We present a new proposal for what to do at limits in the revision theory. The usual criterion for a limit stage is that it should agree with any definite verdicts that have been brought about before that stage. We suggest that one should not only consider definite verdicts that have been brought about but also more general properties; in fact any closed property can be considered. This more general framework is required if we move to considering (...) class='Hi'>revision theories for concepts that are concerned with real numbers, but also has consequences for more traditional revision theories such as the revision theory of truth. (shrink)

We present a theory of truth in fiction that improves on Lewis's [1978] ‘Analysis 2’ in two ways. First, we expand Lewis's possible worlds apparatus by adding non-normal or impossible worlds. Second, we model truth in fiction as belief revision via ideas from dynamic epistemic logic. We explain the major objections raised against Lewis's original view and show that our theory overcomes them.

This article explores ways in which the Revision Theory of Truth can be expressed in the object language. In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed, and we study different axiomatic systems for the Revision Theory of Truth.

The model of self-referential truth presented in this paper, named Revision-theoretic supervaluation, aims to incorporate the philosophical insights of Gupta and Belnap’s Revision Theory of Truth into the formal framework of Kripkean fixed-point semantics. In Kripke-style theories the final set of grounded true sentences can be reached from below along a strictly increasing sequence of sets of grounded true sentences: in this sense, each stage of the construction can be viewed as an improvement on the (...) previous ones. I want to do something similar replacing the Kripkean sets of grounded true sentences with revision-theoretic sets of stable true sentences. This can be done by defining a monotone operator through a variant of van Fraassen’s supervaluation scheme which is simply based on ω-length iterations of the Tarskian operator. Clearly, all virtues of Kripke-style theories are preserved, and we can also prove that the resulting set of “grounded” true sentences shares some nice features with the sets of stable true sentences which are provided by the usual ways of formalising revision. What is expected is that a clearer philosophical content could be associated to this way of doing revision; hopefully, a content directly linked with the insights underlying finite revision processes. (shrink)

We look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta’s theory of truth over arithmetic using \emph{fully varied revision} sequences yields a complete \Pi13 set of integers; (iii) the set of \emph{stably categorical} sentences using their revision (...) operator ψ is similarly \Pi13 and which is complete in Gödel’s universe of constructible sets L; (iv) give an alternative account of a theory of truth—realistic variance that simplifies full variance, whilst at the same time arriving at Kripkean fixed points. (shrink)

Belief revision (BR) and truthlikeness (TL) emerged independently as two research programmes in formal methodology in the 1970s. A natural way of connecting BR and TL is to ask under what conditions the revision of a belief system by new input information leads the system towards the truth. It turns out that, for the AGM model of belief revision, the only safe case is the expansion of true beliefs by true input, but this is not very (...) interesting or realistic as a model of theory change in science. The new accounts of non-prioritized belief revision do not seem more promising in this respect, and the alternative BR account of updating by imaging leads to other problems. Still, positive results about increasing truthlikeness by belief revision may be sought by restricting attention to special kinds of theories. Another approach is to link truthlikeness to epistemic matters by an estimation function which calculates expected degrees of truthlikeness relative to evidence. Then we can study how the expected truthlikeness of a theory changes when probabilities are revised by conditionalization or imaging. Again, we can ask under what conditions such changes lead our best theories towards the truth. (shrink)

In response to the liar’s paradox, Kripke developed the fixed-point semantics for languages expressing their own truth concepts. Kripke’s work suggests a number of related fixed-point theories of truth for such languages. Gupta and Belnap develop their revision theory of truth in contrast to the fixed-point theories. The current paper considers three natural ways to compare the various resulting theories of truth, and establishes the resulting relationships among these theories. The point is to get (...) a sense of the lay of the land amid a variety of options. Our results will also provide technical fodder for the methodological remarks of the companion paper to this one. (shrink)

Gupta’s Rule of Revision theory of truth builds on insights to be found in Martin and Woodruff and Kripke in order to permanently deepen our understanding of truth, of paradox, and of how we work our language while our language is working us. His concept of a predicate deriving its meaning by way of a Rule of Revision ought to impact significantly on the philosophy of language. Still, fortunately, he has left me something to.

In this rather technical paper we establish a useful combination of belief revision and verisimilitude according to which better theories provide better predictions, and revising with more verisimilar data results in theories that are closer to the truth. Moreover, this paper presents two alternative definitions of refined verisimilitude, which are more perspicuous than the algebraic version used in previous publications.

