This paper supports the literature which argues that derivational robustness can have epistemic import in highly idealized economic models. The defense is based on a particular example from mathematical economic theory, the dynamic Walrasian general equilibrium model. It is argued that derivational robustness first increased and later decreased the credibility of the Walrasian model. The example demonstrates that derivational robustness correctly describes the practices of a particular group of influential economic theorists and provides support for the arguments of philosophers who (...) have offered a general epistemic justification of such practices. (shrink)

An increasing amount of twenty-first century metaphysics is couched in explicitly hyperintensional terms. A prerequisite of hyperintensional metaphysics is that reality itself be hyperintensional: at the metaphysical level, propositions, properties, operators, and other elements of the type hierarchy, must be more fine-grained than functions from possible worlds to extensions. In this paper I develop, in the setting of type theory, a general framework for reasoning about the granularity of propositions and properties. The theory takes as primitive the notion of a (...) substitution on a proposition (property, etc.) and, among other things, uses this idea to elucidate a number of theoretically important distinctions. A class of structures are identified which can be used to model a wide range of positions about the granularity of reality; certain of these structures are seen to receive a natural treatment in the category of M-sets. (shrink)

It is hoped that modern sensory substitution and augmentation devices will be able to replace or expand our senses. But to what extent has this been achieved to date? To what extent are the experiences created by sensory substitution devices like the sensory experiences that we are trying to replace? To what extent can we augment people’s senses providing them with new information and new experiences? The first aim of this introduction is to delve deeply into this question to discover (...) the usefulness of these devices, to outline the different sorts of experience that might be created, and what the evidence tells us about these experiences. While there are some reasons to be hopeful about the powers of sensory substitution devices, there are also reasons to wonder whether they will ever really have the practical applications that we hope they might have. The second aim is to look to see whether the study of modern sensory substitution and augmentation devices can shed light on the nature of our senses and perception in general. Much of the philosophical, psychological, and neuroscientific work that takes place concerning sensory substitution and augmentation is keenly aware of the possibility that it might help our understanding and it seeks to comprehend many different aspects of perception. (shrink)

This article elaborates on Christopher Norris's claim that certain aspects of Derrida's work are amenable to formalisation in modal-logical terms. Norris contends that any adequate analysis of the logic behind Derrida's work must provide an account of the notions of possibility, necessity, and necessary possibility, particularly as they are related to Derrida's notion of iterability. This article examines the further hypothesis that Derrida's understanding of modality, according to which possibilities must be accounted for even if they are never realised, might (...) even better be described in terms of possible worlds. In possible-worlds semantics, the conceptual meaning of a statement is constituted by the set of alternative contexts in which that statement is true. This article argues, however, that possible-worlds semantics would be unthinkable without the experience that one referent can be substituted for another. The possibility of this experience is best described in Derridean terms. Read through Derrida's thought of the trace, the properly semantic substitutions may come to be seen as dependent on the substitution of the thing for itself; on what Derrida calls ‘the substitution of the unique for the unique’. (shrink)

Raymond Kelly’s widely cited _Warless Societies and the Origin of War_ (University of Michigan Press, 2000) seeks to explain the origins of two central signatures of human society: war and segmented—i.e., multilevel—societies. Both, he argues, arose with the emergence of a social-substitutability principle, a rule that establishes a collective identity among a set of individuals such that any one member becomes equivalent to, and responsible for the actions of, the others. This principle emerged during the Holocene, when population increase gave (...) rise to the first lethal ambushes. By its nature, ambush obscures attackers’ identities. Those attempting to retaliate for the ambush were therefore obliged to target members of the ambushers’ group indiscriminately—i.e., based on a social-substitutability principle. Kelly’s proposals draw welcome attention to a widespread, deeply influential, and unsettling human behavior, the disposition to hold everyone in a group culpable for the actions of a few, a proclivity that all too often results in mass slaughter. His general argument, however, is logically and empirically deficient, and cross-cultural evidence on ambush in contact-era New Guinea undermines his anonymity-of-ambush hypothesis. What then accounts for war and multilevel society? The New Guinea evidence strongly supports a contention that social-substitutability behavior arose not from offensive military action (i.e., ambush) but from the defensive military response to ambush. These findings render the social-substitutability argument’s unconventional definition of war superfluous, undermine its chronology for the emergence of war, and underwrite an alternative scenario for the origins of multilevel, segmented society. (shrink)

This paper is about the cluster of issues that orbit a well-known thesis of Quine’s, as it applies to attitude ascriptions.

