Truth-values

How to say no less, no more about conditional than what is needed? From a logical analysis of necessary and sufficient conditions, we argue that a proper account of conditional can be obtained by extending the logical notation of Frege’s Begriffsschrift. After discarding his Equivalence Thesis, according to which the denial of a sentence equates with the affirmation of its negation, it becomes possible to characterize the logical meaning of “if”, and only “if”. That is: without irremediably leading from entailment into formal implication, whilst sticking to a bivalent definition of conditional as a speech-act commitment. Finally, the two main inference rules for conditional, viz. Modus Ponens and Modus Tollens, are reassessed in this new light.

摘要：通常所接受对库恩有关不可通约性的分类学解释的理解建立在不可译性概念之上，因而是相当不完善的。为了弥补此不足，本文在分类之逻辑语义理论 (a logical-semantic theory of taxonomy)、真值语义理论 (a semantic theory of truth-value)，以及跨语言交流的真值条件理论 (a truth-value conditional theory of cross-language communication) 之基础上，对库恩有关不可通约性的分类学解释进行了重建。根据这种重建，如果两个科学语言具有不相匹配的分类结构，则当一科学语言的核心语句在其所属语境中具有真值、而在另一科学语言之语境中考虑缺乏真值时，这两种科学语言乃不可通约。通过这种重建，库恩对于不可通约性的成熟解释并非基于保真 (truth-preserving) 可译性或不可译性的概念，而是基于保留真值状态 (truth-value-preserving) 的跨语言交流概念之上。这种重建使得库恩有关不可通约性的解释更具坚实的理论基础、也在概念上更加完整。

关键词：不可通约性 (incommensurability)；托马斯· 库恩 (Thomas, Kuhn)；分类结构 (taxonomy)；词汇系统 (lexicon)；真值 (truth-value)；不可译性 (untranslatability)；跨语言交流 (cross-language communication)

The compound word “truth-value”, sometimes written “truth value”, is a bit monstrous and ambiguous. It is the name of a central concept of modern logic, but has not yet invaded everyday language. An ordinary man will say: it is true that Paris is the capital of France, rather than: the truth-value of “Paris is the capital of France” is true. And a mathematician also will say: it is true that 2 + 3 = 5, rather than the truth-value of “2 + 3 = 5” is true. We don't even find “truth-values” in postmodern or new age discussions side by side with “quantum leap”, “imaginary number”, “betacognition”. It seems that “truth-value” is exclusively used by logicians, philosophers of logic and analytic philosophers. In this paper we will examine the origin of this strange way of speaking and the concept related to it.

Book Blurb/Description

Title: Incommensurability and Cross-Language Communication 

The thesis of incommensurability challenges a dominant epistemological assumption behind Western philosophy—i.e., some form of commonality between any languages, traditions, or cultures exists, which makes full cross-language/tradition/culture communication always attainable—by exploring why and how the communication between two conceptually disparate languages, traditions, or cultures is often problematic and even unattainable. However, this essential thrust of incommensurability is either neglected or misinterpreted in the current literature, as we can see clearly from the accepted translation-failure interpretation of incommensurability.

To rescue the above essence of the thesis of incommensurability, this book presents a presuppositional interpretation of incommensurability, according to which, when two comprehensive languages loaded with incompatible metaphysical presuppositions confront with each other, the confrontation leads to a truth-value gap, and consequently results in a communication breakdown between the two language communities. Therefore, we can never escape the real possibility that the others are radically different from us such that we may fail to fully communicate with alien languages, traditions, or cultures.   

This book not only makes some significant, original contributions to the discussion of incommensurability and related issues in philosophy, such as the notion of conceptual schemes and the issue of cross-language understanding and communication, but also offers many valuable insights to the scholars in other fields, such as anthropology, communication, linguistics, scientific education, and cultural studies.