In this rather technical paper we establish a useful combination of belief revision and verisimilitude according to which better theories provide better predictions, and revising with more verisimilar data results in theories that are closer to the truth. Moreover, this paper presents two alternative definitions of refined verisimilitude, which are more perspicuous than the algebraic version used in previous publications.

The Revision Theory of Truth has been challenged in A. M. Yaqūb's recent book The Liar Speaks the Truth. Yaqūb suggests some non-trivial changes in the original theory - changing the limit rule - to avoid certain artifacts. In this paper it is shown that the proposed changes are not sufficient, i.e., Yaqūb's system also produces artifacts. An alternative solution is proposed and the relation between it and Yaqūb's solution is explored.

Tim Maudlin’s Truth and Paradox, a book that is richly endowed with interesting analyses and original theses, chooses to ignore both the prosentential theory of truth from Grover, Camp and Belnap 1975 and the revision theory in its book form, Gupta and Belnap 1993. There is no discussion of either theory, nor even any mention of them in the list of references. I offer a pair of quotes chosen from among a number of T&P (...) generalizations that Maudlin would doubtless have modified if RTT had been on his mind at the time of composition of T&P. “…every acceptable account of truth seems to imply that the TInferences must be valid”. My response is that the revision theory of truth is built on an explicit denial of this. Rather than taking them as “valid,” RTT takes the T-Inferences as stage-of-revision-shifting revision principles in the context of a definitional account of truth. “…most discussions of the Liar paradox and related paradoxes…do not address [such questions as]…where [T&P’s] Proof Lambda and Proof Gamma go wrong”. In fact, RTT is not open to this criticism. It’s simple natural-deduction calculus C0 addresses exactly such questions. (shrink)

We propose a dynamic hyperintensional logic of belief revision for non-omniscient agents, reducing the logical omniscience phenomena affecting standard doxastic/epistemic logic as well as AGM belief revision theory. Our agents don’t know all a priori truths; their belief states are not closed under classical logical consequence; and their belief update policies are such that logically or necessarily equivalent contents can lead to different revisions. We model both plain and conditional belief, then focus on dynamic belief revision. (...) The key idea we exploit to achieve non-omniscience focuses on topic- or subject matter-sensitivity: a feature of belief states which is gaining growing attention in the recent literature. (shrink)

Straightforward theory revision, taking into account as effectively as possible the established nomic possibilities and, on their basis induced empirical laws, is conducive for (unstratified) nomic truth approximation. The question this paper asks is: is it possible to reconstruct the relevant theory revision steps, on the basis of incoming evidence, in AGM-terms? A positive answer will be given in two rounds, first for the case in which the initial theory is compatible with the established (...) empirical laws, then for the case in which it is incompatible with at least one such a law. (shrink)

In this rigorous investigation into the logic of truth Anil Gupta and Nuel Belnap explain how the concept of truth works in both ordinary and pathological..

The classical theory of definitions bans so-called circular definitions, namely, definitions of a unary predicate P, based on stipulations of the form $$Px =_{\mathsf {Df}} \phi,$$where ϕ is a formula of a fixed first-order language and the definiendumP occurs into the definiensϕ. In their seminal book The Revision Theory of Truth, Gupta and Belnap claim that “General theories of definitions are possible within which circular definitions [...] make logical and semantic sense” [p. IX]. In order to (...) sustain their claim, they develop in this book one general theory of definitions based on revision sequences, namely, ordinal-length iterations of the operator which is induced by the definition of the predicate. Gupta-Belnap’s approach to circular definitions has been criticised, among others, by D. Martin and V. McGee. Their criticisms point to the logical complexity of revision sequences, to their relations with ordinary mathematical practice, and to their merits relative to alternative approaches. I will present an alternative general theory of definitions, based on a combination of supervaluation and ω-length revision, which aims to address some criticisms raised against revision sequences, while preserving the philosophical and mathematical core of revision. (shrink)