Substituted judgment has increasingly become the accepted standard for rendering decisions for incapacitated adults in the USA. A broad exception exists with regard to patients with diminished capacity secondary to depressive disorders, as such patients’ previous wishes are generally not honoured when seeking to turn down life-preserving care or pursue aid-in-dying. The result is that physicians often force involuntary treatment on patients with poor medical prognoses and/or low quality of life as a result of their depressive symptoms when similarly situated (...) incapacitated patients without such depressive symptoms would have their previous wishes honoured via substituted judgment. This commentary argues for reconsidering this approach and for using a substituted judgment standard for a subset of EMP/LQL patients seeking death. (shrink)

Frances Kamm's Principle of Secondary Permissibility specifies a class of exceptions to the general rule not to kill as a means. The principle allows us to harm as a means some of those who would have been otherwise harmed as side effects. ‘For example, suppose it is impermissible to paralyze A's legs as a means to a greater good. It would still be permissible to do this as the alternative to permissibly killing A as a mere indirect side effect.’ I (...) argue that, despite of its great appeal, PSP is incorrect; it is simply not true that the victims of substitutive harm are not worse off than they would otherwise permissibly have been. In fact, there is no moral difference between the purportedly substitutive harm licensed by PSP and the standard sort of harming as means repudiated by nonconsequentialists. (shrink)

If the substitutional interpretation of quantification is tenable, it provides a basis for reinterpreting any formal language-system as nominalist: each substituend for the variables of quantification either designates a concrete object or it is empty.

This book explores an important central thread that unifies Russell's thoughts on logic in two works previously considered at odds with each other, the Principles of Mathematics and the later Principia Mathematica. This thread is Russell's doctrine that logic is an absolutely general science and that any calculus for it must embrace wholly unrestricted variables. The heart of Landini's book is a careful analysis of Russell's largely unpublished "substitutional" theory. On Landini's showing, the substitutional theory reveals the unity (...) of Russell's philosophy of logic and offers new avenues for a genuine solution of the paradoxes plaguing Logicism. (shrink)

Substitution and simple sentences -- Simple sentences and semantics -- Simple sentences and implicatures -- The enlightenment problem and a common assumption -- Abandoning (EOI) -- Beyond matching propositions -- App. A : extending the account -- App. B : belief reporting.

I address a type of circularity threat that arises for the view that we employ general basic logical principles in deductive reasoning. This type of threat has been used to argue that whatever knowing such principles is, it cannot be a fully cognitive or propositional state, otherwise deductive reasoning would not be possible. I look at two versions of the circularity threat and answer them in a way that both challenges the view that we need to apply general logical principles (...) in deductive reasoning and defuses the threat to a cognitivist account of knowing basic logical principles. (shrink)

In the literature three mechanisms are commonly distinguished to make decisions about the care of incompetent patients: A living will, a substituted judgment by a surrogate (who may or may not hold the power of attorney ), and a best interest judgment. Almost universally, the third mechanism is deemed the worst possible of the three, to be invoked only when the former two are unavailable. In this article, I argue in favor of best interest judgments. The evermore common aversion of (...) best interest judgments entails a risk that health care providers withdraw from the decision-making process, abandoning patients (or their family members) to these most difficult of decisions about life and death. My approach in this article is primarily negative, that is, I criticize the alleged superiority of the living will and substituted judgment. The latter two mechanisms gain their alleged superiority because they are supposedly morally neutral, whereas the best interest judgment entails a value judgment on behalf of the patient. I argue that on closer inspection living wills and substituted judgments are not morally neutral; indeed, they generally rely on best interest judgments, even if those are not made explicit. (shrink)

The particular problem which will concern us here is raised by "Leibniz's Rule": Eadem sunt quorum unum in alterius locum substitui potest, salva veritate. The puzzle arises from the following inference.

Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like 'something' permit a replacement, preserving grammaticality or the same reading of the verb: (1) a. John claims that he won. b. ??? John claims a proposition / some thing. c. John claims something. In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements of various other (...) intensional predicates and argued for a Nominalization Theory of special quantifiers. In this paper, I will review and extend the range of linguistic generalizations that motivate the Nominalization Theory and show that they pose serious problems for higher-order and substitutional analyses of special quantifiers. (shrink)

It has been suggested that a substitutional semantics for quantification theory lends itself to nominalistic aims. I should like in this paper to explore that claim.

Holistic accounts of the natural environment in environmental ethics fail to stress the distinction between the concepts of comnlunity and organism. Aldo Leopold’s “Land Ethic” adds to this confusion, for it can be interpreted as promoting either a community or an organic model of nature. The difference between the two concepts lies in the degree of autonomy possessed by constituent entities within the holistic system. Members within a community are autonomous, while the parts of an organism are not. Different moral (...) conclusions and environmental policies may result from this theoretical distinction. Treating natural entities as parts of an organism downgrades their intrinsic value as individual natural beings, since the only relevant moral criterion in an organic environmental ethic is the instrumental value that each natural entity has for the system. This ethic allows instances of the “substitution problem”-the replacement of one entity in an ecosystem by another provided that the overall functioning of the system is notharmed. However, since substitution violates environmentalist principles, for example, calling for respect for the integrity of the entities in a natural system, an organic environmental ethic must be rejected. A community model focuses on both the functional value and the autonomous intrinsie value of natural entities in a system. A community environmental ethic thus avoids the substitution problem. (shrink)

This paper analyzes the process of perceptual recalibration (PR) in light of two cases of technologically-mediated cognition: sensory substitution and perceptual modification. We hold that PR is a very useful concept - perhaps necessary - for explaining the adaptive capacity that natural perceptive systems display as they respond to functional demands from the environment. We also survey critically related issues, such as the role of learning, training, and nervous system plasticity in the recalibrating process. Attention is given to the interaction (...) between technology and cognition, and the case of epistemic prostheses is presented as an illustration. Finally, we address the following theoretical issues: (1) the dynamic character of spatial perception; (2) the role of functional demands in perception; (3) the nature and interaction of sensory modalities. We aim to show that these issues may be addressed empirically and conceptually - hence, the usefulness of sensory-substitution and perceptual-modification studies in the analysis of perception, technologically-mediated cognition, and cognition in general. (shrink)

This paper analyzes the process of perceptual recalibration in light of two cases of technologically-mediated cognition: sensory substitution and perceptual modification. We hold that PR is a very useful concept — perhaps necessary — for explaining the adaptive capacity that natural perceptive systems display as they respond to functional demands from the environment. We also survey critically related issues, such as the role of learning, training, and nervous system plasticity in the recalibrating process. Attention is given to the interaction between (...) technology and cognition, and the case of epistemic prostheses is presented as an illustration. Finally, we address the following theoretical issues: the dynamic character of spatial perception; the role of functional demands in perception; the nature and interaction of sensory modalities. We aim to show that these issues may be addressed empirically and conceptually — hence, the usefulness of sensory-substitution and perceptual-modification studies in the analysis of perception, technologically-mediated cognition, and cognition in general. (shrink)

In 'A Puzzle about Belief' Saul Kripke appeals to a principle of disquotation that allows us to infer a person's beliefs from the sentences to which she assents (in certain conditions). Kripke relies on this principle in constructing some famous puzzle cases, which he uses to defend the Millian view that the sole semantic function of a proper name is to refer to its bearer. The examples are meant to undermine the anti-Millian objection, grounded in traditional Frege-cases, that truth-value is (...) not always maintained when co-referential names are intersubstituted in belief reports. I argue here that our disquotational practice is sensitive to certain shifts in conversational context, and it is only if we overlook these shifts - if we 'misdisquote' - that we can draw the conclusions Kripke wants to draw from his examples. In the wake of this conclusion, I provide a 'contextualist' treatment of Kripke's puzzle cases. I show how this treatment is motivated by certain norms of rationality, and I defend these norms against an intriguing 'anti-Cartesian' theory of mind. Throughout the paper, I develop the larger implications that my treatment of Kripke's argument has for the semantic theory of names and belief reports, and, more generally, for our picture of the relation between linguistic behaviour and our states of mind. (shrink)