斯特劳逊 （Strawson）的语义预设概念在语义学和语言哲学研究上颇有建树。尽管如此，语义预设概念一直遭受来自各方面的批判。概要说来，对语义预设概念之批判主要来自两个方面：其一，试图抽去语义预设概念的逻辑基础，即非真值概念 (the notion of truthvaluelessness)，从而达到间接地拒斥语义预设概念之目的。其二，直接批判语义预设概念本身。他们或者论证此概念在理论上不自恰或微不足道，或者断定即使此概念本身在理论上自恰，但实为一空洞无物之概念。因为我们根本找任何一个语义预设的具体例证。所以，语义预设概念不具任何真正的哲学意义。它只是一个当代神话，理应拒斥。

玻尔(S. Ber)和莱肯(W. Lycan)对语义预设概念的批判集中代表了以上两个方面。据我所知，迄今不曾有人对他们的批判予以全面和公正的反驳，以致于许多人人云亦云，使得他们的论点至今颇有影响。给予玻尔和莱恩的批判以全面反驳乃本文初衷。于此相关，我以为很有必要澄清对语义预设概念的诸多误解，从而确立一个理论上自恰，实际上可行，和确有实质性内容的语义预设概念。基于以上考虑，我对语义预设概念批判之反驳包括正 反两个方面。在第二节，我试图建立一个自恰，完备，非庸俗的语义预设概念。基于这一概念，第三节对玻尔和莱恩反对语义预设的两个核心批判予以全面反驳。第四节着重辩护非真值概念。本文的最后结论是：各种批判并未损伤斯特劳逊的语义预设概念的精髓。语 义预设概念非但不是一个当代神话，而且具有重大哲学意义。

A general framework for translating various logical systems is presented, including a set of partial unary operators of affirmation and negation. Despite its usual reading, affirmation is not redundant in any domain of values and whenever it does not behave like a full mapping. After depicting the process of partial functions, a number of logics are translated through a variety of a rmations and a unique pair of negations. This relies upon two preconditions: a deconstruction of truth-values as ordered and structured objects, contrary to its mainstream presentation as a simple object; a redefinition of the Principle of Bivalence as a set of four independent properties, such that its definition does not equate with normality.

D. Davidson argues that the existence of alternative conceptual schemes presupposes the Kantian scheme-content dualism, which requires a scheme-neutral empirical content and a fixed, sharp scheme-content distinction. The dismantlement of such a Kantian scheme-content dualism, which Davidson calls “the third dogma of empiricism”, would render the notion of alternative conceptual schemes groundless. To counter Davidson’s attack on the notion of alternative conceptual schemes, I argue that alternative conceptual schemes neither entail nor presuppose the Kantian scheme-content dualism. On the contrary, it is exactly the abandonment of the concept-neutral content and the denial of a fixed, absolute scheme-content distinction that turns the Kantian conceptual absolutism upside down and thus makes alternative conceptual schemes possible. Proposing common-sense experience as the empirical content of alternative schemes, I construct and defend a non-Kantian scheme-content dualism based on a non-fixed, relative scheme-content distinction. The proposed non-Kantian scheme-content dualism is not only “innocent” enough to be immune from Davidson’s charge of the third dogma of empiricism, but also “solid” enough to be able to sustain alternative conceptual schemes. I conclude that in terms of our conceptual schemes, we are connected to the world as closely as possible; only through conceptual schemes can we be connected to the world.

Il s’agit de comprendre dans cet article l’opposition formulée par Gilles-Gaston Granger entre deux types de négation : la négation "radicale", d’un côté, et les négations "appliquées" de l’autre. Nous examinerons les propriétés de cette opposition, ainsi que les enseignements à en tirer sur la philosophie de la logique de Granger. Puis nous proposerons une théorie constructive des valeurs logiques considérées comme des objets structurés, consolidant à la fois l’unité de la théorie logique de Granger et son pluralisme philosophique.

The present paper wants to promote epistemic pluralism as an alternative view of non-classical logics. For this purpose, a bilateralist logic of acceptance and rejection is developed in order to make an important difference between several concepts of epistemology, including information and justification. Moreover, the notion of disagreement corresponds to a set of epistemic oppositions between agents. The result is a non-standard theory of opposition for many-valued logics, rendering total and partial disagreement in terms of epistemic negation and semi-negations.

Frege takes logic to be the science of truth throughout his career. However, the mature Frege makes remarks which seem to go against the idea that logic is the science of truth. This paper shows that we can explain away this tension in the mature Frege's conception of logic if we accept that truth is an object, i.e., the truth-vale True qua the reference of a sentence, for Frege. Even though the main thesis of this paper is a conditional, I provide reasons why we ought to consider the possibility seriously that truth is an object for Frege. I also explain how we can make sense of Frege's conception of logic as the science of truth while accepting truth is an object.

