Many attempts have been made to solve Hume's problem. However, the assumptions leading to the problem have remained largely unnoticed. Moreover, since Goodman introduced the predicate "grue", philosophers without relevant mathematical education have been confused. In addition, various delusive arguments from convergence have been presented. In this book, it is maintained that knowledge has to be feasible and relevant and that several solutions fail to meet that demand. It is argued that the crucial presupposition of the problem of induction (...) is that clairvoyance is impossible and that this presupposition is unproven. Generalized Goodman predicates are introduced. To criticize arguments from convergence, the notion of "undecided game" is introduced. A relationship between Zeno's paradox and the problem of induction is revealed. A distinction between "do not know" and "cannot know" is consistently held. It is concluded that, as yet, we do not know the future and that it is impossible to prove that it is impossible to know the future. This book should be useful to professionals in epistemology and philosophy of science, and might be of interest to logicians and mathematicians. (shrink)

In 1993, biologist Margie Profet captured the attention of the popular press with the publication of her radical thesis: menstruation has a function. Traditional theories, she claims, typically view menstruation as a functionless by-product of cyclic flux. The details of Profet's functional account are similarly radical: she argues that menstruation has been naturally selected to defend the female reproductive tract from sperm-borne pathogens. There are a number of weaknesses in Profet's evolutionary analysis. However, I focus on a set of pragmatic (...) problems that arise prior to any details of her evolutionary account. In arguing for the importance of pragmatic considerations, I draw from the linguistic analyses of Nelson Goodman. I conclude that critical investigation of the evolutionary details of Profet's pathogen defense account will be more feasible if and when biologists more frequently feature the female system of pathogen defense in their inductive generalisations. The system needs to be better entrenched before its functional components, such as menstruation, can be thoroughly investigated. (shrink)

Certain realists about properties and relations identify them with universals. Furthermore, some hold that for a wide range of meaningful predicates, the semantic contribution to the propositions expressed by the sentences in which those predicates figure is the universal expressed by the predicate. I here address ontological issues raised by predicates first introduced to us via works of fiction and whether the universal realist should accept that any such predicates express universals. After assessing arguments by Braun, (...) D. and Sawyer, S. for fictional universal anti-realism, I propose a novel, Kripke-inspired argument for the same conclusion. I ultimately defend the claim that while this argument presents the strongest case for fictional universal anti-realism, it is nonetheless unsound. I conclude that nothing stands in the way of accepting that some fictional predicates express fictional universals. (shrink)

The identity predicate can be defined using second-order quantification: a=b =df ∀F(Fa↔Fb). Less familiarly, a dyadic sentential operator analogous to the identity predicate can be defined using third-order quantification: ϕ≡ψ =df ∀X(Xϕ↔Xψ), where X is a variable of the same syntactic type as a monadic sentential operator. With this notion in view, it is natural to ask after general principles governing its application. More grandiosely, how fine-grained is reality? -/- I will argue that reality is not structured in anything like (...) the way that the sentences we use to talk about it are structured. I do so by formulating a higher-order analogue of Russell’s paradox of structured propositions. I then relate this argument to the Frege-Russell correspondence. When confronted with the alleged paradox, Frege agreed that reality was not structured, but maintained that propositions (i.e. thoughts) were structured all the same. Russell replied that his paradox showed Frege’s theory of structured thoughts to be inconsistent, to which Frege replied that Russell’s argument failed to heed the distinction between sense and reference. Most recent commentators have sided with Russell. In defense of Frege, I establish the consistency of one version of his rejoinder. I then consider and reject some ways of resisting the argument against a structured conception of reality. I conclude that, if propositions are structured, this is because they correspond not to distinctions in reality, but rather to ways in which those distinctions can be represented. (shrink)

This chapter offers an opinionated introduction to higher-order formal languages with an eye towards their applications in metaphysics. A simply relationally typed higher-order language is introduced in four stages: starting with first-order logic, adding first-order predicate abstraction, generalizing to higher-order predicate abstraction, and finally adding higher-order quantification. It is argued that both β-conversion and Universal Instantiation are valid on the intended interpretation of this language. Given these two principles, it is then shown how we can use pure higher-order logic to (...) ask, and begin to answer, metaphysical questions with non-trivial implications. In particular, while we must reject the popular idea that structural differences between sentences correspond to parallel distinctions in the logical structure of extra-linguistic reality, it may still be possible to give a purely logical characterization of objectual aboutness and related notions. (shrink)