Assuming that the target of theory oriented empirical science in general and of nomic truth approximation in particular is to characterize the boundary or demarcation between nomic possibilities and nomic impossibilities, I have presented, in my article entitled “Models, postulates, and generalized nomic truth approximation” :3057–3077, 2016. 10.1007/s11229-015-0916-9), the ‘basic’ version of generalized nomic truth approximation, starting from ‘two-sided’ theories. Its main claim is that nomic truth approximation can perfectly be achieved by combining two prima (...) facie opposing views on theories: the traditional view: theories are postulates that exclude certain possibilities from being realizable, enabling explanation and prediction and the model view: theories are sets of models that claim to represent certain realizable possibilities. Nomic truth approximation, i.e. increasing truth-content and decreasing falsity-content, becomes in this way revising theories by revising their models and/or their postulates in the face of increasing evidence. The basic version of generalized nomic truth approximation is in many respects as simple as possible. Among other things, it does not take into account that one conceptual possibility may be more similar to another than a third one. However, for example, one theory may include a possibility that is more similar to a wrongly not included possibility than another theory can offer. Similarly, for wrongly not excluded possibilities. In this article it will be shown that such ‘refined’ considerations can be taken into account by adapted clauses based on a ternary similarity relation between possibilities. This allows again abductive conclusions about refined truth approximation if a theory is persistently more successful in the refined sense than another. It will also be indicated and illustrated that this refined approach enables a specification to the effect that refined truth approximation can be obtained by the method of idealization and subsequent concretization. Finally, the basic and the refined approach will be evaluated with regard to some general principles and objections that have been discussed in the literature. (shrink)

We investigate how to assign probabilities to sentences that contain a type-free truth predicate. These probability values track how often a sentence is satisfied in transfinite revision sequences, following Gupta and Belnap’s revision theory of truth. This answers an open problem by Leitgeb which asks how one might describe transfinite stages of the revision sequence using such probability functions. We offer a general construction, and explore additional constraints that lead to desirable properties of the (...) resulting probability function. One such property is Leitgeb’s Probabilistic Convention T, which says that the probability of φ equals the probability that φ is true. (shrink)

Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning, we explicate inductive truth conduciveness in (...) terms of optimally direct convergence to the truth, where optimal directness is explicated in terms of reversals and cycles of opinion prior to convergence. Concerning, we explicate Ockham’s razor and related principles of choice in terms of the information topology of the empirical problem context and show that the principles are necessary for reversal or cycle optimal convergence to the truth. Concerning, we weaken the standard principles of agm belief revision theory in intuitive ways that are also necessary for reversal or cycle optimal convergence. Then we show that some of our weakened principles of change entail corresponding principles of choice, completing the triangle of relations between,, and. (shrink)

Revision sequences were introduced in 1982 by Herzberger and Gupta as a mathematical tool in formalising their respective theories of truth. Since then, revision has developed in a method of analysis of theoretical concepts with several applications in other areas of logic and philosophy. Revision sequences are usually formalised as ordinal-length sequences of objects of some sort. A common idea of revision process is shared by all revision theories but specific proposals can differ in (...) the so-called limit rule, namely the way they handle the limit stages of the process. The limit rules proposed by Herzberger and by Belnap show different mathematical properties, called periodicity and reflexivity, respectively. In this paper we isolate a notion of cofinally dependent limit rule, encompassing both Herzberger’s and Belnap’s ones, to study periodicity and reflexivity in a common framework and to contrast them both from a philosophical and from a mathematical point of view. We establish the equivalence of weak versions of these properties with the revision-theoretic notion of recurring hypothesis and draw from this fact some observations about the problem of choosing the “right” limit rule when performing a revision-theoretic analysis. (shrink)

The structuralist theory of truth approximation essen-tially deals with truth approximation by theory revision for a fixed domain. However, variable domains can also be taken into account, where the main changes concern domain extensions and restrictions. In this paper I will present a coherent set of definitions of “more truth-likeness”, “empirical progress” and “truth approximation” due to a revision of the domain of intended applications. This set of definitions seems to be the (...) natural counterpart of the basic definitions of similar notions as far as theory revision is concerned. The formal aspects of theory revision strongly suggest an analogy between truth approximation and design research, for example, drug research. Whereas a new drug may be better for a certain disease than an old one, a certain drug may be better for another disease than for the original target disease, a phenomenon which was nicely captured by the title of a study by Rein Vos [1991]: Drugs Looking for Diseases. Similarly, truth approximation may not only take the shape of theory revision but also of domain revision, naturally suggesting the phenomenon of “Theories looking for domains”. However, whereas Vos documented his title with a number of examples, so far, apart from plausible cases of “truth accumulation by domain extension”, I did not find clear-cut empirical instantiations of the analogy, only, as such, very interesting, non-empirical examples. (shrink)