The Russellian approach to the semantics of attitude ascriptions faces a problem in explaining the robust speaker intuitions that it does not predict. A familiar response to the problem is to claim that utterances of attitude ascriptions may differ in their Gricean conversational implicatures. I argue that the appeal to Grice is ad hoc. First, we find that speakers do not typically judge an utterance false merely because it implicates something false. The apparent cancellability of the putative implicatures is irrelevant, (...) since cancellability does not indicate conversational implicature. Finally, the appeal assumes, implausibly, that ordinary speakers generally subscribe to a particular philosophical theory about belief. (shrink)

In this brief note I clarify two points made in my 1996 book Philosophical Perspectives on Language. The clarifications are prompted by some criticisms in a recent Dialogue review of that book.

There are plausible objections to substitutional construals of generalization. But these objections do not apply to a substitutional construal of generalization proposed by Peter Geach several years ago. This paper examines Geach’s conception.

In his 1903 Principles of Mathematics, Russell holds that “it is a characteristic of the terms of a proposition”—that is, its “logical subjects”—“that any one of them may be replaced by any other entity without our ceasing to have a proposition”. Hence, in PoM, Russell holds that from the proposition ‘Socrates is human’, we can obtain the propositions ‘Humanity is human’ and ‘The class of humans is human’, replacing Socrates by the property of humanity and the class of humans, respectively. (...) Hence also, in PoM, Russell accepts the doctrine of the unrestricted variable: if we replace a logical subject of a proposition by a variable to yield a propositional function, the range of that variable includes absolutely every entity. For absolutely any entity can be taken as a value of that variable to yield a proposition, true or false. The doctrine of the unrestricted variable is thus incompatible with any type-theoretic metaphysics, according to which only entities of a certain restricted type can replace a logical subject of a given proposition so as to yield another proposition. (shrink)

In his 1903 Principles of Mathematics, Russell holds that “it is a characteristic of the terms of a proposition”—that is, its “logical subjects”—“that any one of them may be replaced by any other entity without our ceasing to have a proposition”. Hence, in PoM, Russell holds that from the proposition ‘Socrates is human’, we can obtain the propositions ‘Humanity is human’ and ‘The class of humans is human’, replacing Socrates by the property of humanity and the class of humans, respectively. (...) Hence also, in PoM, Russell accepts the doctrine of the unrestricted variable: if we replace a logical subject of a proposition by a variable to yield a propositional function, the range of that variable includes absolutely every entity. For absolutely any entity can be taken as a value of that variable to yield a proposition, true or false. The doctrine of the unrestricted variable is thus incompatible with any type-theoretic metaphysics, according to which only entities of a certain restricted type can replace a logical subject of a given proposition so as to yield another proposition. (shrink)

A term td is called a ternary deductive term for a variety of algebras V if the identity td≈r holds in V and ∈θ yields td≈td for any A∈V and any principal congruence θ on A. A connective f is called td-distributive if td)≈ f,…,td). If L is a propositional logic and V is a corresponding variety that has a TD term td, then any admissible in L rule, the premises of which contain only td-distributive operations, is derivable, and the (...) substitution r↦td is a projective L-unifier for any formula containing only td-distributive connectives. The above substitution is a generalization of the substitution introduced by T. Prucnal to prove structural completeness of the implication fragment of intuitionistic propositional logic. (shrink)

