Minimalism about truth is one of the main contenders for our best theory of truth, but minimalists face the charge of being unable to properly state their theory. Donald Davidson incisively pointed out that minimalists must generalize over occurrences of the same expression placed in two different contexts, which is futile. In order to meet the challenge, Paul Horwich argues that one can nevertheless characterize the axioms of the minimalist theory. Sten Lindström and Tim Button have independently argued that (...) Horwich’s attempt to formulate minimalism remains unsuccessful. We show how to properly state Horwich’s axioms by appealing to propositional functions that are given by definite descriptions. Both Lindström and Button discuss proposals similar to ours and conclude that they are unsuccessful. Our new suggestion avoids these objections. (shrink)

In this article, I discuss parthood status in mereologi- cally interpreted Daoist metaphysics, based on the Daodejing. I depart from the dao and you interrela- tion, which mereologically overlap by sharing parts. I consider the case of a complete overlap, which (a) challenges proper parthood, according to which a part cannot be identical with the whole that it com- poses, and (b) entails the question of identity that, while complying with classical mereology, cannot be consis- tent with Daoist metaphysics. (...) The discussion leads to abandoning proper parthood and antisymmetry axiom from classical axiomatics. It also shows a plausible fur- ther direction for mereological reconstruction. (shrink)

The basic axioms or formal conditions of decision theory, especially the ordering condition put on preferences and the axioms underlying the expected utility formula, are subject to a number of counter-examples, some of which can be endowed with normative value and thus fall within the ambit of a philosophical reflection on practical rationality. Against such counter-examples, a defensive strategy has been developed which consists in redescribing the outcomes of the available options in such a way that the threatened (...) axioms or conditions continue to hold. We examine how this strategy performs in three major cases: Sen's counterexamples to the binariness property of preferences, the Allais paradox of EU theory under risk, and the Ellsberg paradox of EU theory under uncertainty. We find that the strategy typically proves to be lacking in several major respects, suffering from logical triviality, incompleteness, and theoretical insularity. To give the strategy more structure, philosophers have developed “principles of individuation”; but we observe that these do not address the aforementioned defects. Instead, we propose the method of checking whether the strategy can overcome its typical defects once it is given a proper theoretical expansion. We find that the strategy passes the test imperfectly in Sen's case and not at all in Allais's. In Ellsberg's case, however, it comes close to meeting our requirement. But even the analysis of this more promising application suggests that the strategy ought to address the decision problem as a whole, rather than just the outcomes, and that it should extend its revision process to the very statements it is meant to protect. Thus, by and large, the same cautionary tale against redescription practices runs through the analysis of all three cases. A more general lesson, simply put, is that there is no easy way out from the paradoxes of decision theory. (shrink)

The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity in set (...) theory. Thus, the pair of arithmetic and set are to be similar to Euclidean and non-Euclidean geometries distinguishably only by the Fifth postulate now, i.e. after replacing it and its negation correspondingly by the axiom of finiteness (induction) versus that of finiteness being idempotent negations to each other. Indeed, the axiom of choice, as far as it is equivalent to the well-ordering “theorem”, transforms any set in a well-ordering either necessarily finite according to the axiom of induction or also optionally infinite according to the axiom of infinity. So, the Gödel incompleteness statement relies on the logical contradiction of the axiom of induction and the axiom of infinity in the final analysis. Nonetheless, both can be considered as two idempotent versions of the same axiom (analogically to the Fifth postulate) and then unified after logicism and its inherent intensionality since the opposition of finiteness and infinity can be only extensional (i.e., relevant to the elements of any set rather than to the set by itself or its characteristic property being a proposition). So, the pathway for interpreting the Gödel incompleteness statement as an axiom and the originating from that assumption for “Hilbert mathematics” accepting its negation is pioneered. A much wider context relevant to realizing the Gödel incompleteness statement as a metamathematical axiom is consistently built step by step. The horizon of Hilbert mathematics is the proper subject in the third part of the paper, and a reinterpretation of Gödel’s papers (1930; 1931) as an apology of logicism as the only consistent foundations of mathematics is the topic of the next second part. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation needs philosophical (...) means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. A comparison to Mach’s doctrine is used to be revealed the fundamental and philosophical reductionism of Husserl’s phenomenology leading to a kind of Pythagoreanism in the final analysis. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. Thus the problem which of the two mathematics is more relevant to our being is discussed. An information interpretation of the Schrödinger equation is involved to illustrate the above problem. (shrink)