Theories of truth and vagueness are closely connected; in this article, I draw another connection between these areas of research. Gupta and Belnap’s Revision Theory of Truth is converted into an approach to vagueness. I show how revision sequences from a general theory of definitions can be used to understand the nature of vague predicates. The revision sequences show how the meaning of vague predicates are interconnected with each other. The approach is contrasted (...) with the similar supervaluationist approach. (shrink)

Consider the sentence 'This sentence is not true'. It seems that the sentence can be neither true nor not true, on pain of contradiction. Certain notorious paradoxes like this have bedevilled philosophical theories of truth. Tim Maudlin presents an original account of logic and semantics which deals with these paradoxes, and allows him to set out a new theory of truth-values and the norms governing claims about truth. All philosophers interested in logic and language will find (...) Truth and Paradox a stimulating read. (shrink)

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

According to the revision theory of truth, the paradoxical sentences have certain revision periods in their valuations with respect to the stages of revision sequences. We find that the revision periods play a key role in characterizing the degrees of paradoxicality for Boolean paradoxes. We prove that a Boolean paradox is paradoxical in a digraph, iff this digraph contains a closed walk whose height is not any revision period of this paradox. And for (...) any finitely many numbers greater than 1, if any of them is not divisible by any other, we can construct a Boolean paradox whose primary revision periods are just these numbers. Consequently, the degrees of Boolean paradoxes form an unbounded dense lattice. The area of Boolean paradoxes is proved to be rich in mathematical structures and properties. (shrink)

Tim Maudiin’s Truth and Paradox (Maudlin 2004, cited here as T&P), a book that is richly endowed with interesting analyses and original theses, chooses to ignore both the prosentential theory of truth from Grover, Camp and Belnap 1975 and the revision theory in its book form, Gupta and Belnap 1993 (The Revision Theory of Truth, henceforth RTT).1 There is no discussion of either theory, nor even any mention of them in the (...) list of references. I offer a pair of quotes chosen from among a number of T&P generalizations that Maudlin would doubtless have modified if RTT had been on his mind at the time of composition of T&P. (1) "...every acceptable account of truth seems to imply that the Tlnferences must be valid" (p. 15). My response is that the revision theory of truth is built on an explicit denial of this. Rather than taking them as "valid," RTT takes the T—Inferences as stage-of-revision—shifting revision principles in the context of a definitional account of truth. (2) "...most discussions of the Liar paradox and related paradoxes...do not address [such questions as]...where ['l`&P’s] Proof Lambda and Proof Gamma go wrong" (p. 20). In fact, RTT is not open to this criticism. It’s simple natural-deduction calculus C0 addresses exactly such questions. (shrink)

According to the revision theory of truth, the binary sequences generated by the paradoxical sentences in revision sequence are always unstable. In this paper, we work backwards, trying to reconstruct the paradoxical sentences from some of their binary sequences. We give a general procedure of constructing paradoxes with specific binary sequences through some typical examples. Particularly, we construct what Herzberger called “unstable statements with unpredictably complicated variations in truth value.” Besides, we also construct those paradoxes (...) with infinitely many finite primary periods but without any infinite primary period, those with an infinite critical point but without any finite primary period, and so on. This is the first formal appearance of these paradoxes. Our construction demonstrates that the binary sequences generated by a paradoxical sentence are something like genes from which we can even rebuild the original sentence itself. (shrink)

A number of nonmonotonic reasoning formalisms have been introduced to model the set of beliefs of an agent. These include the extensions of a default logic, the stable models of a general logic program, and the extensions of a truth maintenance system among others. In [13] and [16], the authors introduced nonmonotomic rule systems as a nonlogical generalization of all essential features of such formulisms so that theorems applying to all could be proven once and for all. In this (...) paper, we extend Rieter's normal default theories, which have a number of the nice properties which make them a desirable context for belief revision, to the setting of nonmonotonic rule systems. Reiter defined a default theory to be normal if all the rules of the default theory satisfied a simple syntatic condition. However, this simple syntatic condition has no obvious analogue in the setting of nonmonotonic rule systems. Nevertheless, an analysis of the proofs of the main results on normal default theories reveals that the proofs do not rely on the particular syntactic form of the rules but rather on the fact that all rules have a certain consistency property. This led us to extend the notion of normal default theories with respect to a general consistency property. This extended notion of normal default theories, which we call Forward Chaining normal , is easily lifted to nonmonotomic rule systems and hence applies to general logic programs and truth maintenance. (shrink)