The current discussions of conceptual schemes and related topics are misguided; for they have been focused too much on the truth-conditional notions of meaning/concepts and translation/interpretation in Tarski's style. It is exactly due to such a Quinean interpretation of the notion of conceptual schemes that the very notion of conceptual schemes falls prey to Davidson's attack. I argue that what should concern us in the discussions of conceptual schemes and related issues, following the initiatives of I. Hacking, T. Kuhn, and N. Rescher, is not the truth-values of assertions, but rather the truthvalue-status of the sentences used to make the assertions. This is because the genuine conceptual innovation between alternative theories/languages does not lie in differences in determining the truth-values of their sentences, but turns on whether these sentences have truth-values when considered within the context of a competing one. The core of conceptual relativism does not consist in the claim that different conceptual schemes may yield incommensurable truth claims, but rather that different conceptual schemes may yield incompatible truth-value-status and therefore lead to distinct perceptions of reality. Conceptual schemes are no longer seen as sentential languages consisting of a set of sentences accepted as true, but rather seen as metaphysical presuppositions of presuppositional languages.

When Frege reformulated his concept script in the early 1890's he postulated two logical objects as the referents of true and false sentences. He called these objects 'the True' and 'the False' and argued that all true sentences referred to the True and all false sentences referred to the False. Frege's arguments were not entirely convincing, and in the 20th century several logicians and philosophers offered formal arguments for Frege's conclusion, and these came to be known collectively as "the slingshot arguments". In this paper I present a simple refutation of three main arguments--given by Church, Davidson, and Gödel--based on a general principle about meaning and denotation.

We study several relations expressed by the two-place relational verb-phrases ‘X makes Y true’ and ‘X makes Y false’, or synonyms such as ‘X verifies Y’ and ‘X falsifies Y’ [3, pp. 180, 283]. This abstract gives three examples. Notation and terminology follow [2].
  Some usages mislead because the object “made true” or “made false” already had the truth-value in question. Other usages mislead because the object “made true” or “made false” doesn’t—and by nature can’t—have a truth-value. The object “made true” or “made false” isn’t true or false. Aristotle discussed related confusions in Categories xii, 14b16.
  In one usage, the number two makes the proposition “some number is even” true; three makes “every number is even” false. These have been called respectively proexample and counterexample relations [1].  Two is a proexample for “some number is even”; three is a counterexample for “every number is even”. Here we have propositions which by nature have truth-values; those “made true (or false)”didn’t come to have that truth-value.
  In another usage, the intended interpretation of number-theoretic English makes the sentence ‘some number is even’ true and it makes ‘every number is even’ false. Here we have uninterpreted English sentences which by nature cannot have truth-values: they are true (false) under the interpretations that “make them true (false)” [3, passim].
In still another usage, the fact that some number is even makes the proposition “some number is even” true; the fact that not every number is even makes “every number is even” false. Compare Aristotle, ibid.
[1] JOHN CORCORAN, Counterexamples and proexamples, this BULLETIN, vol.11 (2005), p. 460.
[2] JOHN CORCORAN, Sentence, Proposition, Judgment, Statement, and Fact, Many Sides of Logic, (Walter Carnielli et al., editors), College Publications, 2009.
  [3] WARREN GOLDFARB, Deductive logic, Hackett, 2003.

Despite D. Davidson’s influential criticism of the very notion of conceptual schemes, the notion continues enjoying its popularity in contemporary philosophy and, accordingly, conceptual relativism is still very much alive. There is one major reason responsible for Davidson’s failure which has not been widely recognized: What Davidson attacks fiercely is not the very notion, but a notion of conceptual schemes, namely, the Quinean notion of conceptual schemes and its underlying Kantian scheme-content dualism. However, such a notion simply cannot carry the weight of conceptual relativism for it does not catch the essences of conceptual relativism. Consequently, I argue that the very notion of conceptual schemes and conceptual relativism have survived Davidson’s attack. Therefore, the failure of the Quinean notion of conceptual schemes and Kantian scheme-content dualism, even if Davidson can claim victory, does not mark the end of the very notion of conceptual schemes.