In Popper's Logik der Forschung, a theoretical system is a set of sentences that describe a particular sub-area of science, in particular of empirical science. The goal of axiomatizing a theoretical system is to specify a small number of "axioms" describing all presuppositions of the sub-area under consideration, so that all other sentences of this system can be derived from them by means of logical or mathematical transformations. The paper discusses two philosophical interpretations of these proper axioms. (...) First, proper axioms stipulate the use of the signs for the basic concepts of the system. Consequently, the proper axioms turn out to be analytic relative to a class of interpretations of the underlying logic. Hence, they cannot be falsified by refuting their logical consequences because these consequences are analytic as well. Secondly, proper axioms are synthetic, falsifiable and uncertain sentences. Hence, they are not immunized against falsification by refuting their logical consequences. (shrink)

Standard approaches to proper names, based on Kripke's views, hold that the semantic values of expressions are (set-theoretic) functions from possible worlds to extensions and that names are rigid designators, i.e.\ that their values are \emph{constant} functions from worlds to entities. The difficulties with these approaches are well-known and in this paper we develop an alternative. Based on earlier work on a higher order logic that is \emph{truly intensional} in the sense that it does not validate the axiom scheme (...) of Extensionality, we develop a simple theory of names in which Kripke's intuitions concerning rigidity are accounted for, but the more unpalatable consequences of standard implementations of his theory are avoided. The logic uses Frege's distinction between sense and reference and while it accepts the rigidity of names it rejects the view that names have direct reference. Names have constant denotations across possible worlds, but the semantic value of a name is not determined by its denotation. (shrink)

This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is (...) the study of groups of operations. In place of the established view I offer a revised view, according to which Poincaré held that axioms in geometry are in fact assertions about invariants of groups. Groups, as forms of the understanding, are prior in conception to the objects of geometry and afford the proper definition of those objects, according to Poincaré. Poincaré’s view therefore contrasts sharply with Kant’s foundation of geometry in a unique form of sensibility. According to my interpretation, axioms are not definitions in disguise because they themselves implicitly define their terms, but rather because they disguise the definitions which imply them. (shrink)

I defend a weak version of the Pigou-Dalton principle for chances. The principle says that it is better to increase the survival chance of a person who is more likely to die rather than a person who is less likely to die, assuming that the two people do not differ in any other morally relevant respect. The principle justifies plausible moral judgements that standard ex post views, such as prioritarianism and rank-dependent egalitarianism, cannot accommodate. However, the principle can be justified (...) by the same reasoning that has recently been used to defend the core axiom of ex post prioritarianism and egalitarianism, namely, Pigou-Dalton for well-being. The arguably biggest challenge for proponents of Pigou-Dalton for chances is that it violates State Dominance for social prospects. However, I argue that we have independent reason for rejecting State Dominance for social prospects, since it prevents a social planner from properly respecting people's preferences. (shrink)

In his Posterior Analytics Aristotle confronted a problem that threatened his vision of scientific knowledge as an axiomatic system: if scientific knowledge is demonstrative in character, and if the axioms of a science cannot themselves be demonstrated, then the most basic of all scientific principles will remain unknown. In the famous concluding chapter of this work (II 19), he claimed to solve this problem by distinguishing two kinds of knowledge: we cannot have epistêmê of the first principles, but we (...) can have nous of them. This ‘solution’ has struck many students of his thought as hopelessly ad hoc and unpersuasive. And nowhere is Aristotle less persuasive than when he appeals to a faculty of intuition or a priori insight which arrives on the scene precisely when it is most needed. I defend Aristotle’s account by showing how nous is not properly characterized as a faculty of intuition which operates independently of sense experience. Rather, nous is a kind of knowledge that is available to us whenever our mind advances from the perception of particular individuals to grasp the relevant universal concept or general principle. (shrink)