Many different modes of definition have been proposed over time, but none of them allows for circular definitions, since, according to the prevalent view, the term defined would then be lacking a precise signification. I argue that although circular definitions may at times fail uniquely to pick out a concept or an object, sense still can be made of them by using a rule of revision in the style adopted by Anil Gupta and Nuel Belnap in the theory (...) of truth. (shrink)

Philosophical logicians proposing theories of rational belief revision have had little to say about whether their proposals assist or impede the agent's ability to reliably arrive at the truth as his beliefs change through time. On the other hand, reliability is the central concern of formal learning theory. In this paper we investigate the belief revision theory of Alchourron, Gardenfors and Makinson from a learning theoretic point of view.

In this study, we examine the problem of belief revision, defined as deciding whic h of several initially-accepted sentences to disbelieve, when new information presents a l ogical inconsistency with the initial set. In the first three experiments, the initial sentence set included a conditional sentence, a non-conditional sentence, and an inferred conclusi on drawn from the first two. The new information contradicted the inferred conclusion. Results indicated that the conditional sentences were more readily abandoned than non-c onditional sentences, (...) even when either choice would lead to a consistent belief state, and that this preference was more pronounced when problems used natural language cover sto ries rather than symbols. The pattern of belief revision choices differed depending on whe ther the contradicted conclusion from the initial belief set had been a modus ponens or m odus tollens inference. Two additional experiments examined alternative model-theoretic definitions of minimal change to a belief state, using problems that contained multiple mo dels of the initial belief state and of the new information that provided the contradiction. The results indicated that people did not follow any of four formal definitions of minimal change on these problems. The new information and the contradiction it offered was not, for example, used to select a particular model of the initial belief state as a way of reconci ling the contradiction. The preferred revision was to retain only those initial sentences th at had the same, unambiguous truth value within and across both the initial and new info rmation sets. The study and results are presented in the context of certain logic-based for malizations of belief revision, syntactic and model-theoretic representations of belief stat es, and performance models of human deduction. Principles by which some types of sent ences might be more "entrenched" than others in the face of contradiction are also discuss ed from the perspective of induction and theory revision. (shrink)

Logical orthodoxy has it that classical first-order logic, or some extension thereof, provides the right extension of the logical consequence relation. However, together with naïve but intuitive principles about semantic notions such as truth, denotation, satisfaction, and possibly validity and other naïve logical properties, classical logic quickly leads to inconsistency, and indeed triviality. At least since the publication of Kripke’s Outline of a theory of truth , an increasingly popular diagnosis has been to restore consistency, or at (...) least non-triviality, by restricting some classical rules. Our modest aim in this note is to briefly introduce the main strands of the current debate on paradox and logical revision, and point to some of the potential challenges revisionary approaches might face, with reference to the nine contributions to the present volume.For a recent introduction to non-classical theories of truth and other semantic notions, see the excellent Beall a .. (shrink)

Revision sequences are a kind of transfinite sequences which were introduced by Herzberger and Gupta in 1982 as the main mathematical tool for developing their respective revision theories of truth. We generalise revision sequences to the notion of cofinally invariant sequences, showing that several known facts about Herzberger’s and Gupta’s theories also hold for this more abstract kind of sequences and providing new and more informative proofs of the old results.

We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth (even in a relative sense). Our method is to emphasize the incomplete picture of both theories and treat models as their syntactical counterparts. Insisting on the incomplete picture will allow us to argue in favor of the revisability of the standard model interpretation. We then show that it is hopeless to expect (...) that the relative grounding provided by a standard interpretation can resist being revisable. We start briefly characterizing the expansion of arithmetic `truth' provided by the interpretation in a set theory. Further, we show that, for every well-founded interpretation of recursive extensions of PA in extensions of ZF, the interpreted version of arithmetic has more theorems than the original. This theorem expansion is not complete however. We continue by defining the coordination problem. The problem can be summarized as follows. We consider two independent communities of mathematicians responsible for deciding over new axioms for ZF and PA. How likely are they to be coordinated regarding PA’s interpretation in ZF? We prove that it is possible to have extensions of PA not interpretable in a given set theory ST. We further show that the probability of a random extension of arithmetic being interpretable in ST is zero. (shrink)

An important question for proponents of non-contractive approaches to paradox is why contraction fails. Zardini offers an answer, namely that paradoxical sentences exhibit a kind of instability. I elaborate this idea using revision theory, and I argue that while instability does motivate failures of contraction, it equally motivates failure of many principles that non-contractive theorists want to maintain.