The focus of this essay is on substitute materials, particularly the research on substitute metals. The two periods of autarky in Germany were of primary influence on this field. Engineers and construction engineers proved most important in this context despite inter-institutional cooperation between the disciplines of metals research, materials testing, and technical mechanics. Engineers had to solve construction problems respecting the materials used and to analyse components in terms of economic efficiency. However, the research on substitute metals not only meant (...) the substitution of one substance for another. It also implied economizing and recycling scarce materials. These activities required tacit knowledge. Engineers succeeded to some degree but the German war economy paid a high price for it. Each technical system demanded a case-specific approach. Typically a loss of effectiveness, reliability and durability of the products containing substitutes had to be taken into account. (shrink)

In this chapter, I am going to discuss a very interesting case brought to our attention by Saul and references therein: NP-related substitution failure in simple sentences. Whereas it is well known that opacity occurs in intensional contexts and that in such contexts it is not licit to replace an NP with a co-referential one, one would not expect that substitution failure should also be exhibited by simple sentences in the context of stories about Superman. The suggested explanation of these (...) cases is to posit an embedding explicature, that is to say the insertion of structure that ipso facto creates an intensional context capable of blocking substitution. I consider various complications to this story in the light of important objections by García-Carpintero and, finally, I consider how this story fares when one applies constraints on explicatures along the lines of those proposed by Hall in an interesting paper.In general, this chapter exploits interesting considerations by Norrick on the structural similarities between stories and indirect reports. Norrick believes there are important differences, but he is inclined to concede that we could study structural similarities. An important similarity, brought out by the examples discussed by Saul, is that the narrative frame, once it is inserted into the interaction, can be left implicit and, during the act of narrating or referring to the story, one need not repeat the words ‘the story says’ or ‘we are told that…’ every time. Although implicit, these words are heard because they do some work at the structural level, as is shown by this attempt to resolve an otherwise intractable philosophical problem. The explicatures of simple sentences are perceived because they are integrated into the speakers’/hearers’ perception of the overall plan of discourse, as Haugh most interestingly notes:As Haugh and Jaszczolt note, this means that any putative “communicative intention of A is embedded within his higher-order intention”. In other words, to figure out the implicature that evidently arises here, the participants are necessarily making inferences about some kind of overall aim. According to this view, then, inferences about the intended implicature arise concomitant with inferences about the overall aim of the speaker.It follows from the considerations by Haugh that, since the explicature connected with simple sentences depends on the perception of the overall aim or plan of the conversation, it is not easily cancelled. Readers can check by themselves that the explicatures due to simple sentences cannot be cancelled, as cancelling them would involve returning to illogical discourses.. Haugh’s considerations about the overall aim of the discourse are precious in explaining how the embedding explicatures I posit are calculated once and for all for the whole stretch of the discourse framed by the narrative act. (shrink)

. The term inversion principle goes back to Lorenzen who coined it in the early 1950s. It was later used by Prawitz and others to describe the symmetric relationship between introduction and elimination inferences in natural deduction, sometimes also called harmony. In dealing with the invertibility of rules of an arbitrary atomic production system, Lorenzen’s inversion principle has a much wider range than Prawitz’s adaptation to natural deduction. It is closely related to definitional reflection, which is a principle for reasoning (...) on the basis of rule-based atomic definitions, proposed by Hallnäs and Schroeder-Heister. After presenting definitional reflection and the inversion principle, it is shown that the inversion principle can be formally derived from definitional reflection, when the latter is viewed as a principle to establish admissibility. Furthermore, the relationship between definitional reflection and the inversion principle is investigated on the background of a universalization principle, called the ω- principle, which allows one to pass from the set of all defined substitution instances of a sequent to the sequent itself. (shrink)

A unified theory is offered to account for three types of definite descriptions: with singular, plural, & mass predicates, & to provide an account for the word the in descriptions. It is noted that B. Russell's analysis ("On Denoting," Mind, 1905, 14, 479-493) failed to account for plural & mass descriptions. The proposed theory differs from Russell's only by the substitution of the notation (less than or equal to) for Russell's =. It is suggested that for every predicate G there (...) is an appropriate "part of" or "some of" relation on the extension of G. For singular predicates, (less than or equal to) becomes just the identity relation =. The predicate G is formulated as "the G" & analyzed with the formula ((schwa)x) (Gx . (Gy (includes) yy (less than or equal to) x)), which accounts for all cases of definite descriptions. It is suggested that the primary use of the is not to indicate uniqueness, but totality. C. Ornatowski. (shrink)