Pettigrew offers new axiomatic constraints on legitimate measures of inaccuracy. His axiom called ‘Decomposition’ stipulates that legitimate measures of inaccuracy evaluate a credence function in part based on its level of calibration at a world. I argue that if calibration is valuable, as Pettigrew claims, then this fact is an explanandum for accuracy-rst epistemologists, not an explanans, for three reasons. First, the intuitive case for the importance of calibration isn’t as strong as Pettigrew believes. Second, calibration is a perniciously global (...) property that both contravenes Pettigrew’s own views about the nature of credence functions themselves and undercuts the achievements and ambitions of accuracy-rst epistemology. Finally, Decomposition introduces a new kind of value compatible with but separate from accuracy-proper in violation of Pettigrew’s alethic monism. introduction. (shrink)

There are at least three vaguely atomistic principles that have come up in the literature, two explicitly and one implicitly. First, standard atomism is the claim that everything is composed of atoms, and is very often how atomism is characterized in the literature. Second, superatomism is the claim that parthood is well-founded, which implies that every proper parthood chain terminates, and has been discussed as a stronger alternative to standard atomism. Third, there is a principle that lies between these (...) two theses in terms of its relative strength: strong atomism, the claim that every maximal proper parthood chain terminates. Although strong atomism is equivalent to superatomism in classical extensional mereology, it is strictly weaker than it in strictly weaker systems in which parthood is a partial order. And it is strictly stronger than standard atomism in classical extensional mereology and, given the axiom of choice, in such strictly weaker systems as well. Though strong atomism has not, to my knowledge, been explicitly identified, Shiver appears to have it in mind, though it is unclear whether he recognizes that it is not equivalent to standard atomism in each of the mereologies he considers. I prove these logical relationships which hold amongst these three atomistic principles, and argue that, whether one adopts classical extensional mereology or a system strictly weaker than it in which parthood is a partial order, standard atomism is a more defensible addition to one’s mereology than either of the other two principles, and it should be regarded as the best formulation of the atomistic thesis. (shrink)

With regards to the inefficiencies and uncompromising situations within the humanities and social sciences field in Iran, the challenge of problematizing these sciences is inevitable. So far, numerous research analyzing humanities and social sciences’ problems in the Iranian academic system have been published. Considering the important role of humanities and social sciences in the modern Iranian society, we attempt to suggest a theoretical framework for the problematization of humanities and social sciences in Iran. The exploration of the main challenges facing (...) humanities and social sciences in Iran from the community, academy and administration point of view, sparks three hypotheses. First, humanities and social sciences’ theories and teachings are not applied accurately. Second, the humanities and social sciences’ schools of thought are not chosen properly according to Iranian circumstances. And third, there are metaphysical differences between axioms and presupposition of humanities and social sciences having western origins and those with Islamic-Iranian culture. (shrink)

Overall, it is first rate with accurate, sensitive and penetrating accounts of his life and thought in roughly chronological order, but, inevitably (ie, like everyone else) it fails, in my view, to place his work in proper context and gets some critical points wrong. It is not made clear that philosophy is armchair psychology and that W was a pioneer in what later became cognitive or evolutionary psychology. One would not surmise from this book that he laid out the (...) foundations of the modern concept of intentionality (roughly, personality or higher order thought) which has been further advanced by many (most notably in philosophy by John Searle in “The Construction of Social Reality” and “Rationality in Action”). There is no clear explanation of how W defined the class of potential actions, which he called dispositions or inclinations, (now often called propositional attitudes), differentiating them from perceptions, memories and actions and showing how they lack truth value. He notes that W spent much of his time discussing the foundations of mathematics but fails to provide any explanation as to how this relates to his work on language and logic. In fact, as W came to realize, they are all names for groups of functions of our innate psychology with many differences and none are dependent on the others. It is not really made clear that all our behavior depends on the unquestionable axioms of our evolved psychology and thus differs totally from the testable empirical facts which they enable us to discover. It is not explained that W’s frequent references to “grammar” and to “language games” refer to our innate psychology. All these failings are the norm in behavioral studies. -/- He notes that W described thinking and other dispositions or inclinations (W’s terms)-- (ie, judging, feeling, remembering, believing etc)-- as behaviors and not as mental activities but I don’t see that he really makes it clear that another pioneering discovery of W’s was that dispositions describe public actions and cannot be mental phenomena for the same reason that he so famously rejected the possibility of a private language. -/- He repeatedly and correctly notes (eg, p176) that the core of W’s work is the nature of language but (again the universal failing) does not make it clear that language is for humans (as opposed to animals) almost coextensive with thought (public behavior as W insisted) and thus with our evolved psychology. Like most people, philosophers or not, Kanterian has not followed W and taken the final step towards understanding and describing behavior from an evolutionary standpoint, the only viewpoint that makes sense of it, or indeed of anything. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

