Are Knowledge Claims Indexical?

David Lewis, Stewart Cohen, and Keith DeRose have proposed that sentences of the form S knows P are indexical, and therefore differ in truth value from one context to another.¹ On their indexical contextualism, the truth value of S knows P is determined by whether S meets the epistemic standards of the speakers context. I will not be concerned with relational forms of contextualism, according to which the truth value of S knows P is determined by the standards of the subject Ss context, regardless of the standards applying to the speaker making the knowledge claim. Relational contextualism is a form of normative relativism. Indexical contextualism is a semantic theory. When the subject is the speaker, as when S is the first person pronoun I, the two forms of contextualism coincide. But otherwise, they diverge. I critically examine the principal arguments for indexicalism, detail linguistic evidence against it, and suggest a pragmatic alternative.     

Some aspects of eloquence in Descartes's works

In Descartes's philosophy, communicating scientific and philosophical truth does not represent a problem that can be traced back to humanistic rhetoric, meant as the art of persuasion. Descartes states his belief in the eloquence of reason: a clear, precise, and adequately expressed thought cannot fail to convince the listener. This is the measure of the distance between the level of truth and the level of opinion. However, the moment of confrontation with the public is also the very moment when the truth of the new knowledge enters into conflict with other, different conceptions. Education and history influence communication with the result that the distinction between intellectual conviction and persuasion becomes less straightforward. Rational eloquence, as Descartes is well aware, must be articulated in such a way as to avoid any possible language equivocation and to adopt exposition strategies ensuring effective access to readers. The aim of this paper is to illustrate some aspects of this tension as expressed by the writer Descartes with reference to a number of texts (from the Regulae to the Meditationes) that were essential for the elaboration and dissemination of his philosophy.     

Some modifications of Scott's theorem on injective spaces

D. Scott in his paper [5] on the mathematical models for the Church-Curry -calculus proved the following theorem.A topological space X. is an absolute extensor for the category of all topological spaces iff a contraction of X. is a topological space of Scott's open sets in a continuous lattice.In this paper we prove a generalization of this theorem for the category of , -closure spaces. The main theorem says that, for some cardinal numbers , , absolute extensors for the category of , -closure spaces are exactly , -closure spaces of , -filters in , >-semidistributive lattices (Theorem 3.5).If = and = we obtain Scott's Theorem (Corollary 2.1). If = 0 and = we obtain a characterization of closure spaces of filters in a complete Heyting lattice (Corollary 3.4). If = 0 and = we obtain a characterization of closure space of all principial filters in a completely distributive complete lattice (Corollary 3.3).     

Tarski on “essentially richer” metalanguages

It is well known that Tarski proved a result which can be stated roughly as: no sufficiently rich, consistent, classical language can contain its own truth definition. Tarski's way around this problem is to deal with two languages at a time, an object language for which we are defining truth and a metalanguage in which the definition occurs. An obvious question then is: under what conditions can we construct a definition of truth for a given object language. Tarski claims that it is necessary and sufficient that the metalanguage be essentially richer. Our contention, put bluntly, is that this claim deserves more scrutiny from philosophers than it usually gets and in fact is false unless essentially richer means nothing else than sufficient to contain a truth definition for the object language.     

Natural deduction rules for English

A system of natural deduction rules is proposed for an idealized form of English. The rules presuppose a sharp distinction between proper names and such expressions as the c, a (an) c, some c, any c, and every c, where c represents a common noun. These latter expressions are called quantifiers, and other expressions of the form that c or that c itself, are called quantified terms. Introduction and elimination rules are presented for any, every, some, a (an), and the, and also for any which, every which, and so on, as well as rules for some other concepts. One outcome of these rules is that Every man loves some woman is implied by, but does not imply, Some woman is loved by every man, since the latter is taken to mean the same as Some woman is loved by all men. Also, Jack knows which woman came is implied by Some woman is known by Jack to have come, but not by Jack knows that some woman came.     

An extension of the Łukasiewicz logic to the modal logic of quantum mechanics

An attempt is made to include the axioms of Mackey for probabilities of experiments in quantum mechanics into the calculus _x0 of ukasiewicz. The obtained calculusQ contains an additional modal signQ and four modal rules of inference. The propositionQx is read x is confirmed. The most specific rule of inference may be read: for comparable observations implication is equivalent to confirmation of material implication.The semantic truth ofQ is established by the interpretation with the help of physical objects obeying to the rules of quantum mechanics. The embedding of the usual quantum propositional logic inQ is accomplished.Allatum est die 9 Junii 1976     

Intuitionistic uniformity principles for propositions and some applications

This note deals with the prepositional uniformity principlep-UP: p x N A (p, x) x N p A (p, x) ( species of all propositions) in intuitionistic mathematics.p-UP is implied by WC and KS. But there are interestingp-UP-cases which require weak KS resp. WC only. UP for number species follows fromp-UP by extended bar-induction (ranging over propositions) and suitable weak continuity. As corollaries we have the disjunction property and the existential definability w.r.t. concrete objects. Other consequences are: there is no non-trivial countable partition of;id is the only injective function from to; there are no many-place injective prepositional functions; card () is incomparable with the cardinality of all metric spaces containing at least three elements.     