Prior’s puzzle is standardly taken to be the puzzle of why, given the assumption that that-clauses denote propositions, substitution of “the proposition that P” for “that P” within the complements of many propositional attitude verbs is invalid. I show that Prior’s puzzle is much more general than is ordinarily supposed. There are two variants on the substitutional form of the puzzle—a quantificational variant and a pronominal variant—and all three forms of the puzzle arise in a wide range of grammatical (...) positions, rather than merely in the complements of propositional attitude verbs. The generalized puzzle shows that a range of proposed solutions to the original puzzle fail, or are radically incomplete, and also reveals the connections between Prior’s puzzle and debates over the nature of semantic types and higher-order quantification. I go on to develop a novel, higher-order solution to the generalized form of the puzzle, and I argue that this higher-approach is superior to its first-order alternatives. (shrink)

(1) Harry believes that Twain is a writer. (2) Harry believes that Clemens is a writer. I say that this is Russellianism's most notorious consequence because it is so often used to argue against the view: many philosophers think that it is obvious that (1) and (2) can differ in truth value, and so they conclude that Russellianism is false. Let's call this the Substitution Objection to Russellianism.

Part of the standard protection of decisionally incapacitated research subjects is a prohibition against enrolling them unless surrogate decision makers authorize it. A common view is that surrogates primarily ought to make their decisions based on what the decisionally incapacitated subject would have wanted regarding research participation. However, empirical studies indicate that surrogate predictions about such preferences are not very accurate. The focus of this article is the significance of surrogate accuracy in the context of research that is not expected (...) to benefit the research subject. We identify three morally relevant asymmetries between being enrolled and not being enrolled in such non-beneficial research, and conclude that when there is a non-negligible probability that surrogates’ predictions are wrong, it will generally be better to err on the side of not authorizing enrollment. (shrink)

Williamson (2000) [Knowledge and its Limits, Oxford: Oxford University Press] argues that attempts to substitute narrow mental states or narrow/environmental composites for broad and factive mental states will result in poorer explanations of behavior. I resist Williamson.

As it is well known, in the forties of the past century, Curry proved that in any logic S closed under Modus Ponens, uniform substitution of propositional variables and the Contraction Law, the naïve Comprehension axiom trivializes S in the sense that all propositions are derivable in S plus CA. Not less known is the fact that, ever since Curry published his proof, theses and rules weaker than W have been shown to cause the same effect as W causes. Among (...) these, the Contraction rule or the Modus Ponens axiom, for example, are to be noted. But, moreover, as Brady has proved, even the Generalized Modus Ponens axiom or the Generalized Contraction rule give rise to “Curry’s Paradox” under the same circumstances as W does. In some previous work by us, “weak relevant model structures” are defined on “weak relevant matrices” by generalizing Brady’s model structure MCL built upon Meyer’s Crystal matrix CL. We have proved that wr-ms only verify logics with the “depth relevance condition”. The aim of this paper is to show how to falsify gMPa and gRW in certain wr-ms. In particular, it will be shown that gMPa is falisfied in any wr-ms and gRW in any wr-ms verifying Routley and Meyer’s basic positive logic B+. (shrink)

A Finslerian extension of general relativity is examined with particular emphasis on the Finslerian generalization of the equation of motion in a gravitational field. The construction of a gravitational Lagrangian density by substituting the osculating Riemannian metric tensor in the Einstein density is studied. Attention is drawn to an interesting possibility for developing the theory of test bodies against the Finslerian background.