The discussion of the Principle of Non-Contradiction (PNC) in Aristotle’s Metaphysics Γ is usually taken to include three ‘versions’ of the principle: an ontological, psychological, and logical one. In this article I develop an interpretation of Metaphysics Γ3 and a parallel text, De interpretatione 14, in order to show that these texts are concerned with two related but different principles: a version of the Principle of Identity, and a corollary to this, which concerns the ability to accept two ‘opposite’ items (...) at the same time. I argue that these principles must be considered separately in order to properly understand Aristotle’s remarks about PNC in Metaphysics Γ, and in order to defend his approach in these remarks against certain objections raised against the discussion in Metaphysics Γ by Jan Łukasiewicz in his "Über den Satz des Widerspruchs bei Aristoteles". The main result of my interpretation is to distinguish in the discussion of PNC in Metaphysics Γ three principles: one concerning linguistic items (words and statements), one concerning thoughts (δόξαι), and one concerning objects or states of affairs. (shrink)

Overall, it is first rate with accurate, sensitive and penetrating accounts of his life and thought in roughly chronological order, but, inevitably (i.e., like everyone else) it fails, in my view, to place his work in proper context and gets some critical points wrong. It is not made clear that philosophy is armchair psychology and that W was a pioneer in what later became cognitive or evolutionary psychology. One would not surmise from this book that he laid out the (...) foundations of the modern concept of intentionality (roughly, personality or higher order thought) which has been further advanced by many (most notably in philosophy by John Searle in “The Construction of Social Reality” and “Rationality in Action”). -/- There is no clear explanation of how W defined the class of potential actions, which he called dispositions or inclinations, (now often called propositional attitudes), differentiating them from perceptions, memories and actions and showing how they lack truth value. He notes that W spent much of his time discussing the foundations of mathematics but fails to provide any explanation as to how this relates to his work on language and logic. In fact, as W came to realize, they are all names for groups of functions of our innate psychology with many differences and none are dependent on the others. It is not really made clear that all our behavior depends on the unquestionable axioms of our evolved psychology and thus differs totally from the testable empirical facts which they enable us to discover. It is not explained that W’s frequent references to “grammar” and to “language games” refer to our innate psychology. All these failings are the norm in behavioral studies. -/- He notes that W described thinking and other dispositions or inclinations (W’s terms) -- (i.e., judging, feeling, remembering, believing etc.) -- as behaviors and not as mental activities but I don’t see that he really makes it clear that another pioneering discovery of W’s was that dispositions describe public actions and cannot be mental phenomena for the same reason that he so famously rejected the possibility of a private language. -/- He repeatedly and correctly notes (e.g., p176) that the core of W’s work is the nature of language but (again the universal failing) does not make it clear that language is for humans (as opposed to animals) almost coextensive with thought (public behavior as W insisted) and thus with our evolved psychology. Like most people, philosophers or not, Kanterian has not followed W and taken the final step towards understanding and describing behavior from an evolutionary standpoint, the only viewpoint that makes sense of it, or indeed of anything. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019) . (shrink)

This paper looks at the nature of normal-proper functions and the role they play in theories of representational content. More specifically: I lay down two desiderata for a theory which tries to capture what's distinctive of normal-proper functions and discuss two prominent theories which claim to satisfy them. I discuss the advantages of having normal-proper functions ground a theory of representational content. And, I look at both orthodox and heterodox versions of such theories.

