually cooperative, based on three ontological modes: the expressive, the cognitive, and the symbolic. Its primary focus, then, is not so much on the story events of the narrative, as the way that they are visualized and characterized as the fairy story unfolds. It is suggested that the interpreting activity involved in allegory and diagram ties interpretation to metacognition, ultimately (re)recognizing the image in The Shape of Water in an attempt to ascertain the meaning of love. (shrink)

We study the theory of lovely pairs of geometric structures, in particular o-minimal structures. We use the pairs to isolate a class of geometric structures called weakly locally modular which generalizes the class of linear structures in the settings of SU-rank one theories and o-minimal theories. For o-minimal theories, we use the Peterzil–Starchenko trichotomy theorem to characterize for a sufficiently general point, the local geometry around it in terms of the thorn U-rank of its type inside a lovely pair.

The seventh sign in Charles Peirce’s well-known 10-sign taxonomy of the 1903 Syllabus has received relatively little attention compared to many other types of sign that he described. It is the sign type of “Dicent Indexical Legisigns”, a result of the combinatory strategy of the 3x3 elementary sign aspects defined by the three basic sign trichotomies of Qualisign-Sinsign-Legisign, Icon-Index-Symbol and Rheme-Dicisign-Argument, a new strategy developed by Peirce in that famous text. It is well known how such aspects do not (...) combine freely, hence not resulting in 3 × 3 × 3 = 27 sign types, but only in 10 sign types, due to the application of the rule aptly summarized by Bellucci as “a certain combination... (shrink)

What is it for a car, a piece of art or a person to be good, bad or better than another? In this first book-length introduction to value theory, Francesco Orsi explores the nature of evaluative concepts used in everyday thinking and speech and in contemporary philosophical discourse. The various dimensions, structures and connections that value concepts express are interrogated with clarity and incision. -/- Orsi provides a systematic survey of both classic texts including Plato, Aristotle, Kant, Moore and Ross (...) and an array of contemporary theorists. The reader is guided through the moral maze of value theory with everyday examples and thought experiments. Rare stamps, Napoleon's hat, evil demons, and Kant's good will are all considered in order to probe our intuitions, question our own and philosophers' assumptions about value, and, ultimately, understand better what we want to say when we talk about value. -/- 1. Value and Normativity 1.1 Introduction 1.2 Which Evaluations? 1.3 The Idea of Value Theory 1.4 Value and Normativity 1.5 Overview 1.6 Meta-ethical Neutrality 1.7 Value Theory: The Questions -/- 2. Meet the Values: Intrinsic, Final & Co. 2.1 Introduction 2.2 Final and Unconditional Value: Some Philosophical Examples 2.3 Intrinsic Value and Final Value 2.4 The Reduction to Facts 2.5 Intrinsic and Conditional Value 2.6 Elimination of Extrinsic Value? 2.7 Summary -/- 3. The Challenge against Absolute Value 3.1 Introduction 3.2 Geach and Attributive Goodness 3.3 Foot and the Virtues 3.4 Thomson and Goodness in a Way 3.5 Zimmerman's Ethical Goodness 3.6 A Better Reply: Absolute Value and Fitting Attitudes 3.7 Summary -/- 4. Personal Value 4.1 Introduction 4.2 Moore on Good and Good For 4.3 Good For and Fitting Attitudes 4.4 Moore Strikes Back? 4.5 Agent-relative Value 4.6 Impersonal/Personal and Agent-neutral/Agent-relative 4.7 Summary -/- 5. The Chemistry of Value 5.1 Introduction 5.2 Supervenience and Other Relations 5.3 Organic Unities 5.4 Alternatives to Organic Unities: Virtual Value 5.5 Alternatives to Organic Unities: Conditional Value 5.6 Holism and Particularism 5.7 Summary -/- 6. Value Relations 6.1 Introduction 6.2 The Trichotomy Thesis and Incomparability 6.3 A Fitting Attitude Argument for Incomparability 6.4 Against Incomparability: Epistemic Limitations 6.5 Against Incomparability: Parity 6.6 Parity and Choice 6.7 Parity and Incomparability 6.8 Summary -/- 7. How Do I Favour Thee? 7.1 Introduction 7.2 Three Dimensions of Favouring 7.3 Responses to Value: Maximizing 7.4 Two Concepts of Intrinsic Value? 7.5 Summary -/- 8. Value and the Wrong Kind of Reasons 8.1 Introduction 8.2 The Fitting Attitude Account and its Rivals 8.3 The Wrong Kind of Reasons Problem 8.4 The Structure of the Problem and an Initial Response 8.5 Reasons for What? 8.6 Characteristic Concerns and Shared Reasons 8.7 Circular Path: No-Priority 8.8 Summary . (shrink)