In lieu of an abstract, here is a brief excerpt of the content:Justice and the General Will:Affirming Rousseau's Ancient OrientationDavid Lay WilliamsThere is much confusion about how to characterize the work of Jean-Jacques Rousseau. His thought has at various times been related to such dissimilar thinkers as Plato and Hobbes. From Plato he is said to have acquired his affinities for community and civic virtue. And one does not have to look too hard to find his praise for the great (...) sage of the Academy: "Plato only purified the heart of man."1 He was often eager to affiliate his ideas with those of antiquity. He yearned for modern society to rekindle the flames of a once-great civilization. "[W]hat keeps us [the moderns] from being men like them [the ancients]? Our prejudices, our base philosophy, and the passions of petty self-interest, concentrated together with egoism in all hearts by inept institutions in which genius never had any share."2 Despite his obvious admiration for the perceived greater ideas of the past, however, Rousseau also expressed some skepticism. James Miller has suggested that he held Plato's theory of the Forms to be unsustainable.3 Allan Bloom has likewise argued that Rousseau's "teaching is not... a revival of those of Plato.... If he admires the practice of antiquity, he does not accept the theory."4This has led many to argue that Rousseau is best understood as student of Thomas Hobbes. Roger D. Masters, for example, has suggested that "Rousseau's principles of political right can... be best described as a reformulation [End Page 383] of Hobbes' conception of the social contract."5 Arthur Melzer also argues, "The purpose of the doctrine Rousseau elaborates in the Social Contract is essentially the same [as Hobbes']."6 This view is argued on the grounds that the General Will is a positive or arbitrary standard, functioning as the primary principle of Rousseau's constructive political program. Yet the vision of Rousseau as a Hobbesian or modernist also merits skepticism. While he employs a social contract, as does Hobbes, he explicitly rejects traditional forms of positivism. "What is good and conformable to order is so by the nature of things and independently of human conventions."7 Whatever one might say about such passages, it at least raises the possibility that Rousseau is no modernist in the Straussian sense of defining Justice as human agreement.Much of what contributes to the conflicting interpretations of Rousseau can be attributed to different understandings of the relative priority and relationship of two central concepts in his writings. One of these is the well-discussed notion of the General Will. The dominant fashion is to read the General Will as a conventional substitute for natural law or transcendent Ideas. According to this reading, the General Will is grounded on nothing more than consent and functions as the first principle of all legitimate political societies. The other term central to Rousseau's program is the far less discussed but equally important concept of Justice. Little has been written on his understanding of Justice and, for that matter, he himself rarely discussed it explicitly. But it, too, could also be considered a primary principle. While it would be foolish to dismiss the importance of the General Will to Rousseau, it would be equally problematic to explore it independently of his Idea of Justice. The question in understanding his work is which of these two principles—the General Will or Justice—is primary or fundamental. If it is the General Will, a case can be made that the Straussians are right, and Rousseau is a positivist. If Justice is prior, on the other hand, then there is reason to believe that he was something much different.I argue that the positivist reading of Rousseau is flawed. Indeed, my thesis is that he is among the greatest and most thorough Platonists of the modern era.8 His rejection of Hobbes is not merely rhetorical. In fact, it represents the [End Page 384] true impetus of his social contract. This contract is designed explicitly to counter Hobbesian positivism. In the same way that Plato responds to Protagoras' positivism with his theory of the Forms, Rousseau responds to Hobbes... (shrink)

From 1905–1908 onward, Russell thought that his new ‘substitutional theory’ provided him with the right framework to resolve the set-theoretic paradoxes. Even if he did not finally retain this resolution, the substitutional strategy was instrumental in the development of his thought. The aim of this paper is not historical, however. It is to show that Russell's substitutional insight can shed new light on current issues in philosophy of mathematics. After having briefly expounded Russell's key notion of a (...) ‘structured variable’, I connect it to two ongoing discussions: the Caesar problem, and absolute generality. (shrink)

Prawitz conjectured that the proof-theoretically valid logic is intuitionistic logic. Recent work on proof-theoretic validity has disproven this. In fact, it has been shown that proof-theoretic validity is not even closed under substitution. In this paper, we make a minor modification to the definition of proof-theoretic validity found in Prawitz’s 1973paper ‘Towards a foundation of a general proof theory’ and refined by Schroeder-Heister in ‘Validity concepts in proof-theoretic semantics’ (2006). We will call the new notion generalized proof-theoretic validity and show (...) that the logic of generalized proof-theoretic validity is intuitionistic logic. (shrink)