This paper analyses the hidden use of new axioms in set-theoretic practice with a focus on large cardinal axioms and presents a general overview of set-theoretic practices using large cardinal axioms. The hidden use of a new axiom provides extrinsic reasons in support of this axiom via the idea of verifiable consequences, which is especially relevant for set-theoretic practitioners with an absolutist view. Besides that, the hidden use has pragmatic significance for further important sub-groups of the set-theoretic (...) community---set-theoretic practitioners with a pluralist view and set-theoretic practitioners who aim for ZFC-proofs. By describing this, the paper gives a more complete picture of new axioms in set-theoretic practice. These observations, for instance, show that set-theoretic practitioners interested in ZFC-proofs use tools that go beyond ZFC. The analysis is based on empirical data that was collected in an extensive interview study with set-theoretic practitioners. (shrink)

There is a fairly general consensus that names are Millian (or Russellian) genuine terms, that is, are singular terms whose sole semantic function is to introduce a referent into the propositions expressed by sentences containing the term. This answers the question as to what sort of proposition is expressed by use of sentences containing names. But there is a second serious semantic problem about proper names, that of how the referents of proper names are determined. This is the (...) question that I will discuss in this paper. Various views consistent with Millianism have been proposed as to how the semantic referents of proper names are determined. These views can be classified into (1) description theories and (2) causal theories, but they can also be classified into (3) social practice theories, on which a name’s referent is determined by a social practice involving the referent, and (4) individualistic theories, on which the referent of the use of a name is determined by the speaker’s state of mind. Here I argue against social practice theories of the sorts proposed by Kripke and Evans and in favor of an individualistic approach to name reference. I argue that social practice is irrelevant to determining name reference and that, as a consequence, names have no meanings in natural languages. In the second part of the paper I motivate and propose a new form of individualistic theory which incorporates features of both description theories and Evans’s social practice theory. (shrink)

Fictional names present unique challenges for semantic theories of proper names, challenges strong enough to warrant an account of names different from the standard treatment. The theory developed in this paper is motivated by a puzzle that depends on four assumptions: our intuitive assessment of the truth values of certain sentences, the most straightforward treatment of their syntactic structure, semantic compositionality, and metaphysical scruples strong enough to rule out fictional entities, at least. It is shown that these four assumptions, (...) taken together, are inconsistent with referentialism, the common view that names are uniformly associated with ordinary individuals as their semantic value. Instead, the view presented here interprets names as context-sensitive expressions, associated in a context of utterance with a particular act of introduction, or dubbing, which is then used to determine their semantic value. Some dubbings are referential, which associate names with ordinary individuals as their semantic values; others are fictional, which associate names, instead, with sets of properties. Since the semantic values of names can be of different sorts, the semantic rule interpreting predication must be complex as well. In the body of the paper, I show how this new treatment of names allows us to solve our original puzzle. I defend the complexity of the semantic predication rule, and address additional worries about ontological commitment. (shrink)

Proper functionalism explicates epistemic warrant in terms of the function and normal functioning of the belief-forming process. There are two standard substantive views of the sources of functions in the literature in epistemology: God (intelligent design) or Mother Nature (evolution by natural selection). Both appear to confront the Swampman objection: couldn’t there be a mind with warranted beliefs neither designed by God nor the product of evolution by natural selection? Is there another substantive view that avoids the Swampman objection? (...) There are two. The first is the generalized selected-effects theory of functions. The second is the organizational theory of functions. Both, however, require some history to assign functions, for both are etiological theories of functions: past effects help explain current function. Swampman can then acquire functions, perhaps soon after creation, though he has none at the moment of inception. (shrink)

This is review essay of Mark Sainsbury's Reference without Referents. Its main part is a critical discussion of Sainsbury's proposal for the individuation of proper name using practices.

Although the concept of uncertainty is as old as Epicurus’s writings, and an excellent quantitative theory, with entropy as the measure of uncertainty having been developed in recent times, there has been little exploration of the qualitative theory. The purpose of the present paper is to give a qualitative axiomatization of uncertainty, in the spirit of the many studies of qualitative comparative probability. The qualitative axioms are fundamentally about the uncertainty of a partition of the probability space of events. (...) Of course, it is common to speak of the uncertainty, or randomness, of a random variable, but only the partition defined by the values of the random variable enter into the definition of uncertainty, not the actual values. It is straightforward to add axioms for decision making following the general line of Savage from the 1950s. Indeed, in the spirit of Epicurus, it is really our intuitive feeling about the uncertainty of the future that motivates much of our thinking about decisions. Here, the distinction between the concepts of probability and uncertainty can be made by citing many familiar examples. Without spelling out the technical details, the axiomatization of qualitative probability with uncertainty as the most important primitive concept, it is possible to raise a different kind of question about bounded rationality. This new question is whether or not one should bound the uncertainty in thinking and investigating any detailed framework of decision making. Discussion of this point is certainly different from the question of bounding rationality by not maximizing expected utility. In practice, we naturally bound uncertainty in our analysis of decision-making problems. As in the case of formulating an alternative for maximizing expected utility, so is the case of rational alternatives to maximizing uncertainty. There are several issues to consider. In the spirit of my other work in qualitative probability, I explore alternatives rather than attempt to give a definitive argument for one single solution. (shrink)