This paper presents a new argument for necessitism, the claim that necessarily everything is necessarily something. The argument appeals to principles about the metaphysics of quantification and predication which are best seen as constraints on reality’s fineness of grain. I give this argument in section 4; the impatient reader may skip directly there. Sections 1-3 set the stage by surveying three other arguments for necessitism. I argue that none of them are persuasive, but I think it is illuminating to consider (...) my argument in light of the others and vice versa. These interconnections should be of interest even to those who reject necessitism; of particular interest may be the new conception of validity proposed in section 5. (shrink)

Epistemological naturalists reject the demand for a priori justification of empirical knowledge; no such thing is possible. Observation reports, being the foundation of empirical knowledge, are neither justified by other sentences, nor certain; but they may be agreed upon as starting points for inductive reasoning and they function as implicit definitions of predicates used. Making inductive generalisations from observations is a basic habit among humans. We do that without justification, but we have strong intuitions that some inductive generalisations will (...) fail, while for some other we have better hopes. Why? This is the induction problem according to Goodman. He suggested that some predicates are projectible when becoming entrenched in language. This is a step forward, but not entirely correct. Inductions result in universally generalised conditionals and these contain two predicates, one in the antecedent, one in the consequent. Counterexamples to preliminary inductive generalisations can be dismissed by refining the criteria of application for these predicates. This process can be repeated until the criteria for application of the predicate in the antecedent includes the criteria for the predicate in the consequent, in which case no further counterexample is possible. If that is the case we have arrived at a law. Such laws are implicit definitions of theoretical predicates. An accidental generalisation has not this feature, its predicates are unrelated. Laws are said to be necessary, which may be interpreted as ‘“Laws” are necessarily true’. ‘Necessarily true’ is thus a semantic predicate, not a modal operator. In addition, laws, being definitions, are necessarily true in the sense of being necessary assumptions for further use of the predicates implicitly defined by such laws. Induction, when used in science, is thus our way of inventing useful scientific predicates; it is a heuristic, not an inference principle. (shrink)

M. I. Finley in his Politics in the Ancient World , 92–6 has recently cast doubt on the extent to which religious phenomena were taken seriously in ancient times. We believe that in stressing the reasons for scepticism he has overlooked much positive evidence for the impact of religious scruples on political behaviour and that in generalising he has undervalued the differences in this respect between ancient societies. The significance of some of this positive evidence is admittedly uncertain since in (...) civilian life scruples might be easy to observe without great suffering. The acid test is in time of war, so that is the concern of our present enquiry. That attitudes varied can be shown only by comparing societies. We have here limited our discussion to three for which the evidence is well preserved: the world of the Greek city before Alexander the Great, Rome before Constantine, and the Jews in the Hellenistic and Roman period. Elucidation of the reasons for their distinct attitudes would reveal much about each of these societies and its religious practices and conceptions, but there will be space here only to show that considerable variety did indeed exist. Most ancient peoples assumed that their gods approved of war; the pacifism of some pre-Constantinian Christians was exceptional. Nor did such rules in combat as were observed necessarily have a religious foundation. Ancient like modern scruples were often based on moral and humanitarian grounds, as in the treatment of corpses and civilians; the gods, as the guardians of general morality, might be involved in such matters, but only at a remove. (shrink)

First Logic is an introduction to the study of logic. Understanding the concepts of validity, invalidity, and acceptability, unacceptability of arguments is the primary focus of this book. The first chapter introduces the reader to some of the basic concepts, such as validity, soundness, and acceptability. Chapters two and three are devoted to Aristotelian logic, including the traditional square of opposition and Venn diagrams for sentences and arguments. Chapter four is a treatment of a number of important informal fallacies of (...) reasoning . Chapters five through eight are on various aspects of formal/symbolic logic: translating from natural language to the artificial language of logic; truth tables and truth trees; the method of natural deduction; predicate logic, including the logic of relations; and the concept and use of identity and its symbolization. (shrink)