We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete 1/2 set.

In this book, Yaqub describes a simple conception of truth and shows that it yields a semantical theory that accommodates the whole range of our seemingly conflicting intuitions about truth. This conception takes the Tarskian biconditionals as correctly and completely defining the notion of truth. The semantical theory, which is called the revision theory, that emerges from this conception paints a metaphysical picture of truth as a property whose applicability is given by (...) a revision process rather than by a fixed extension. The main advantage of this revision process is its ability to explain why truth seems in many cases almost redundant, in others substantial, and yet in others paradoxical. Yaub offers a comprehensive defense of the revision theory of truth by developing consistent and adequate formal semantics for languages in which all sorts of problematic sentences can be constructed. Yaqub concludes by introducing a logic of truth that further demonstrates the adequacy of the revision theory. (shrink)

After a chapter which is an introduction to and summary of the rest of the book, chapter 2 begins by criticizing various attempts to do away with theories, such as the Reichenbach-Salmon conception of theoretical truth in terms of observational consequences, and the Ramsey strategy of replacing first-order theoretical sentences by second-order nontheoretical ones; it then argues against hypothetico-deductivist theories of confirmation on the grounds that they are unable to handle the relevance of evidence to theory, whether or (...) not other formal constraints or even nonformal ones such as simplicity and explanatory power are added to those theories; it ends with an exposition of the Reichenbach-Carnap conventionalist thesis that the confirmation of hypotheses with evidence presupposes analytic principles connecting hypothetical and empirical concepts. Chapter 3 criticizes Bayesian theories of confirmation on such grounds as that the a priori arguments for Bayesian restrictions on beliefs are insufficient; that the Bayesian explanations of notions like variety of evidence, ad hocness, and simplicity are inadequate; and that they cannot account, without drastic revisions, for the relevance of evidence to theory, especially old evidence to new theory. Chapter 4 is an unsympathetic account of historically oriented philosophies of science; Lakatos’s notion of progressive research programs and Laudan’s theory of problem-solving effectiveness are found to be insufficiently precise and dubbed examples of "new fuzziness", while the Sneed-Stegmüller dynamics of theories is regarded as "a paradigm of misplaced rigor" ; and all three are criticized as unable to explicate the concept of evidential relevance. Chapter 5 is a formal and informal elaboration of the basic idea in Glymour’s account of theory and evidence, namely that confirmation or support is a three-term relation among evidence, hypothesis, and theory, so that evidence confirms an hypothesis only relative to a theory, and such that evidence e confirms hypothesis h relative to T if T with e implies, but T without e does not imply, an instance of h, and T with e does not imply a comparable hypothesis h’ different from h; the most interesting part of this chapter is a series of discussions showing how such an idea makes sense of the "methodological truisms" that it is possible selectively to test certain parts of a theory but not others, that a theory is supported better by a greater variety of evidence, that redundant or physically meaningless quantities are an undesirable feature of theories, that there are no inviolable rules, that a "white shoe" does not confirm "all ravens are black," that a theory is more useful and better supported than the set of its observational consequences, and that the hypothetico-deductive method often works. Since Glymour claims no originality for the conception of this general account, but only for its description, he plausibly thinks it necessary to apply it to some important historical cases of actual science; he does so in the next chapter by discussing at some length the structure and merits of Ptolemaic and Copernican astronomy, of Newton’s universal gravitation, of nineteenth century atomism, of Freud’s Rat Man, and of general relativity. For example, he argues convincingly that Copernicanism was better supported by the evidence available even before the telescope because it alone, and not the Ptolemaic theory, can determine some planetary properties which are presupposed by both theories, can test and confirm some common hypotheses, and can be confirmed in an essential rather than incidental manner; and though Glymour admits that the Copernicans tended to argue in terms of explanatory rather than confirmatory superiority, he sketches an interesting account of the relation between explanation and confirmation which strengthens his case. He also analyzes the text at the beginning of book 3 of Newton’s Principia and compiles a reconstruction of the intricate details of the inferential structure of the argument to universal gravitation; his impressive reconstruction clearly shows that Newton’s method is neither the inductivist one he himself thought he was following, nor the one attributed to him by Pierre Duhem, but rather one in accordance with Glymour’s so-called "bootstrap strategy" of repeatedly using the evidence from Kepler’s second and third laws, from lunar data, and from falling bodies, together with the theory consisting of the second and third laws of motion, to arrive at increasingly general instances of the principle of universal gravitation. Glymour’s account of arguments for and against the atomic theory from Thomson to Cannizzaro is his longest historical example, but he himself admits that this illustration of the bootstrap strategy is "certainly not the neatest", and rather "diffuse, and perhaps disconnected". Chapter 7 is a detailed application of the same principles to the technique known among social scientists as "causal modeling"; since such "causal models" are essentially systems of algebraic equations, Glymour’s account shows indirectly that the bootstrap strategy is applicable to any scientific theory presented as a set of algebraic equations; this, of course is not surprising, since the formal considerations with which Glymour begins the exposition of his theory in chapter 5 involve systems of algebraic equations. Chapter 8 is an attempt to apply Glymour’s theory of evidence to the very common scientific practice of curve-fitting, where one measures values of two or more quantities and then infers a functional relationship; Glymour argues that simpler polynomials are preferred because they are tested more frequently and more severely by the data and because they are more informative; but then he criticizes his own explanation and concludes that "the bootstrap procedures of chapter 5 do not seem to help the problem much more than a whit" ; this is admirably honest, but if one wants an additional logical or methodological rationale, then one would perhaps have to go to the meta-level and say that Glymour is here testing his own theory, and he is more interested in a further illustration of the bootstrap methodology even with a failed test, than he is to claim universal or exclusive validity for it. In chapter 9 Glymour uses his bootstrap theory of confirmation to criticize geometrical conventionalism; he considers the alternative theories of space or space-time proposed by conventionalists to show the radical undetermination of geometries by evidence, for example, a non-Euclidean geometry with no universal force instead of Newtonian gravitation with Euclidean geometry; he argues that such alternatives are simply not as well tested as the originals and that their equivalence to the originals is questionable. The last chapter is a brief discussion of further problems worthy of future investigation. (shrink)