Corcoran, J. 2010. One of four entries for a Spanish-language dictionary of logic: “counterarguments and counterexamples”(137–42), “deduction and deducibility” ”(168–70), “logical form and formalization” ”(257–59), “truth-values”(627–63). Luis Vega, Ed. Compendio de Lógica, Argumentación, y Retórica. Madrid: Trotta.

Valores de verdad


A lo largo de los tiempos, la lógica ha adoptado muchos términos técnicos extraños y extravagantes: asertórico, probar, prueba, modelo, constante, variable, particular, mayor, menor, y así sucesivamente. Pero valor de verdad no es un ejemplo típico. Toda proposición, aunque sea falsa, y sin interés, tiene un valor de verdad. Hasta “uno más dos es cuatro” y “uno no es uno”. De hecho, todo par de proposiciones falsas tienen el mismo valor de verdad—sin importar cuán diferentes éstas pudieran ser, aunque una sea auto-contradictoria y una sea consistente. No es una gran sorpresa que toda proposición verdadera, sin importar su interés, tenga un valor de verdad. Toda proposición, sea valiosa o inútil, tiene un valor de verdad.

According to the accepted translation-failure interpretation, the problem of incommensurability involves the nature of the meaning-referential relation between scientific languages. The incommensurability thesis is that some competing scientific languages are mutually untranslatable due to the radical variance of meaning or/and reference of the terms they employ. I argue that this interpretation faces many difficulties and cannot give us a tenable, coherent, and integrated notion of incommensurability. It has to be rejected. ;On the basis of two case studies, I find that the confrontations between many classical incommensurable languages are not confrontations between two untranslatable languages with different distribution of truth values, but rather the confrontations between incompatible fundamental presuppositions at the ontological level. We can always identify a truth-value gap between two incommensurable languages. Such a truth-value gap indicates a communication breakdown between the two language communities on the one hand, and is caused by the incompatible fundamental presuppositions underlying them on the other. ;I thereby identify the truth-value functional relationship between sentences, instead of the meaning-referential relationship between terms, as the dominant semantic relation between two incommensurable languages. According to my presuppositional interpretation of incommensurability, the real secret of incommensurability lies in the ontological setup of two competing presuppositional languages. When two presuppositional languages with incompatible factual commitments encounter with each other, the confrontation leads to a truth-value gap, and consequently a communication breakdown between them. Formally put, 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 an ontological gap between them. ;The presuppositional interpretation makes many significant contributions to the discussion of the issue of incommensurability and the related metaphysical and epistemological issues: It confirms the existence of the phenomenon of incommensurability and makes it metaphysically and epistemologically significant. It establishes the tenability and integrity of the notion of incommensurability. It avoids many alleged unattractive epistemological and metaphysical consequences of the translation-failure interpretation.

In the traditional fuzzy logic, as truth values, we take all real numbers from the interval [0; 1]. In some situations, this set is not fully adequate for describing expert uncertainty, so a more general set is needed. From the mathematical viewpoint, a natural extension of real numbers is the set of complex numbers. Complex-valued fuzzy sets have indeed been successfully used in applications of fuzzy techniques. This practical success leaves us with a puzzling question: why complex-valued degree of belief, degrees which do not seem to have a direct intuitive meaning, have been so successful? In this paper, we use latest results from theory of computation to explain this puzzle. Namely, we show that the possibility to extend to complex numbers is a necessary condition for fuzzy-related computations to be feasible. This computational result also explains why complex numbers are so efficiently used beyond fuzzy, in physics, in control, etc.

Misunderstanding occurs between speakers when they disagree about the meaning of words in use. In the case of truth-values, Frege took these to be referents of sentences which consist of classes of accepted (i.e. “true”) or rejected (i.e. “false”) sentences. From this usual depiction of truth and falsity, a general algebraic framework is proposed to systematize the use of truth-values from a dialogical point of view of logic. A special attention will be paid to two radically opposed pseudo-speakers: Heraclites and Nagarjuna, according to whom truth-values respectively refer to everything or nothing. Finally, dialectical (pseudo-Hegelian) negation will be rendered as a very special function: an ontological object-forming operator, similar to the arithmetic successor-forming operator Sn+1(x) on integers and consistent within our generalized theory of truth-values as variable referents.

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 (un)translatability, but rather depends on the notion of truth-value-status-preserving crosslanguage
communication. The reconstruction makes Kuhn’s notion of incommensurability a
well grounded, tenable and integrated notion.