Nelson Goodman’s paper ‘About’ (1961) was a milestone in aboutness theory. Although it has been much discussed, an interesting fact about it has so far been completely ignored: the important debt it owes to two papers it cites by Gilbert Ryle. With Ryle’s ‘About’ (1933) it shares much more than the title – it, too, offers a three-fold account of different ways a sentence can relate to a subject matter and a separate account for fictitious objects. More importantly, although (...) Goodman’s approach is quite different, the inspiration for the crucial element in his account, ‘differential consequence’, may well have come from a parenthetical suggestion of entailment in Ryle’s ‘About’. The second essential tool Goodman uses, viz. compound predicates which incorporate the (fictitious) object, is also the crucial element in Ryle’s ‘Imaginary Objects’ (also 1933). Goodman turns them into a predicate schema for fictitious subject matters as well as for a nominalist version of his account. (shrink)

In Fact, Fiction and Forecast, Nelson Goodman claims that the problem of justifying induction is not something over and above the problem of describing valid induction. Such claim, besides suggesting his commitment to the collapse of the distinction between the context of description and the context of justification, seems to open the possibility that the new riddle of induction could be addressed empirically. Discoveries about psychological preferences for projecting certain classes of objects could function as a criterion for determining (...) which predicates are after all projectible. In this paper, I argue that Goodman's claim must be construed within his project for constructional definitions, which is methodologically oriented by reflective equilibrium. The description of inductive practice is committed to the articulation of the extension of the class selected by the predicate ‘valid induction’. The mutual adjustment between theoretical considerations and inductive practice involved in the proposal of a definition of ‘valid induction’ must preserve that practice as much as possible, there is no way to get rid of entrenchment. Empirical discoveries about the psychological mechanism that underlies projections may help that adjustment but they cannot substitute the role played by the entrenchment of predicates. (shrink)

The new field of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements ("if P then Q") as material conditionals. In this methodological paper, I present a simple unified model of judgment aggregation in general logics. I show how many realistic decision problems can (...) be represented in it. This includes decision problems expressed in languages of classical propositional logic, predicate logic (e.g. preference aggregation problems), modal or conditional logics, and some multi-valued or fuzzy logics. I provide a list of simple tools for working with general logics, and I prove impossibility results that generalise earlier theorems. (shrink)

When Goodman put forward his “New Riddle of Induction”, he distinguished if from the old problem of justifying the so-called “Principle of Uniformity of Nature”: proving that the future will resemble the past, and that still standing lawful regularities will continue to hold. He intended to break with these ancient questions, while asking about lawlike generalizations and projectible predicates instead: how are we to separate those generalizations which are rightfully confirmed by their observed instances (i.e. nomological) and those (...) accidental ones which are nonetheless empirically equivalent? One shall not seek a ground for induction anymore, but a criterion for nomological hypothesis. Therefore Goodman’s claim seems twofold: (A) one has to face a second problem of induction, which is distinct from the old one while genuinely being a problem about induction, and (B) this new problem is solvable by a criterion of empirical confirmability, which discriminates nomological from accidental generalizations. We claim that one cannot genuinely (A) face this new problem of induction while (B) looking for such a criterion. Indeed, we argue, when one compares several hypothesis or generalizations on the same observational basis, then they must appear as equally nomological. Conversely, if one is considering hypothesis or generalizations which are not equally nomological, then one is actually unable to compare them on the same observational basis, hence to formulate the “New Riddle”. Therefore the issue raised in (A) cannot be adequately solved in (B). Yet we do accept the claim (A) that a new and distinct problem of induction is to be confronted. Thus we deny that (B) offer an adequate type of solutions to this problem, which we shall finally formulate in a more suitable manner. (shrink)

In this article I present a disagreement between classical and constructive approaches to predicativity regarding the predicative status of so-called generalised inductive definitions. I begin by offering some motivation for an enquiry in the predicative foundations of constructive mathematics, by looking at contemporary work at the intersection between mathematics and computer science. I then review the background notions and spell out the above-mentioned disagreement between classical and constructive approaches to predicativity. Finally, I look at possible ways of defending the (...) constructive predicativity of inductive definitions. (shrink)

Disquotational theories of truth are often criticised for being too weak to prove interesting generalisations about truth. In this paper we will propose a certain formal theory to serve as a framework for a solution of the generalisation problem. In contrast with Horwich’s original proposal, our framework will eschew psychological notions altogether, replacing them with the epistemic notion of believability. The aim will be to explain why someone who accepts a given disquotational truth theory Th, should also accept various generalisations (...) not provable in Th. The strategy will consist of the development of an axiomatic theory of believability, one permitting us to show how to derive the believability of generalisations from basic axioms that characterise the believability predicate, together with the information that Th is a theory of truth that we accept. (shrink)