The paper proposes a formal account of Aristotle's trichotomy of verbs, in terms of properties of their continuous tensings, into S(state)-verbs, K(kinesis)-verbs, and E-(energeia)-verbs. Within a Fregean tense framework in which predicates are relativized to times, an account of the continuous tenses is presented and a preliminary account of the trichotomy devised, which permits an illuminating analogy to be drawn between the temporal properties of E- and K-verbs and the spatial properties of stuffs and substances. This analogy is drawn upon (...) in constructing a sophisticated version of the preliminary theory accommodating more of the linguistic data. (shrink)

The essay addresses the well‐known idea that there has to be a place for intuition, thought of as a kind of non‐inferential rational insight, in the epistemology of basic logic if our knowledge of its principles is non‐empirical and is to allow of any finite, non‐circular reconstruction. It is argued that the error in this idea consists in its overlooking the possibility that there is, properly speaking, no knowledge of the validity of principles of basic logic. When certain important distinctions (...) are observed, for instance that between recognising that Modus Ponenes is sound and recognising that it is proof against the competent discovery of basic counterexamples, the case for thinking that there is indeed no space for genuine recognition of the validity of Modus Ponens becomes increasingly impressive. It is argued however that, the impossibility of knowledge notwithstanding, we are, in an important sense, entitled to take it that Modus Ponens is sound and that this notion of entitlement can help break the trichotomy ‐ intuition, inference, experience ‐ which imprisons our ordinary thinking about logical knowledge. (shrink)

This paper begins with a response to Josh Gert’s challenge that ‘on a par with’ is not a sui generis fourth value relation beyond ‘better than’, ‘worse than’, and ‘equally good’. It then explores two further questions: can parity be modeled by an interval representation of value? And what should one rationally do when faced with items on a par? I argue that an interval representation of value is incompatible with the possibility that items are on a par (a mathematical (...) proof is given in the appendix). I also suggest that there are three senses of ‘rationally permissible’ which, once distinguished, show that parity does distinctive practical work that cannot be done by the usual trichotomy of relations or by incomparability. In this way, we have an additional argument for parity from the workings of practical reason. (shrink)

In his 1903 Syllabus, Charles S. Peirce makes a distinction between icons and iconic signs, or hypoicons, and briefly introduces a division of the latter into images, diagrams, and metaphors. Peirce scholars have tried to make better sense of those concepts by understanding iconic signs in the context of the ten classes of signs described in the same Syllabus. We will argue, however, that the three kinds of hypoicons can better be understood in the context of Peirce's sixty-six classes of (...) signs. We analyze examples of hypoicons taken from the field of information design, describing them in the framework of the sixty-six classes, and discuss the consequences of those descriptions to the debate about the order of determination of the 10 trichotomies that form those classes. (shrink)

