This paper considers two reasons that might support Russell’s choice of a ramified-type theory over a simple-type theory. The first reason is the existence of purported paradoxes that can be formulated in any simple-type language, including an argument that Russell considered in 1903. These arguments depend on certain converse-compositional principles. When we take account of Russell’s doctrine that a propositional function is not a constituent of its values, these principles turn out to be too implausible to make these arguments troubling. (...) The second reason is conditional on a substitutional interpretation of quantification over types other than that of individuals. This reason stands up to investigation: a simple-type language will not sustain such an interpretation, but a ramified-type language will. And there is evidence that Russell was tacitly inclined towards such an interpretation. A strong construal of that interpretation opens a way to make sense of Russell’s simultaneous repudiation of propositions and his willingness to quantify over them. But that way runs into trouble with Russell’s commitment to the finitude of human understanding. (shrink)

Discourse carries thin commitment to objects of a certain sort iff it says or implies that there are such objects. It carries a thick commitment to such objects iff an account of what determines truth-values for its sentences say or implies that there are such objects. This paper presents two model-theoretic semantics for mathematical discourse, one reflecting thick commitment to mathematical objects, the other reflecting only a thin commitment to them. According to the latter view, for example, the semantic role (...) of number-words is not designation but rather the encoding of cardinality-quantifiers. I also present some reasons for preferring this view. (shrink)

I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what I will call the Cut-for-Formulas to Cut-for-Sets Theorem: for a set F and a binary relation |- on Power(F), if |- is finitary, monotonic, and satisfies cut for formulas, then it also satisfies cut for sets. I deduce the CF/CS Theorem from the Ultrafilter Theorem twice; each proof uses a different order-theoretic variant of the Tukey- Teichmüller Lemma. I then discuss relationships between various (...) cut-conditions in the absence of finitariness or of monotonicity. (shrink)

This paper and its sequel “look under the hood” of the usual sorts of proof-theoretic systems for certain well-known intuitionistic and classical propositional modal logics. Section 1 is preliminary. Of most importance: a marked formula will be the result of prefixing a formula in a propositional modal language with a step-marker, for this paper either 0 or 1. Think of 1 as indicating the taking of “one step away from 0.” Deductions will be constructed using marked formulas. Section 2 presents (...) the model-theoretic concepts, based on those in [7], that guide the rest of this paper. Section 3 presents Natural Deduction systems IK and CK, formalizations of intuitionistic and classical one-step versions of K. In these systems, occurrences of step-markers allow deductions to display deductive structure that is covered over in familiar “no step” proof-theoretic systems for such logics. Box and Diamond are governed by Introduction and Elimination rules; the familiar K rule and Necessitation are derived (i.e. admissible) rules. CK will be the result of adding the 0-version of the Rule of Excluded Middle to the rules which generate IK. Note: IK is the result of merely dropping that rule from those generating CK, without addition of further rules or axioms (as was needed in [7]). These proof-theoretic systems yield intuitionistic and classical consequence relations by the obvious definition. Section 4 provides some examples of what can be deduced in IK. Section 5 defines some proof-theoretic concepts that are used in Section 6 to prove the soundness of the consequence relation for IK (relative to the class of models defined in Section 2.) Section 7 proves its completeness (relative to that class). Section 8 extends these results to the consequence relation for CK. (Looking ahead: Part 2 will investigate one-step proof-theoretic systems formalizing intuitionistic and classical one-step versions of some familiar logics stronger than K.). (shrink)

David Chalmers argues that consciousness -- authentic, first-person, conscious consciousness -- cannot be reduced to brain events or to any physical event, and that efforts to find a workable mind-body identity theory are, therefore, doomed in principle. But for Chalmers and non-reductionist in general consciousness consists exclusively, or at least paradigmatically, of phenomenal or qualia-consciousness. This results in a seriously inadequate understanding both of consciousness and of the “hard problem.” I describe other, higher-order cognitional events which must be conscious if (...) the “hard problem” is to be solved -- in any sense of ‘solve’ which would make us any the wiser about it -- but whose consciousness is quite different from the qualia and phenomena usually inventoried. Events of this kind are both part of the hard problem and the means by which we will solve it, if we ever do. (shrink)