Science is always presupposing some basic concepts that are held to be useful. These absolute presuppositions (Collingwood) are rarely debated and form the framework for what has been termed paradigm by Kuhn. Our currently accepted scientific model is predicated on a set of presuppositions that have difficulty accommodating holistic structures and relationships and are not geared towards incorporating non-local correlations. Since the theoretical models we hold also determine what we perceive and take as scientifically viable, it is important to look (...) for an alternative model that can deal with holistic relationships. One approach is to generalise algebraic quantum theory, which is an inherently holistic framework, into a generic model. Relaxing some restrictions and definitions from quantum theory proper yields an axiomatic framework that can be applied to any type of system. Most importantly, it keeps the core of the quantum theoretical formalism. It is capable of handling complementary observables, i.e. descriptors which are non-commuting, incompatible and yet collectively required to fully describe certain situations. It also predicts a generalised form of non-local correlations that in quantum theory are known as entanglement. This generalised version is not quantum entanglement but an analogue form of holistic, non-local connectedness of elements within systems, predicted to occur whenever elements within systems are described by observables which are complementary to the description of the whole system. While a considerable body of circumstantial evidence supports the plausibility of the model, we are not yet in a position to use it for clear cut predictions that could be experimentally falsified. The series of papers offered in this special issue are the beginning of what we hope will become a rich scientific debate. (shrink)

It is now commonly accepted that N. Goodman's predicate "grue" presents the theory of confirmation of C. G. Hempel (and other such theories) with grave difficulties. The precise nature and status of these "difficulties" has, however, never been made clear. In this paper it is argued that it is very unlikely that "grue" raises any formal difficulties for Hempel and appearances to the contrary are examined, rejected and an explanation of their intuitive appeal offered. However "grue" is shown to (...) raise an informal, "over-arching" difficulty of great magnitude for all theories of confirmation, including Hempel's theory. (shrink)

In this paper, I consider Goodman’s new riddle of induction and how we should best respond to it. Noticing that all the emeralds so far observed are green, we infer that all emeralds are green. However, all emeralds so far observed are also grue, so we could also infer that they are grue. Only one of these inductive inferences or projections could, however, be valid. For the hypothesis that all emeralds are green predicts that the next observed emerald will (...) be green; whereas the hypothesis that they are grue predicts that it will blue. Goodman’s new riddle is the problem of saying why the inductive inference involving “green” is the valid one. Goodman’s own solution appeals to the idea of entrenchment. His idea is that “green” is a more entrenched predicate than “grue” in the sense that it has figured many more times in our past projections than has “grue”. In his view, this explains why “green” is projectible whereas “grue” isn’t. I argue that this response doesn’t go far enough and that we additionally need an explanation of why “green” is more entrenched than “grue”—that we are otherwise left with the unsatisfactory view that its superior entrenchment is a mere linguistic accident. I try to supplement Goodman’s solution with an explanation of this kind. I argue that “grue” is not entrenched be- cause past successful inductions involving “green” show that past projections that could have been made using what I call “grue-like” predicates—predicates which are like “grue” except that the times featuring in their definitions are past—would have been unsuccessful. (shrink)

The extensions of Goodman’s ‘grue’ predicate and Kripke’s ‘quus’ are constructed from the extensions of more familiar terms via a reinterpretation that permutes assignments of reference. Since this manoeuvre is at the heart of Putnam’s model-theoretic and permutation arguments against metaphysical realism (‘Putnam’s Paradox’), both Goodman’s New Riddle of Induction and the paradox about meaning that Kripke attributes to Wittgenstein are instances of Putnam’s. Evidence cannot selectively confirm the green-hypothesis and disconfirm the grue-hypothesis, because the theory of which (...) the green-hypothesis is a part has an unintended model in which the grue-hypothesis is equally confirmed; and there are no meaning-facts that determine reference, because the objects referred to by the referring terms of any language or set of intentional mental states are permutable in a way that is consistent with the truth-values of all other sentences in that language or beliefs in that set. The upshot is that the three paradoxes need to be solved in a unified way. (shrink)