A Revenge-Immune Solution to the Semantic Paradoxes

The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema True(A)A, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in ordinary contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are defective. We can in fact define a hierarchy of defectiveness predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (revenge problems) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various levels of defectiveness can all be made coherent together within a single object language.     

A reduction rule for Peirce formula

A reduction rule is introduced as a transformation of proof figures in implicational classical logic. Proof figures are represented as typed terms in a -calculus with a new constant P ⁽⁽⁾⁾. It is shown that all terms with the same type are equivalent with respect to -reduction augmented by this P-reduction rule. Hence all the proofs of the same implicational formula are equivalent. It is also shown that strong normalization fails for P-reduction. Weak normalization is shown for P-reduction with another reduction rule which simplifies of (( ) ) into an atomic type.This work was partially supported by a Grant-in-Aid for General Scientific Research No. 05680276 of the Ministry of Education, Science and Culture, Japan and by Japan Society for the Promotion of Science. Hiroakira Ono     

Saving the Truth Schema from Paradox

The paper shows how we can add a truth predicate to arithmetic (or formalized syntactic theory), and keep the usual truth schema Tr(A)A (understood as the conjunction of Tr(A)A and ATr(A)). We also keep the full intersubstitutivity of Tr(A)) with A in all contexts, even inside of an . Keeping these things requires a weakening of classical logic; I suggest a logic based on the strong Kleene truth tables, but with as an additional connective, and where the effect of classical logic is preserved in the arithmetic or formal syntax itself. Section 1 is an introduction to the problem and some of the difficulties that must be faced, in particular as to the logic of the ; Section 2 gives a construction of an arithmetically standard model of a truth theory; Section 3 investigates the logical laws that result from this; and Section 4 provides some philosophical commentary.     

On the logic of conscious belief

In this paper we are discussing a version of propositional belief logic, denoted by LB, in which so-called axioms of introspection (B BB and B B B) are added to the usual ones. LB is proved to be sound and complete with respect to Boolean algebras equipped with proper filters (Theorem 5). Interpretations in classical theories (Theorem 4) are also considered. A few modifications of LB are further dealt with, one of which turns out to be S5.     

Distance and fusion in Robinson Jeffers' “the purse-seine” and other poems

Distance and fusion are fundamental ideas in Bowenian thinking, especially as expressed in the dynamic of distancing and pursuing. In this paper I have used these ideas as a means to briefly examine a short selection of Robinson Jeffers' poetry, which provides us with a literary example of these concepts in action.My thanks to M. K. Lane and the anonymous reviewers of an earlier draft of this article for their many suggestions, especially to the reviewer who helped me better distinguish between distance and fusion, and intimacy and autonomy.     

A gentzen system for conditional logic

Conditional logic is the deductive system , where is the set of propositional connectives {, ,} and is the structural finitary consequence relation on the absolutely free algebra that preserves degrees of truth over the structure of truth values C, . HereC is the non-commutative regular extension of the 2-element Boolean algebra to 3 truth values {t, u, f}, andf<u<t. In this paper we give a Gentzen type axiomatization for conditional logic.Presented byJan Zygmunt     

Omega-consistency and the diamond

G is the result of adjoining the schema (qAA)qA to K; the axioms of G* are the theorems of G and the instances of the schema qAA and the sole rule of G* is modus ponens. A sentence is -provable if it is provable in P(eano) A(rithmetic) by one application of the -rule; equivalently, if its negation is -inconsistent in PA. Let -Bew(x) be the natural formalization of the notion of -provability. For any modal sentence A and function mapping sentence letters to sentences of PA, inductively define A by: p = (p) (p a sentence letter); = ; (AB)su}= (A B); and (qA)= -Bew(A )(S) is the numeral for the Gödel number of the sentence S). Then, applying techniques of Solovay (Israel Journal of Mathematics 25, pp. 287–304), we prove that for every modal sentence A, _G A iff for all , _PA A ; and for every modal sentence A, _G* A iff for all , A is true.I should like to thank David Auerbach and Rohit Parikh.     