In this paper, I develop and motivate a novel formulation of the safety condition in terms of etiological proper function. After testing this condition against the most pressing objections to safety-theoretic accounts of knowledge in the literature, my conclusion will be the following: once safety is suitably understood in terms of etiological proper function, it stands a better chance as the right anti-Gettier condition on knowledge.

Spinoza's causal axiom is at the foundation of the Ethics. I motivate, develop and defend a new interpretation that I call the ‘causally restricted interpretation’. This interpretation solves several longstanding puzzles and helps us better understand Spinoza's arguments for some of his most famous doctrines, including his parallelism doctrine and his theory of sense perception. It also undermines a widespread view about the relationship between the three fundamental, undefined notions in Spinoza's metaphysics: causation, conception and inherence.

The question of transtemporal identity of objects in general and persons in particular is an important issue in both philosophy and psychology. While the focus of philosophers traditionally was on questions of the nature of identity relation and criteria that allow to settle ontological issues about identity, psychologists are mostly concerned with how people think about identity, and how they track identity of objects and people through time. In this article, we critically engage with widespread use of inferring folk judgments (...) of identity from study participants’ use of proper names in response to experimental vignettes. We provide reasons to doubt that using this method one can reliably infer judgments of numerical identity over time and transformations. We also critically examine allegedly-Kripkean justification of this method and find it lacking. Merely assuming that names are rigid designators will not help. A study participant’s use of proper names can be taken to track the participant’s identity judgments only if supported by the participant’s belief that names used in the scenario are used rigidly. (shrink)

Axiom weakening is a technique that allows for a fine-grained repair of inconsistent ontologies. Its main advantage is that it repairs on- tologies by making axioms less restrictive rather than by deleting them, employing the use of refinement operators. In this paper, we build on pre- viously introduced axiom weakening for ALC, and make it much more irresistible by extending its definitions to deal with SROIQ, the expressive and decidable description logic underlying OWL 2 DL. We extend the definitions (...) of refinement operator to deal with SROIQ constructs, in particular with role hierarchies, cardinality constraints and nominals, and illustrate its application. Finally, we discuss the problem of termi- nation of an iterated weakening procedure. (shrink)

In this paper, I argue that what counts as the proper function of a trait is a matter of the de facto perspective that the biological system, itself, possesses on what counts as proper functioning for that trait. Unlike non-perspectival accounts, internal perspectivalism does not succumb to generality problems. But unlike external perspectivalism, internal perspectivalism can provide a fully naturalistic, mind-independent grounding of proper function and natural norms. The attribution of perspectives to biological systems is intended to (...) be neither metaphorical nor anthropomorphic: I do not mean to imply that such systems thereby must possess agency, cognition, intentions, concepts, or mental or psychological states. Instead, such systems provide the grounding for norms of performance when they internally enforce their own standard of (i.e., their own perspective on) what constitutes proper functioning or malfunctioning. By operating with a fixed, determinate level of generality, such systems provide the basis for an account of proper function that is immune to generality problems. (shrink)

"Modern History" versions of the etiological theory claim that in order for a trait X to have the proper function F, individuals with X must have been recently favored by natural selection for doing F (Godfrey-Smith 1994; Griffiths 1992, 1993). For many traits with prototypical proper functions, however, such recent selection may not have occurred: traits may have been maintained due to lack of variation or due to selection for other effects. I examine this flaw in Modern History (...) accounts and offer an alternative etiological theory, the Continuing Usefulness account, which appears to avoid such problems. (shrink)