Logicism is, roughly speaking, the doctrine that mathematics is fancy logic. So getting clear about the nature of logic is a necessary step in an assessment of logicism. Logic is the study of logical concepts, how they are expressed in languages, their semantic values, and the relationships between these things and the rest of our concepts, linguistic expressions, and their semantic values. A logical concept is what can be expressed by a logical constant in a language. So the question “What (...) is logic?” drives us to the question “What is a logical constant?” Though what follows contains some argument, limitations of space constrain me in large part to express my Credo on this topic with the broad brush of bold assertion and some promissory gestures. (shrink)

Proof uses forcing on perfect trees for 2-quantifier sentences in the language of arithmetic. The result extends to exact pairs for the hyperarithmetic degrees.

Bernard Lonergan has argued for a theory of cognition that is transcendentally secure, that is, one such that any plausible attempt to refute it must presuppose its correctness, and one that also grounds a correct metaphysics and ontology. His proposal combines an identity theory of knowledge with an intentional relation between knower and known. It depends in a crucial way upon an appropriation of one’s own cognitional motives and acts, that is, upon “knowing one’s own knowing.” I argue that because (...) of conflicts between the identity and intentionality components of the theory, rational self-appropriation cannot, as Lonergan claims, be an iteration of just the same acts by which we acquire other sorts of knowledge. I propose an amended theory in which the relation between intending-subject and intended-object of first-level cognition becomes, in RSA, a numerical identity of knower and known and of the epistemic and the ontological. (shrink)

This note calls attention to the fact that efficient causes – the sort of cause that changes something or makes something happen – can play no constitutive role in the immediate, cognitively conscious relation between cognitive subject and a cognit-ive object. It notes that: (1) it is a necessary condition for an efficient causal relation that it alter its relata; and (2) it is a necessary condition for a conscious cognitive relat-ion that it does not alter its relata. This has (...) important implication for the theories of knowledge and consciousness, the “Hard Problem,” and related puzzles. (shrink)

In this paper I argue that Bonjour’s claim that empirical beliefs can only be justified by other empirical beliefs and his use of non-normative “spontaneous empirical beliefs” and the “The Doxastic Preumption” fail to solve the problems of coherence theory. I propose a justification of empirical (and other beliefs) based on the work of B. Lonergan.

Relative to any reasonable frame, satisfiability of modal quantificational formulae in which “= ” is the sole predicate is undecidable; but if we restrict attention to satisfiability in structures with the expanding domain property, satisfiability relative to the familiar frames (K, K4, T, S4, B, S5) is decidable. Furthermore, relative to any reasonable frame, satisfiability for modal quantificational formulae with a single monadic predicate is undecidable ; this improves the result of Kripke concerning formulae with two monadic predicates.

A model-theoretic approach to the semantics of set-theoretic discourse.

Let I be a countable jump ideal in $\mathscr{D} = \langle \text{The Turing degrees}, \leq\rangle$ . The central theorem of this paper is: a is a uniform upper bound on I iff a computes the join of an I-exact pair whose double jump a (1) computes. We may replace "the join of an I-exact pair" in the above theorem by "a weak uniform upper bound on I". We also answer two minimality questions: the class of uniform upper bounds on I (...) never has a minimal member; if ∪ I = L α [ A] ∩ ω ω for α admissible or a limit of admissibles, the same holds for nice uniform upper bounds. The central technique used in proving these theorems consists in this: by trial and error construct a generic sequence approximating the desired object; simultaneously settle definitely on finite pieces of that object; make sure that the guessing settles down to the object determined by the limit of these finite pieces. (shrink)