[Note: Picture of Peirce available] Charles S. Peirce’s Philosophy of Signs Essays in Comparative Semiotics Gérard Deledalle Peirce’s semiotics and metaphysics compared to the thought of other leading philosophers. "This is essential reading for anyone who wants to find common ground between the best of American semiotics and better-known European theories. Deledalle has done more than anyone else to introduce Peirce to European audiences, and now he sends Peirce home with some new flare."—Nathan Houser, Director, Peirce Edition Project Charles S. (...) Peirce’s Philosophy of Signs examines Peirce’s philosophy and semiotic thought from a European perspective, comparing the American’s unique views with a wide variety of work by thinkers from the ancients to moderns. Parts I and II deal with the philosophical paradigms which are at the root of Peirce’s new theory of signs, pragmatic and social. The main concepts analyzed are those of "sign" and "semiosis" and their respective trichotomies; formally in the case of "sign," in time in the case of semiosis. Part III is devoted to comparing Peirce’s theory of semiotics as a form of logic to the work of other philosophers, including Bertrand Russell, Wittgenstein, Frege, Philodemus, Lady Welby, Saussure, Morris, Jakobson, and Marshall McLuhan. Part IV compares Peirce’s "scientific metaphysics" with European metaphysics. Gérard Deledalle holds the Doctorate in Philosophy from the Sorbonne. A research scholar at Columbia University and Attaché at the Centre National de la Recherche Scientifique, Paris, he has also been Professor of Philosophy and Head of the Philosophy Department of the universities of Tunis, Perpignan, and Libreville. In 1990 he received the Herbert W. Schneider Award "for distinguished contributions to the understanding and development of American philosophy. In 2001, he was appointed vice-president of the Charles S. Peirce Society. Contents Introduction—Peirce Compared: Directions for Use Part I—Semeiotic as Philosophy Peirce’s New Philosophical Paradigms Peirce’s Philosophy of Semeiotic Peirce’s First Pragmatic Papers The Postscriptum of 1893 Part II—Semeiotic as Semiotics Sign: Semiosis and Representamen—Semiosis and Time Sign: The Concept and Its Use—Reading as Translation Part III—Comparative Semiotics Semiotics and Logic: A Reply to Jerzy Pelc Semeiotic and Greek Logic: Peirce and Philodemus Semeiotic and Significs: Peirce and Lady Welby Semeiotic and Semiology: Peirce and Saussure Semeiotic and Semiotics: Peirce and Morris Semeiotic and Linguistics: Peirce and Jakobson Semeiotic and Communication: Peirce and McLuhan Semeiotic and Epistemology: Peirce, Frege, and Wittgenstein Part IV—Comparative Metaphysics Gnoseology—Perceiving and Knowing: Peirce, Wittgenstein, and Gestalttheorie Ontology—Transcendentals "of" or "without" Being: Peirce versus Aristotle and Thomas Aquinas Cosmology—Chaos and Chance within Order and Continuity: Peirce between Plato and Darwin Theology—The Reality of God: Peirce’s Triune God and the Church’s Trinity Conclusion—Peirce: A Lateral View. (shrink)