The Kripke/Wittgenstein paradox and Goodman’s riddle of induction can be construed as problems of multiple redescription, where the relevant sceptical challenge is to provide factual grounds justifying the description we favour. A choice of description or predicate, in turn, is tantamount to the choice of a curve over a set of data, a choice apparently governed by implicitly operating constraints on the relevant space of possibilities. Armed with this analysis of the two paradoxes, several realist solutions of Kripke’s paradox (...) are examined that appeal to dispositions or other non-occurrent properties. It is found that all neglect crucial epistemological issues: the entities typically appealed to are not observational and must be inferred on the basis of observed entities or events; yet, the relevant sceptical challenge concerns precisely the factual basis on which this inference is made and the constraints operating on it. All disposition ascriptions, the thesis goes on to argue, contain elements of idealization. To ward off the danger of vacuity resulting from the fact that any disposition ascription is true under just the right ideal conditions, dispositional theories need to specify limits on legitimate forms of idealization. This is best done by construing disposition ascriptions as forms of (implicit) curve-fitting, I argue, where the “data” is not necessarily numeric, and the “curve” fitted not necessarily graphic. This brings us full circle: Goodman’s and Kripke’s problems are problems concerning curve-fitting, and the solutions for it appeal to entities the postulation of which is the result of curve-fitting. The way to break the circle must come from a methodology governing the idealizations, or inferences to the best idealization, that are a part of curve-fitting. The thesis closes with an argument for why natural science cannot be expected to be of much help in this domain, given the ubiquity of idealization. (shrink)

One of the fundamental problems in the fields of inductive logic and the philosophy of science is the one concerning inferences or projections containing so-called “grue-like” or “pathological” predicates. This problem was first put into sharp focus by Nelson Goodman, who called it the “new riddle of induction.”Goodman has shown that the few attempts by others to solve this problem are not adequate. However, very little has been written concerning Goodman's own attempt to solve the problem, (...) namely his theory of entrenchment. The purpose of this article is to show that Goodman's entrenchment theory also is inadequate as a solution to the new riddle of induction. I shall try to do this by presenting two kinds of counterexamples to the entrenchment theory: one kind illustrating a general objection to the theory as a whole ; the other kind, specific objections to particular parts of the theory. (shrink)

Nelson Goodman's new riddle of induction wears many faces. In one of its guises the new riddle of induction appears as the problem of providing a general account of the distinction between projectible and non-projectible predicates. This is the form of the riddle which is supposed to point up a lacuna in the foundations of confirmation theories such as Carnap's which, Goodman charges, work only to the extent that one builds into them just the right predicates. (...) As a new riddle of induction, the problem of distinguishing projectible from non-projectible predicates has the virtue that it is in fact new—a virtue not shared by some other forms of the riddle.Philosophers had recognized previously that some predicates are more projectible than others in the sense that, for instance, the prediction that a certain toss of a die will turn up an even face is safer and more likely to be true than the prediction that the same toss will turn up six. (shrink)

Goodman'snew riddle of induction can be characterized by the following questions: What is the difference between grue and green?; Why is the hypothesis that all emeralds are grue not lawlike?; Why is this hypothesis not confirmed by its positive instances?; and, Why is the predicate grue not projectible? I argue in favor of epistemological answers to Goodman's questions. The notions of lawlikeness, confirmation, and projectibility have to be relativized to (actual and counterfactual) epistemic situations that are determined by (...) the available background information. In order to defend this thesis, I discuss an example that is less strange than the grue example. From the general conclusions of this discussion, it follows that grue is not projectible in the actual epistemic situation, but it is projectible in certain counterfactual epistemic situations. (shrink)

An account of predicate reference is presented which attempts to steer a middle course between reductionism, which construes the notion in terms of speakers' inclinations, and {transcendent) realism, which construes the notion in terms of properties. It is first introduced in the context of a discussion of the accounts of length (distance) advanced by Hans Reichenbach, Adolf Grünbaum and Hilary Putnam. A general account of predicate reference is then developed that explains the notion in terms of speakers' inclinations, while rejecting (...) the idea that this explanation should take the form of a reduction. The view is presented as a vindication of extreme nominalism, as it explains predicate reference solely in terms of the notion of qualia introduced by C.I. Lewis and developed by Nelson Goodman, which, it is argued, is definable in terms of speakers' classificatory propensities. Some connections are explored between the position that is presented and the views of Michael Dummett, John McDowell, Mark Johnston and Hilary Putnam, among others. (shrink)