Part 1 [Hodes, 2021] “looked under the hood” of the familiar versions of the classical propositional modal logic K and its intuitionistic counterpart. This paper continues that project, addressing some familiar classical strengthenings of K and GL), and their intuitionistic counterparts. Section 9 associates two intuitionistic one-step proof-theoretic systems to each of the just mentioned intuitionistic logics, this by adding for each a new rule to those which generated IK in Part 1. For the systems associated with the intuitionistic (...) counterparts of D and T, these rules are “pure one-step”: their schematic formulations does not use □ or ♢. For the systems associated with the intuitionistic counterparts of K4, etc., these rules meet these conditions: neither □ nor ♢ is iterated; none use both □ and ♢. The join of the two systems associated with each of these familiar logics is the full one-step system for that intuitionistic logic. And further “blended” intuitionistic systems arise from joining these systems in various ways. Adding the 0-version of Excluded Middle to their intuitionistic counterparts yields the one-step systems corresponding to the familiar classical logics. Each proof-theoretic system defines a consequence relation in the obvious way. Section 10 examines inclusions between these consequence relations. Section 11 associates each of the above consequence relations with an appropriate class of models, and proves them sound with respect to their appropriate class. This allows proofs of some failures of inclusion between consequence relations. Section 12 proves that the each consequence relation is complete or weakly complete, that relative to its appropriate class of models. The Appendix presents three further results about some of the intuitionistic consequence relations discussed in the body of the paper. For Keywords, see Part 1. (shrink)

Where $\underline{a}$ is a Turing degree and ξ is an ordinal $ , the result of performing ξ jumps on $\underline{a},\underline{a}^{(\xi)}$ , is defined set-theoretically, using Jensen's fine-structure results. This operation appears to be the natural extension through $(\aleph_1)^{L^\underline{a}}$ of the ordinary jump operations. We describe this operation in more degree-theoretic terms, examine how much of it could be defined in degree-theoretic terms and compare it to the single jump operation.

The idea that some objects are metaphysically “cheap” has wide appeal. An influential version of the idea builds on abstractionist views in the philosophy of mathematics, on which numbers and other mathematical objects are abstracted from other phenomena. For example, Hume's Principle states that two collections have the same number just in case they are equinumerous, in the sense that they can be correlated one‐to‐one:. The principal aim of this article is to use the notion of grounding to develop this (...) sort of abstractionism. The appeal to grounding enables a unified response to the two main challenges that confront abstractionism. First, we must explicate the metaphor of metaphysical “cheapness.” Second, we must rebut the “bad company” objection, which rejects abstraction principles like (HP) as tarnished by their similarity to inconsistent principles like Frege's Basic Law V. By enforcing a simple requirement that all abstraction be properly grounded, we propose a unified solution to these two hard, and prima facie unrelated, problems. On our view, grounded abstraction simultaneously ensures “cheap” abstracta and permissible abstraction. (shrink)

A compelling idea holds that reality has a layered structure. We often disagree about what inhabits the bottom layer, but we agree that higher up we find chemical, biological, geological, psychological, sociological, economic, /etc./, entities: molecules, human beings, diamonds, mental states, cities, interest rates, and so on. How is this intuitive talk of a layered structure of entities to be understood? Traditionally, philosophers have proposed to understand layered structure in terms of either reduction or supervenience. But these traditional views face (...) well-known problems. A plausible alternative is that layered structure is to be explicated by appeal to explanations of a certain sort, termed / grounding explanations/. Grounding explanations tell us what obtains in virtue of what. Unfortunately, the use of grounding explanations to articulate the layered conception faces a problem, which I call /the collapse/. The collapse turns on the question of how to ground the facts stated by the explanations themselves. In this paper I make a suggestion about how to ground explanations that avoids the collapse. Briefly, the suggestion is that the fact stated by a grounding explanation is grounded in its /explanans/. (shrink)

This summary is not exactly the way I would have done it myself but I must admit that my writing is sometimes a challenge to read. So I asked an AI to do this summary expecting that it will give an easily understandable although not totally accurate view on Ontology of Knowledge and from this general understanding help the reader to read the original papers. Jean-Louis Boucon’s works, "Introduction to the Ontology of Knowledge" and "Time, Space, and World as (...) Knowledge," delve into the intricate nature of reality, meaning, and the process of knowing. Boucon challenges traditional dichotomies in philosophy and science, presenting a cohesive framework where the knowing subject and the world are intertwined aspects of a single dynamic reality. His ideas provide a robust foundation for exploring ontological and epistemological questions, including the interpretation of quantum mechanics. (shrink)