Therapists and related theorists and practitioners of mental health tend to hold one of two broad views about how to help patients. On the one hand, some maintain that, or at least act as though, the basic point of therapy is to help patients become clear about what they want deep down and to enable them to achieve it by overcoming mental blockages. On the other hand, there are those who contend that the aim of therapy should instead be to (...) psychologically enable patients to live objectively desirable lives, say, ones that involve developing their inherent talents or exhibiting an authentic/strong/integrated self. In this chapter, I argue that neither of these prominent approaches is complete. Contra the former, sometimes what patients want deep down is not something to promote, and, against the latter, it can sometimes be reasonable for patients to want to sacrifice their own objective interests and for therapists to assist them in this regard. I argue that the category of meaningfulness does well at accounting for these counterexamples to the two dominant approaches, while capturing the kernels of truth in them. The proper aim of therapy, I suggest, is to enable patients to live meaningfully. (shrink)

Alvin Plantinga’s Warrant and Proper Function gives two major definitions of warrant. One states that reliable cognitive faculties aimed at true belief and functioning properly in the right environment are necessary and sufficient for warrant; the other definition only states that they are necessary. The latter definition is the more important one. There are different kinds of knowledge, and justification is necessary for some beliefs to be warranted. Even a belief warranted by proper function can receive a higher (...) degree of warrant by justification. This implies that natural theology has a useful role within the contours of a Plantingian epistemology. (Please note that the pagination here does not match the pagination in the published edition.). (shrink)

Crucially, blame can be addressed to its targets, as an implicit demand for recognition. But when we ask whether offenders would actually appreciate this demand, via a sound deliberative route from their existing motivations, we face a puzzle. If they would, their offense reflects a deliberative mistake, and blame’s hostility seems unnecessary. If they wouldn’t, addressing them is futile, and blame’s emotional engagement seems unwarranted. To resolve this puzzle, I develop an account of blame as a proleptic response to indeterminacy (...) in its target’s reasons, yielding attractive accounts of blame’s relation both to internal reasons claims and to free will. (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness (...) and a four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagora’s theorem. We conclude with a Representation Theorem relating models of our system that satisfy second order continuity to the mathematical structure called ‘Minkowski spacetime’ in physics textbooks. (shrink)

Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: (...) the parallel postulate. -/- Euclid’s axioms are general principles of magnitude: they concern geometric magnitudes and magnitudes of other kinds as well even numbers. The first is often translated “Things that equal the same thing equal one another”. -/- There are other differences that are or might become important. -/- Aristotle [fl. 350 BCE] meticulously separated his basic principles [archai, singular archê] according to subject matter: geometrical, arithmetic, astronomical, etc. However, he made no distinction that can be assimilated to Euclid’s postulate/axiom distinction. -/- Today we divide basic principles into non-logical [topic-specific] and logical [topic-neutral] but this too is not the same as Euclid’s. In this regard it is important to be cognizant of the difference between equality and identity—a distinction often crudely ignored by modern logicians. Tarski is a rare exception. The four angles of a rectangle are equal to—not identical to—one another; the size of one angle of a rectangle is identical to the size of any other of its angles. No two angles are identical to each other. -/- The sentence ‘Things that equal the same thing equal one another’ contains no occurrence of the word ‘magnitude’. This paper considers the problem of formalizing the proposition Euclid intended as a principle of magnitudes while being faithful to the logical form and to its information content. (shrink)

Kant has a number of harsh-sounding things to say about beggars and giving to beggars. He describes begging as “closely akin to robbery”, and says that it exhibits self-contempt. In this paper I argue that on a particular interpretation of his political philosophy his critique of giving to beggars can be seen as part of a concern with social justice, and that his analysis makes sense of some troubling aspects of the phenomenology of being confronted with beggars. On Kant's view, (...) without absolute poverty relief, the poor persons' external freedom is subject to the arbitrary choices of those who have means. But the legitimacy of the state is based on ensuring that no one's basic freedom is subject to the arbitrary choices of another. This means that in a legitimate state public structures must ensure that there is unconditional poverty relief. Having your basic needs met through private charity wrongs you. Kant's analysis is that when you encounter someone in a public space who asks you for money to meet their basic survival needs, you are being asked to solve a public problem in a private interaction, and there is no rightful way for you to do this. (shrink)