Discrete tense logic with infinitary inference rules and systematic frame constants: A Hilbert-style axiomatization

The paper deals with the problem of axiomatizing a system 1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 (immediate successor) and -1 (immediate predecessor). 1 is like the Segerberg-Sundholm system W1 in working with so-called infinitary inference rules; on the other hand, it differs from W1 with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a now operator, and, most importantly, with respect to (iii) the presence in of so-called systematic frame constants, which are meant to hold at exactly one point in a temporal structure and to enable us to express the irreflexivity of such structures. Those frame constants will be seen to play a paramount role in our axiomatization of 1.The present contribution reports research done under the auspices of the Swedish Council for Research in the Humanities and the Social Sciences (HSFR), project On the Legal Concepts of Rights and Duties: an Analysis Based on Deontic and Causal Conditional Logic. I wish to thank the anonymous referee for his/her extremely patient and accurate revision work, and Krister Segerberg for his helpful suggestions.     

“Anchor-range” results with “same” and “different” responses and similar and dissimilar stimuli

Summary Blocks of pairs of dissimilar (anchor-like) circles were unexpectedly followed by single pairs of similar circles and vice versa. The dissimilar circles were 3 and 10 mm in diameter, and the similar circles were 3 and 5 mm, 5 and 7 mm, and 7 and 10 mm in diameter. In a second experiment, the dissimilar and similar circles did not overlap in size (e.g., they were 1.5 and 5 mm and 7 and 10 mm, respectively). The same responses to the unexpected same pairs of similar circles were faster than the same responses to the identical pairs in the blocks. In contrast, the different responses to the unexpected different pairs of similar circles were slower than the different responses to the identical pairs in the blocks. Similar stimuli accelerate same responses and slow down different responses. So the time results (and the error results as well) suggest that the context of the block dissimilar circles increased the perceived similarity of the unexpected similar circles. These anchor-range results are not explained by Thurstonian theories, which are based on the absolute properties of stimuli. Instead, they imply that the relation between the similar circles in the context of the relation between the dissimilar circles affected performance.     

Lying and intersubjective truth: A communication based approach to understanding lying

This project was undertaken as a response to a perceived deficiency regarding the role of communication in a large block of the phenomenological discourse on lying. The arguments presented here attempt to make the communication process an explicit, rather than an implicit component of this discussion. First, a lie is explained as a communicative act that is identified by making a simple comparison between two contradictory realities, the reality presented by the lie, and some sort of true reality. Existing discussions of lying are examined and judged to be deficient because they limit their explanations of this true reality to subjective and objective standards of truth. Intersubjectivity is presented as an alternative truth standard, and it is argued that lies can only be discovered and understood through a process of interpretation or negotiation (dialogue) by human interactants.     

A paradigm shift in Heidegger research

The Beiträge zur Philosophie mandates a paradigm shift in Heidegger scholarship. In the face of (1) widespread disarray in the current model, the new paradigm (2) abandons Sein as a name for die Sache selbst, (3) understands Welt/Lichtung/Da as that which gives being, (4) interprets Dasein as apriori openedness rather than as being-there, (5) understands the Kehre as the interface of Geworfenheit and Entwurf, not as a shift in Heidegger's thinking, (6) interprets Ereignis as the opening of the Da rather than as appropriation, and (7) understands human finitude as what gives all forms of being and all epochs in the history of being. The conclusion alludes to the function of Mitdasein (co-openness) as die Sache selbst.     

How to frame the free will problem

Conclusion The exchange is almost complete. I have argued that if we wish to view the free will problem in a non-question-begging way, we should frame the problem in more radical terms than we usually do. If we frame the problem this way, then we discover a compelling reason for rejecting all of the familiar isms in favor of my non-realism thesis. This thesis holds that free choice has a coherent meaning just in case it is treated as a subjective term; thus, if we try to view free choice as denoting classes of entities that themselves possess the characteristic of freeness, it is logically inconsistent. My thesis is supported by a certain metaphilosophical view. I admit that this metaphilosophical view — which tries to locate everything where it belongs — is neither provable nor refutable. But if my argument in this paper is correct, when we assert any of the positions that presuppose the coherence of free will (Hard Determinism, Soft Determinism, Libertarianism, Incompatibilism, Compatibilism), we should add the fact that we have adopted a metaphilosophical view that supports these. Since these metaphilosophies are non-truth-tracking views, our joint declaration of our lower level free will theory and its supporting metaphilosophy will sound Pickwickian (e.g., I believe that Libertarianism is true and I support that view with the metaphilosophical thesis that the most important role of philosophy is not to track truth, but to create an intellectual climate best for improving the human condition.) If I have shown that my opponents are forced to such declarations, I will be satisfied.     

Self and others in “private language”

The aim of this paper is to restore the interdependent or complementary relationship between self and others against the universalistic one (as I call it) that Kant, for example, once insisted on, by reexamining the concept of so-called private language. I shall consider some views in speech act theory and pragmatics, since there has often been discussion about such a private occurrence as the speaker's sincerity. For example, Jürgen Habermas situates it in the speaker's internal nature as will be seen later. In my opinion, alter ego is an ego because we can empathize (einfühlen) with it, and yet it is alter ego because it has some private experiences which we cannot perfectly comprehend.