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of the original pure system (...) with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b). (shrink)

Research in experimental philosophy has increasingly been turning to corpus methods to produce evidence for empirical claims, as they open up new possibilities for testing linguistic claims or studying concepts across time and cultures. The present article reviews the quasi-experimental studies that have been done using textual data from corpora in philosophy, with an eye for the modeling and experimental design that enable statistical inference. I find that most studies forego comparisons that could control for confounds, and that only a (...) little less than half employ statistical testing methods to control for chance results. Furthermore, at least some researchers make modeling decisions that either do not take into account the nature of corpora and of the word-concept relationship, or undermine the experiment's capacity to answer research questions. I suggest that corpus methods could both provide more powerful evidence and gain more mainstream acceptance by improving their modeling practices. (shrink)

In this paper I call attention to the fact that Lonergan gives two radically opposed accounts of how sense perception relates us to the external world and of how we know that this relation exists. I argue that the position that Lonergan characteristically adopts is not the one implied by what is most fundamental in his theory of cognition. I describe the initial epistemic position with regard to the problem of skepticism about the external material world that is in fact (...) implied by his theory of cognition, and I sort out some confusion about various forms of direct and representative perceptual realism. The paper concludes with a critique of Lonergan’s theory of description and explanation in empirical science that makes evident the difficulties into which he is led by lack of clarity in his theory of perception. (shrink)

Where AR is the set of arithmetic Turing degrees, 0 (ω ) is the least member of { $\mathbf{\alpha}^{(2)}|\mathbf{a}$ is an upper bound on AR}. This situation is quite different if we examine HYP, the set of hyperarithmetic degrees. We shall prove (Corollary 1) that there is an a, an upper bound on HYP, whose hyperjump is the degree of Kleene's O. This paper generalizes this example, using an iteration of the jump operation into the transfinite which is based on (...) results of Jensen and is detailed in [3] and [4]. In $\S1$ we review the basic definitions from [3] which are needed to state the general results. (shrink)

The scientific successes of the last 400 years strongly suggest a picture on which our scientific theories exhibit a layered structure of dependence and determination. Economics is dependent on and determined by psychology; psychology in its turn is, plausibly, dependent on and determined by biology; and so it goes. It is tempting to explain this layered structure of dependence and determination among our theories by appeal to a corresponding layered structure of dependence and determination among the entities putatively treated by (...) those theories. In this paper, I argue that we can resist this temptation: we can explain the sense in which, e.g., the biological truths are dependent on and determined by chemical truths without appealing to properly biological or chemical entities. This opens the door to a view on which, though there are more truths than just the purely physical truths, there are no entities, states, or properties other than the purely physical entities, states, and properties. I argue that some familiar strategies to explicate the idea of a layered structure of theories by appeal to reduction, ground, and truthmaking encounter difficulties. I then show how these difficulties point the way to a more satisfactory treatment which appeals to something very close to the notion of ground. Finally, I show how this treatment provides a theoretical setting in which we might fruitfully frame debates about which entities there really are. (shrink)

A raft of new philosophical problems concerning truth have recently been discovered by several theorists. These problems concern the question of how ascriptions of truth are to be grounded. Most previous commentators have taken the problems to shed light on the theory of ground. In this paper, I argue that they also shed light on the theory of truth. In particular, I argue that the notion of ground can be deployed to clearly articulate one strand of deflationary thinking about truth, (...) according to which truth is “metaphysically lightweight.” I offer a ground-theoretic explication of the lightness of truth and show how it yields a novel solution to the problems concerning how truth is grounded. So, the theory of truth and the theory of ground interact fruitfully: we can apply the notion of ground to offer a clear explication of the deflationist claim that truth is “metaphysically lightweight” that both captures the motivations for that claim and solves the problems. (shrink)