In the framework of set theory we cannot distinguish between natural and non-natural predicates. To avoid this shortcoming one can use mathematical structures as conceptual spaces such that natural predicates are characterized as structurally nice subsets. In this paper topological and related structures are used for this purpose. We shall discuss several examples taken from conceptual spaces of quantum mechanics (orthoframes), and the geometric logic of refutative and affirmable assertions. In particular we deal with the problem of structurally (...) distinguishing between natural colour predicates and Goodmanian predicates like grue and bleen. Moreover the problem of characterizing natural predicates is reformulated in such a way that its connection with the classical problem of geometric conventionalism becomes manifest. This can be used to shed some new light on Goodman's remarks on the relative entrenchment of predicates as a criterion of projectibility. (shrink)

Historically, Nelson Goodman’s paradox involving the predicates ‘grue’ and ‘bleen’ has been taken to furnish a serious blow to Carl Hempel’s theory of confirmation in particular and to purely formal theories of confirmation in general. In this paper, I argue that Goodman’s paradox is no more serious of a threat to Hempel’s theory of confirmation than is Hempel’s own paradox of the ravens. I proceed by developing a suggestion from R. D. Rosenkrantz into an argument for the (...) conclusion that these paradoxes are, in fact, equivalent. My argument, if successful, is of both historical and philosophical interest. Goodman himself maintained that Hempel’s theory of confirmation was capable of handling the paradox of the ravens. And Hempel eventually conceded that Goodman’s paradox showed that there could be no adequate, purely syntactical theory of confirmation. The conclusion of my argument entails, by contrast, that Hempel’s theory of confirmation is incapable of handling Goodman’s paradox if and only if it is incapable of handling the paradox of the ravens. It also entails that for any adequate solution to one of these paradoxes, there is a corresponding and equally adequate solution to the other. (shrink)

Philosophers have had difficulty in explaining the difference between disjunctive and non-disjunctive predicates. Purely syntactical criteria are ineffective, and mention of resemblance begs the question. I draw the distinction by reference to relations between borderline cases. The crucial point about the disjoint predicate 'red or green', for example, is that no borderline case of 'red' is a borderline case of 'green'. Other varieties of disjunctive predicates are: inclusively disjunctive (such as 'red or hard'), disconnected (such as 'grue' on (...) the usual definitions), and skew (such as 'grue' on an emended definition). 'Green' is not a disjunctive predicate. Nelson Goodman's new riddle of induction elicits yet another response. (shrink)

This paper establishes model-theoretic properties of \, a variation of monadic first-order logic that features the generalised quantifier \. We will also prove analogous versions of these results in the simpler setting of monadic first-order logic with and without equality and \, respectively). For each logic \ we will show the following. We provide syntactically defined fragments of \ characterising four different semantic properties of \-sentences: being monotone and continuous in a given set of monadic predicates; having truth (...) preserved under taking submodels or being truth invariant under taking quotients. In each case, we produce an effectively defined map that translates an arbitrary sentence \ to a sentence \ belonging to the corresponding syntactic fragment, with the property that \ is equivalent to \ precisely when it has the associated semantic property. As a corollary of our developments, we obtain that the four semantic properties above are decidable for \-sentences. (shrink)

IF "ALL A’S ARE B" AND "ALL A’S ARE C" ARE BOTH EQUALLY WELL SUPPORTED BY OBSERVATIONS SO FAR, YET YIELD CONFLICTING PREDICTIONS, WHICH OUGHT WE TO ADOPT? GOODMAN’S CONFLICT BETWEEN "ALL EMERALDS ARE GREEN" AND "ALL EMERALDS ARE GRUE" IS A SPECIAL CASE OF SUCH CONFLICT, WHICH MAY BE DEALT WITH BY A RULE STATING THAT WE OUGHT NOT TO PROJECT POSITIONAL IN PREFERENCE TO QUALITATIVE PREDICATES. THIS PAPER ATTEMPTS TO ELUCIDATE THE RULES GOVERNING A LARGER CLASS (...) OF SUCH CONFLICTS, IN CASES WHERE ONE PREDICATE B IS "EPISTEMOLOGICALLY PRIOR" TO ANOTHER ONE C. (shrink)

Collin Howson (2000) challenges van Cleve’s reliabilist defense of induction (1984) based on an adaptation of Goodman Paradox (or new riddle of induction). I will try to show that Howson’s argument does not succeed once it is self-defeating. Nevertheless, I point out another way which Howson could have employed the new riddle to undermine the reliabilist defense.