We show that the set of ultimately true sentences in Hartry Field's Revenge-immune solution model to the semantic paradoxes is recursively isomorphic to the set of stably true sentences obtained in Hans Herzberger's revision sequence starting from the null hypothesis. We further remark that this shows that a substantial subsystem of second-order number theory is needed to establish the semantic values of sentences in Field's relative consistency proof of his theory over the ground model of the standard (...) natural numbers: -CA0 (second-order number theory with a -comprehension axiom scheme) is insufficient. We briefly consider his claim to have produced a solution to the semantic paradoxes by introducing this conditional. We remark that the notion of a operator can be introduced in other settings. (shrink)

I shall argue that those who hold that there are factual complexes, or facts, and who subscribe to a correspondence theory of truth, according to which truth is analyzed in terms of correspondence to facts, need not hold that, in addition to facts, there are propositions.

This chapter argues that logic is a theory, and can be revised as any other scientific theory. The comparison with geometry is helpful in this regard. It also discusses Quine’s views on the matter, particularly the claim that any changing of logic is a changing of subject.

In Saving Truth from Paradox, Hartry Field presents and defends a theory of truth with a new conditional. In this paper, I present two criticisms of this theory, one concerning its assessments of validity and one concerning its treatment of truth-preservation claims. One way of adjusting the theory adequately responds to the truth-preservation criticism, at the cost of making the validity criticism worse. I show that in a restricted setting, Field has a way (...) to respond to the validity criticism. I close with some general considerations on the use of revision-theoretic methods in theories of truth. (shrink)

We present some proof-theoretic results for the normal modal logic whose characteristic axiom is \. We present a sequent system for this logic and a hypersequent system for its first-order form and show that these are equivalent to Hilbert-style axiomatizations. We show that the question of validity for these logics reduces to that of classical tautologyhood and first-order logical truth, respectively. We close by proving equivalences with a Fitch-style proof system for revision theory.

In this paper a logic for reasoning disquotationally about truth is presented and shown to have a standard model. This work improves on Hartry Field's recent results establishing consistency and omega-consistency of truth-theories with strong conditional logics. A novel method utilising the Banach fixed point theorem for contracting functions on complete metric spaces is invoked, and the resulting logic is shown to validate a number of principles which existing revision theoretic methods have heretofore failed to provide.