Alternative currencies are means of payment that circulate alongside—as an alternative or complement to—official currencies. While these currencies have existed for a long time, both society and academia have shown a renewed interest in their potential to decentralize the governance of monetary affairs and to bring people and organizations together in more ethical or sustainable ways. This article is a review of the ethical and philosophical implications of these alternative monetary projects. We first discuss various classifications of these currencies before (...) analyzing the ethical challenges linked to the way they tackle social and environmental issues. We also examine the incentive-based and coercive mechanisms used by these currencies from an ethical perspective and debate the promises and perils of monetary decentralization and democracy. We conclude by identifying an agenda for future research. (shrink)

Consider the kinds of macroscopic concrete objects that common sense and the sciences allege to exist: tables, raindrops, tectonic plates, galaxies, and the rest. Are there any such things? Opinions differ. Ontological liberals say they do; ontological radicals say they don't. Liberalism seems favored by its plausible acquiescence to the dictates of common sense abetted by science; radicalism by its ontological parsimony. Priority theorists claim we can have the virtues of both views. They hold that tables, raindrops, etc., exist, but (...) they aren't fundamental. The ontological liberal's ontology provides the correct inventory of existent individuals. The ontological radical's more restricted ontology provides the correct inventory of fundamental individuals. The priority theorist claims that the derivative individuals are "no addition in being" to the fundamental ones, so we can have our cake and eat it too. It would be nice if priority theorists were right. In this paper I argue, with regret, that they are not. One upshot is that the sort of explanations which underwrite the priority theorist's distinction between fundamental and derivative individuals do not mitigate our ontological commitments. Another is that we still have to choose between the charms of liberalism and radicalism. (shrink)

In Objects: Nothing Out of the Ordinary, Daniel Z. Korman defends a view he calls conservatism. Conservatives hold that there are ordinary objects, but no extraordinary objects. But Korman never explicitly characterizes what would qualify an object as ordinary in the relevant sense. We have some paradigm cases of ordinary objects, including tables, dogs, and trees; and we have some paradigm cases of extraordinary objects of sorts familiar from the philosophical literature. Here I attempt to fill this gap, surveying a (...) number of attempts to characterize the commitments of conservatism. All fail. In particular, no specification of what it takes for an object to be ordinary is both plausible and consistent with the conservative verdicts on the paradigms. I argue that this is no coincidence, since it turns out to be implausible in light of the results of settled science to deny the existence of one of Korman's paradigms of an extraordinary object. The upshot is that plausibility requires being a little more liberal than conservatism seems to allow. (shrink)

An impressive variety of new forms of money has aroused in recent decades from various groups of people and various kinds of institutions. These currencies are at the heart of intense debates, which raise important, but often neglected, normative issues. The diversity of their goals, uses and charac-teristics is so large that it makes some preliminary distinctions necessary. This paper aims at provid-ing a proper background for the discussion of the possible merits and drawbacks of different kinds of currencies. It (...) proposes a classification that demarcates currencies according to how they relate to several crucial normative issues. Its aim is to show, for every type of currency, and as unambiguously as possible, to which side of these controversies it lies. (shrink)

This article aims to defend a novel account of pluralism in economics. First, it argues that what justifies pluralism is its epistemological benefits. Second, it acknowledges that pluralism has limits, and defends reasonable pluralism, or the view that we should only accept those theories and methods that can be justified by their communities with reasons that other communities can accept. Clearly, reasonable pluralism is an ideal, which requires economists of different persuasions to respect certain norms of communication while evaluating each (...) other’s theories. The article ends with a discussion of the conditions under which reasonable communication becomes possible. (shrink)

The market for environmental, social and governance (ESG) rating and data is expected to grow immensely in the next decades. This brief zooms in both on the integration of ESG risks into “traditional” operations of Credit Rating Agencies (CRAs) as well as on the emergence of a market exclusively dedicated to ESG rating. As will become clear, the market for ESG ratings suffers from serious shortcomings, a lack of transparency and standardisation, significant biases and conflicts of interests, and a dependence (...) on large, oligopolistic, credit rating agencies. (shrink)