[Note: Picture of Peirce available] Charles S. Peirce’s Philosophy of Signs Essays in Comparative Semiotics Gérard Deledalle Peirce’s semiotics and metaphysics compared to the thought of other leading philosophers. "This is essential reading for anyone who wants to find common ground between the best of American semiotics and better-known European theories. Deledalle has done more than anyone else to introduce Peirce to European audiences, and now he sends Peirce home with some new flare."—Nathan Houser, Director, Peirce Edition Project Charles S. (...) Peirce’s Philosophy of Signs examines Peirce’s philosophy and semiotic thought from a European perspective, comparing the American’s unique views with a wide variety of work by thinkers from the ancients to moderns. Parts I and II deal with the philosophical paradigms which are at the root of Peirce’s new theory of signs, pragmatic and social. The main concepts analyzed are those of "sign" and "semiosis" and their respective trichotomies; formally in the case of "sign," in time in the case of semiosis. Part III is devoted to comparing Peirce’s theory of semiotics as a form of logic to the work of other philosophers, including Bertrand Russell, Wittgenstein, Frege, Philodemus, Lady Welby, Saussure, Morris, Jakobson, and Marshall McLuhan. Part IV compares Peirce’s "scientific metaphysics" with European metaphysics. Gérard Deledalle holds the Doctorate in Philosophy from the Sorbonne. A research scholar at Columbia University and Attaché at the Centre National de la Recherche Scientifique, Paris, he has also been Professor of Philosophy and Head of the Philosophy Department of the universities of Tunis, Perpignan, and Libreville. In 1990 he received the Herbert W. Schneider Award "for distinguished contributions to the understanding and development of American philosophy. In 2001, he was appointed vice-president of the Charles S. Peirce Society. Contents Introduction—Peirce Compared: Directions for Use Part I—Semeiotic as Philosophy Peirce’s New Philosophical Paradigms Peirce’s Philosophy of Semeiotic Peirce’s First Pragmatic Papers The Postscriptum of 1893 Part II—Semeiotic as Semiotics Sign: Semiosis and Representamen—Semiosis and Time Sign: The Concept and Its Use—Reading as Translation Part III—Comparative Semiotics Semiotics and Logic: A Reply to Jerzy Pelc Semeiotic and Greek Logic: Peirce and Philodemus Semeiotic and Significs: Peirce and Lady Welby Semeiotic and Semiology: Peirce and Saussure Semeiotic and Semiotics: Peirce and Morris Semeiotic and Linguistics: Peirce and Jakobson Semeiotic and Communication: Peirce and McLuhan Semeiotic and Epistemology: Peirce, Frege, and Wittgenstein Part IV—Comparative Metaphysics Gnoseology—Perceiving and Knowing: Peirce, Wittgenstein, and Gestalttheorie Ontology—Transcendentals "of" or "without" Being: Peirce versus Aristotle and Thomas Aquinas Cosmology—Chaos and Chance within Order and Continuity: Peirce between Plato and Darwin Theology—The Reality of God: Peirce’s Triune God and the Church’s Trinity Conclusion—Peirce: A Lateral View. (shrink)

The work on set theory made by A. Tarski in the years 1924-1950 is very interesting, but little know.We develope partial questions in set theory in the moment that A. Tarski intervenes and his contributionsand also influences.The principals aims in this development are:1. The axiom of choice [A.C.] and his equivalents;2. the general continuum hypothesis [G.C.H.] and the A.C.;3. the dual trichotomy principle;4. the inaccessible cardinals and his relation with the A.C. and the G.C.H.;5. the notion of finite set and (...) his relation with the A.C and the G.C.H.;6. the almost disjoint set and their relation with the G.C.H.;and finally,7. the results in Berkeley. (shrink)

Active reciprocity is a process of human harmonious development, which is based on reciprocity. Reciprocity is the result of trichotomy and the expression of golden mean; Active reciprocity is the expression of active golden mean, which discards the passive part of reciprocity. Active reciprocity is a form of rational collectivism which, generally speaking, has two rules for individual communication behavior, namely mutually benefiting and mutually tolerating. It also has three rules for individual behavior, namely benefiting the others without harming oneself, (...) benefiting both oneself and others, benefiting oneself without harming others. It has, through norms, incorporated values and ideas such as fairness, reason, democracy, philanthropism, freedom, harmony, as well as right, responsibility, respect, tolerance, trust, sustainable development. However, it has to be pointed out that active reciprocity should oriented towards altruism, with the minimum requirement of doing no harm to others. Otherwise it will result in moral relativism. (shrink)

In other work I have argued that items can be on a par, where being on a par is a fourth, basic, sui generis value relation beyond the usual trichotomy of ‘better than’, ‘worse than’, and ‘equally good’. In this paper, I aim to marshal non-technical, intuitive arguments for this view. First, I try to cast doubt on the leading source of intuitive resistance to parity, the conviction that if two items are comparable, one must be better than the other, (...) worse than it, or they must be equally good. Second, I explain how parity can arise by appealing to an uncontroversial distinction between quantity and quality of value. I propose both sufficient conditions for parity and a nontechnical model of the notion. My overall aim is to bring into view a simple and intuitive picture of value – and more generally of normativity – in which parity plays a significant role. (shrink)