Keywords: Incommensurability; Thomas Kuhn; Taxonomic structures; Lexicons; Truth-value; Untranslatability;
Cross-language communication

In this paper, we consider the problem of executing a fuzzy knowledge base (FKB) with rule chaining. The inference process used as starting point is the one based on forward reasoning functions which, obtained from the compositional rule of inference, permits performing the execution of rules in the truth space. This way the process is totally independent from the universes of discourse in which the different variables are defined, allowing a homogeneous treatment for all the variables in the FKB. The execution of the rules is interpreted as the "propagation" of linguistic truth values of the linguistic truth variable that reflect the linguistic degree of fulfillment of each of the propositions in the rules. This execution process is analyzed in two fields of application: control systems, where it is customary to assume t-norm operators as implication functions, and the aggregation process is implemented through the maximum operator and expert systems applications, where other implication functions may be needed and t-norm operators are generally used as aggregation operators. For both of these situations, we present a compaction mechanism which allows a noticeable part of the operations to be performed a priori, thus achieving an important computation time saving.

According to logical pluralism, there is more than one way to say that a logic is correct. According to pluralist pluralism, there is more than one way to say that there is more than one way to say that a logic is correct.

I illustrate three dimensions of such a plural correctness: logical pluralism (about the meaning of logical constants, and logical consequence); epistemic pluralism (about the criteria of justification); axiological pluralism (about the meaning of logical values).

All the three purport to depict logic as a three-dimensional science of values, in the vein of Lukasiewicz.

I propose a formal framework for social epistemology, in which a number of various sorts of agents may obey alternative sets of acceptance and rejection conditions on sentences.

The talk consists of two main parts.
After making a difference between information and justification, I propose two sorts of logical systems within a common dialogical framework AR_m^n of question-answer games. The first system, AR4, is a four-valued logic of information analogous to Belnap’s FDE, with the notable exception that it includes a strong version of implication and depicts logical values as structured pairs of yes-no answers. The second system, AR4B, is a logic of justification including at least four belief unary and truth-functional operators on justification sentences.

A taxonomy of several kinds of agents is suggested, namely: rational, irrational, and intelligible agents. By this way, I construct a formal epistemology that develops some problem raised by Martin Kusch’s works (on the relations between pluralism, skepticism, and relativism) whilst relying upon two fundamental data: yes-, and no-answers.

Then the notions of agreement and disagreement between agents are reviewed in the light of two basic concepts: negation, and opposition.
On the one hand, the occurrence of partial or total (dis)agreements makes room for a distinction between (full) negation and two semi-negations.
On the other hand, oppositions are then defined not as a
relation between ontic truth-values but, rather, epistemic attitudes of agreement or disagreement. This results in a more fine-grained theory where any two agents can stand into different relations of opposition with respect to the same sentence. These ensuing, “non-standard” oppositions correspond to pairs <X,Y> of standard, Aristotelian
oppositions X and Y.

To conclude, a number of philosophical applications will be exposed to make sense of such issues as partial or complete disagreement.

IS THE NOTION OF SEMANTIC PRESUPPOSITION EMPTY?
Xinli Wang
in Dialogos 73 (1999), pp. 61-91.

This paper is an attempt to clarify the notion of semantic presupposition and to refute Böer and Lycan's critique of that notion. I present a feasible and coherent formal definition of semantic presupposition after examining several popular definitions of the notion. In terms of my definition, two central arguments against semantic presup¬position presented by Böer and Lycan are analyzed and responded to with care. The conclusion is that the notion of semantic presupposition is not empty but rather is philo¬sophically interesting and fruitful.

How we choose to answer personal identity questions serves as the “You Are Here” marker on the directory of life and shapes our worldview. Phenomenologically, it seems as though ‘I’ am the cause of my decisions. This is the catalyst for my position that agency is the most fundamental aspect of personal identity.
I do not attempt to argue that alternative accounts are nonsensical or false outright, but rather that their benefits do not outweigh their costs. My own account is not without its own problems. Because the strength of a philosophical position is in how well it responds to objections, I introduce and address the most significant concession that my position forces me to make. If my account has the least significant cost and the most substantial benefit, then it ought to be abductively presumed.