Nelson Goodman's own solution to his new riddle of induction turns on the degree to which predicates are entrenched in our use of language. However, this solution requires that judgements concerning the degree to which a predicate is entrenched can be made independently of any canon of perceptible similarity. I argue that this requirement cannot be met. The riddle itself depends upon the claim that since ‘green’ can be defined positionally in terms of ‘grue’ and ‘bleen’, ‘grue’ and (...) ‘bleen’ are symmetrically related to ‘green’ and ‘blue’, and positionality is therefore ‘an entirely relative matter’. However, in order to establish that positionality is an entirely relative matter, we would need to provide a non‐positional definition of ‘grue’, rather than a positional definition of ‘green’. We therefore need to decide whether ‘grue’ can be defined ostensively by means of a single sample, as ‘green’ can. I argue that any attempt to provide such a definition is bound to fail, and hence the new riddle of induction does not reveal that ‘the roots of inductive validity are to be found in our use of language’. (shrink)

Objective Bayesian probability is often defined over rather simple domains, e.g., finite event spaces or propositional languages. This paper investigates the extension of objective Bayesianism to first-order logical languages. It is argued that the objective Bayesian should choose a probability function, from all those that satisfy constraints imposed by background knowledge, that is closest to a particular frequency-induced probability function which generalises the λ = 0 function of Carnap’s continuum of inductive methods.

This paper contains a reconstruction and discussion of some central subjects in Nelson Goodman's philosophical work. Goodman's creative symbol-constructional philosophy concerns fundamental aspects of human cognition and practice. It is argued that this provides us with the intellectual tools for constructing a genuine relationship between logic, knowledge, art, and understanding. This is shown by focusing on subjects ranging from the projectibility of predicates and nominalistic mereology to constructive relativity, ways of worldmaking and a general theory of symbols.

We prove that the positive fragment of first-order intuitionistic logic in the language with two individual variables and a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable. This holds true regardless of whether we consider semantics with expanding or constant domains. We then generalise this result to intervals \ and \, where QKC is the logic of the weak law of the excluded middle and QBL and QFL are first-order counterparts of Visser’s basic and formal logics, (...) respectively. We also show that, for most “natural” first-order modal logics, the two-variable fragment with a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable, regardless of whether we consider semantics with expanding or constant domains. These include all sublogics of QKTB, QGL, and QGrz—among them, QK, QT, QKB, QD, QK4, and QS4. (shrink)

I here aim to show that a particular approach to the problem of induction, which I will call “induction by direct inference”, comfortably handles Goodman’s problem of induction. I begin the article by describing induction by direct inference. After introducing induction by direct inference, I briefly introduce the Goodman problem, and explain why it is, prima facie, an obstacle to the proposed approach. I then show how one may address the Goodman problem, assuming one adopts induction by (...) direct inference as an approach to the problem of induction. In particular, I show that a relatively standard treatment of what some have called the “Reference Class problem” addresses the Goodman Problem. Indeed, plausible and relatively standard principles of direct inference yield the conclusion that the Goodman inference (involving the grue predicate) is defeated, so it is unnecessary to invoke considerations of ‘projectibility’ in order to address the Goodman problem. I conclude the article by discussing the generality of the proposed approach, in dealing with variants of Goodman’s example. (shrink)

This article is an attempt to clarify the idea that narratives cohere by representing stories. Stories are causally related in the way proposed by Noël Carroll, i.e., the events and states constitute necessary conditions or sufficient conditions or INUS-conditions of each other. Then, a general concept of propositional coherence is suggested. It is based on Nelson Goodman's and Joseph Ullian's ideas about unitary formulas. Narrative coherence is defined as the propositional understanding of a text (in the wide sense, including (...) non-verbal narratives) that constitutes one unitary string built upon conditional relations, i.e., relations between individuals matching Carroll's types of conditions. (shrink)

Barker and Achinstein think that it is not possible for a predicate like grue to serve as well as a predicate like green in the role of a qualitative or non-positional predicate. Their arguments consist in a number of attempts to show that one who possesses green in his language can do things with that predicate which one who must work with grue instead cannot do. However, they succeed in showing only that a qualitative predicate is better adapted to our (...) needs than its positional counterpart, rather than that grue is not capable of being a qualitative predicate. (shrink)