The Hyperuniverse Programme, introduced in Arrigoni and Friedman (2013), fosters the search for new set-theoretic axioms. In this paper, we present the procedure envisaged by the programme to find new axioms and the conceptual framework behind it. The procedure comes in several steps. Intrinsically motivated axioms are those statements which are suggested by the standard concept of set, i.e. the `maximal iterative concept', and the programme identi fies higher-order statements motivated by the maximal iterative concept. The satisfaction (...) of these statements (H-axioms) in countable transitive models, the collection of which constitutes the `hyperuniverse' (H), has remarkable 1st-order consequences, some of which we review in section 5. (shrink)

In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides (...) the Weyl’s system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics. (shrink)

In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum statistical mechanics, where it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms that (...) guarantee that every state can be diagonalized. The first axiom is Causality, which ensures that the marginal of a bipartite state is well defined. Then, Purity Preservation states that the set of pure transformations is closed under composition. The third axiom is Purification, which allows to assign a pure state to the composition of a system with its environment. Finally, we introduce the axiom of Pure Sharpness, stating that for every system there exists at least one pure effect occurring with unit probability on some state. For theories satisfying our four axioms, we show a constructive algorithm for diagonalizing every given state. The diagonalization result allows us to formulate a majorization criterion that captures the convertibility of states in the operational resource theory of purity, where random reversible transformations are regarded as free operations. (shrink)

Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular (...) ways) face complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology. (shrink)

Evolutionary biology is a field currently animated by much discussion concerning its conceptual foundations. On the one hand, we have supporters of a classical view of evolutionary theory, whose backbone is provided by population genetics and the so-called Modern Synthesis (MS). On the other hand, a number of researchers are calling for an Extended Synthe- sis (ES) that takes seriously both the limitations of the MS (such as its inability to incorporate developmental biology) and recent empirical and theoretical research on (...) issues such as evolvability, modularity, and self-organization. In this article, I engage in an in-depth commentary of an influential paper by population geneticist Michael Lynch, which I take to be the best defense of the MS-population genetics position published so far. I show why I think that Lynch’s arguments are wanting and propose a modification of evolutionary theory that retains but greatly expands on population genetics. (shrink)

Ontology engineering is a hard and error-prone task, in which small changes may lead to errors, or even produce an inconsistent ontology. As ontologies grow in size, the need for automated methods for repairing inconsistencies while preserving as much of the original knowledge as possible increases. Most previous approaches to this task are based on removing a few axioms from the ontology to regain consistency. We propose a new method based on weakening these axioms to make them less (...) restrictive, employing the use of refinement operators. We introduce the theoretical framework for weakening DL ontologies, propose algorithms to repair ontologies based on the framework, and provide an analysis of the computational complexity. Through an empirical analysis made over real-life ontologies, we show that our approach preserves significantly more of the original knowledge of the ontology than removing axioms. (shrink)

The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper, I argue that whether or not large cardinal axioms count as maximality principles depends on prior commitments concerning the richness of the subset forming operation. In particular I argue that there is a conception of maximality through absoluteness, on which large cardinal (...) axioms are restrictive. I argue, however, that large cardinals are still important axioms of set theory and can play many of their usual foundational roles. (shrink)

According to proper functionalist theories of warrant, a belief is warranted only if it is formed by cognitive faculties that are properly functioning according to a good, truth-aimed design plan, one that is often thought to be specified either by intentional design or by natural selection. A formidable challenge to proper functionalist theories is the Swampman objection, according to which there are scenarios involving creatures who have warranted beliefs but whose cognitive faculties are not properly functioning, or are (...) poorly designed, or are not aimed at truth. In this paper, we draw lessons from cognitive science in order to develop a novel argument for the conclusion that the Swampman objection fails against proper functionalist theories of warrant. Our argument not only shows that the underlying, central intuition motivating Swampman-like scenarios is false but also motivates proper function as a necessary condition for warrant, thereby lending support to the claim that any theory of knowledge that lacks a proper function requirement is false. (shrink)

Philosophy &Public Affairs, Volume 52, Issue 1, Page 69-100, Winter 2024.