Two slogans define structuralism: contemporary mathematics studies structures; mathematical objects are places in those structures. Shapiro’s version of structuralism posits abstract objects of three sorts. A system is “a collection of objects with certain relations” between these objects. “An extended family is a system of people with blood and marital relationships.” A baseball defense, e.g., the Yankee’s defense in the first game of the 1999 World Series, is a also a system, “a collection of people with on-field spatial and ‘defensive-role’ (...) relations”. “A structure is the abstract form of a system” ; it consists of “a collection of places [sometimes called positions or offices] and a finite collection of functions and relations on these places”. (shrink)

This paper assesses the proposal to transform the monetary system into an Ecology of money, that is, into a system made of a large diversity of complementary currencies. Its central aim is to examine whether this proposal could provide a systemic solution to both the ecological and financial crises, as several authors, most notably Lietaer and Douthwaite, have argued. To this end, it analyses the two main arguments in favour of this proposal. First, it focuses on the claim that an (...) Ecology of money would be more resilient and less prone to crisis than the present monetary system. It shows that this argument suffers from several conceptual flaws and argues that it fails to provide sufficient normative reasons to favour an Ecology of money. Second, this paper analyses the claim that an Ecology of money could help defeat the monetary growth imperative that supposedly plagues our economies. The paper raises serious doubts about the existence of such an imperative and questions the claim that an Ecology of money could contribute to weaken it in a significant way. (shrink)

A major source of latter-day skepticism about necessity is the work of David Hume. Hume is widely taken to have endorsed the Humean claim: there are no necessary connections between distinct existences. The Humean claim is defended on the grounds that necessary connections between wholly distinct things would be mysterious and inexplicable. Philosophers deploy this claim in the service of a wide variety of philosophical projects. But Saul Kripke has argued that it is false. According to Kripke, there are necessary (...) connections between distinct existences; in particular, there are necessary connections between material objects and their material origins. In this paper I argue that the primary motivation for the Humean claim, Hume's datum, also motivates the key premise in an argument for the necessity of origins. The very considerations that the Humean takes to show that necessary connections between wholly distinct things would be mysterious and inexplicable indicate that there must be some such necessary connections. Thus, in the absence of alternative support, there is no reason to believe the Humean claim. (shrink)

Louis Pojman and Robert Westmoreland have compiled the best material on the subject of equality, ranging from classical works by Aristotle, Hobbes and Rousseau to contemporary works by John Rawls, Thomas Nagel, Michael Walzer, Harry Frankfurt, Bernard Williams and Robert Nozick; and including such topics as: the concept of equality; equal opportunity; Welfare egalitarianism; resources; equal human rights and complex equality.

A standard view of reference holds that a speaker's use of a name refers to a certain thing in virtue of the speaker's associating a condition with that use that singles the referent out. This view has been criticized by Saul Kripke as empirically inadequate. Recently, however, it has been argued that a version of the standard view, a /response-based theory of reference/, survives the charge of empirical inadequacy by allowing that associated conditions may be largely or even entirely implicit. (...) This paper argues that response-based theories of reference are prey to a variant of the empirical inadequacy objection, because they are ill-suited to accommodate the successful use of proper names by pre-school children. Further, I argue that there is reason to believe that normal adults are, by and large, no different from children with respect to how the referents of their names are determined. I conclude that speakers typically refer /positionally/: the referent of a use of a proper name is typically determined by aspects of the speaker's position, rather than by associated conditions present, however implicitly, in her psychology. (shrink)

John Searle has proposed one of the most influential contemporary accounts of social ontology. According to Searle, institutional facts are created by the collective assignment of a specific kind of function —status-function— to pre-existing objects. Thus, a piece of paper counts as money in a certain context because people collectively recognize it as money, and impose a status upon it, which in turn enables that piece of paper to deliver certain functions (means of payment, etc.). The first part of this (...) essay presents Searle’s theory of social ontology and summarizes his views on money. The second part centers on criticisms of his views and compares his theory with its main competitors, including the theories of Tuomela, Guala and Hindriks, and Smit, Buekens and Duplessis. The conclusion attempts to see what may remain of Searle’s theory after careful examination. (shrink)