It is a striking fact from reverse mathematics that almost all theorems of countable and countably representable mathematics are equivalent to just five subsystems of second order arithmetic. The standard view is that the significance of these equivalences lies in the set existence principles that are necessary and sufficient to prove those theorems. In this article I analyse the role of set existence principles in reverse mathematics, and argue that they are best understood as closure conditions on the powerset of the natural numbers.
This article follows on the introductory article “Direct Logic for Intelligent Applications” [Hewitt 2017a]. Strong Types enable new mathematical theorems to be proved including the Formal Consistency of Mathematics. Also, Strong Types are extremely important in Direct Logic because they block all known paradoxes[Cantini and Bruni 2017]. Blocking known paradoxes makes Direct Logic safer for use in Intelligent Applications by preventing security holes.
Adverbialist theories of thought such as those advanced by Hare (1969) and Sellars (1969) promise an ontologically sleek understanding of a variety of intentional states, but such theories have been largely abandoned due to the ‘many-property problem’. In an attempt to revitalize this otherwise attractive theory, in a series of papers as well as his recent book, Uriah Kriegel has offered a novel reply to the ‘many-property problem’ and on its basis he argues that ‘adverbialism about intentionality is alive and well’. If true, Kriegel will have shown that the logical landscape has long been unnecessarily constrained. His key idea is that the many-property problem can be overcome by appreciating that mental states stand in the determinable-determinate relation to one another. The present paper shows that this relation can’t save adverbialism because it would require thinkers to think more thoughts than they need be thinking.
Weak supplementation says that if x is a proper part of y, then y has a proper part that doesn’t overlap x. Suppose that we are impressed by standard counterexamples to weak supplementation like the following. …
Giacomo (Jacopo) Zabarella (b. 1533 in Padua, d. 1589 in Padua) is
considered the prime representative of Renaissance Italian
Aristotelianism. Known most of all for his writings on logic and
methodology, Zabarella was an alumnus of the University of Padua,
where he received his Ph.D. in philosophy. Throughout his teaching
career at his native university, he also taught philosophy of nature
and science of the soul (De anima). Among his main works are
the collected logical works Opera logica (1578) and writings
on natural philosophy, De rebus naturalibus (1590). Zabarella
was an orthodox Aristotelian seeking to defend the scientific status
of theoretical natural philosophy against the pressures emanating from
the practical disciplines, i.e., the art of medicine and anatomy.
I will begin by reviewing three classic points in philosophy of mind. Point 1 is that there is a theory, which I will call here ‘the reflexive theory’ or ‘RT’ for short, according to which a (psychological) state is a conscious state of a subject only if the subject of the state is conscious of being in the state. Since ‘is conscious of’ is a rough synonym of ‘is aware of’, we may also say that, according to RT, a psychological state is a conscious state of a subject only if the subject of the state is aware of being in the state. Point 2 is that RT faces a regress objection; that is, it is apparently committed to an infinite regress of a problematic sort. The objection might be formulated this way. First Premise: if RT is true, then, if you instantiate one conscious state you instantiate an infinity of conscious states. Second Premise: you do not instantiate an infinity of conscious states. Conclusion: either RT is false or you never instantiate a conscious state—a disaster for a theory of consciousness!
Humean accounts of natural lawhood (such as Lewis’s) have often been criticized as unable to account for the laws’ characteristic explanatory power in science. Loewer (Philos Stud 160:115–137, 2012) has replied that these criticisms fail to distinguish grounding explanations from scientific explanations. Lange (Philos Stud 164:255–261, 2013) has replied by arguing that grounding explanations and scientific explanations are linked by a transitivity principle, which can be used to argue that Humean accounts of natural law violate the prohibition on self-explanation. Lange’s argument has been sharply criticized by Hicks and van Elswyk (Philos Stud 172:433– 443, 2015), Marshall (Philos Stud 172:3145–3165, 2015), and Miller (Philos Stud 172:1311–1332, 2015). This paper shows how Lange’s argument can withstand these criticisms once the transitivity principle and the prohibition on self-explanation are properly refined. The transitivity principle should be refined to accommodate contrasts in the explanans and explanandum. The prohibition on self-explanation should be refined so that it precludes a given fact p from helping to explain why some other fact q helps to explain why p. In this way, the transitivity principle avoids having counterintuitive consequences in cases involving macrostates having multiple possible microrealizations. The transitivity principle is perfectly compatible with the irreducibility of macroexplanations to microexplanations and with the diversity of the relations that can underwrite scientific explanations.
The meta-problem of consciousness is (to a first approximation) the problem of explaining why we think that there is a problem of consciousness. Just as metacognition is cognition about cognition, and a metatheory is a theory about theories, the metaproblem is a problem about a problem. The initial problem is the hard problem of consciousness: why and how do physical processes in the brain give rise to conscious experience? The relevant sort of consciousness here is phenomenal consciousness. A system is phenomenally conscious if there is something it is like to be that system, from the first-person point of view. The meta-problem is roughly the problem of explaining why we think phenomenal consciousness poses a hard problem, or in other terms, the problem of explaining why we think consciousness is hard to explain.
I argue for patternism, a new answer to the question of when some objects compose a whole. None of the standard principles of composition comfortably capture our natural judgments, such as that my cat exists and my table exists, but there is nothing wholly composed of them. Patternism holds, very roughly, that some things compose a whole whenever together they form a “real pattern”. Plausibly we are inclined to acknowledge the existence of my cat and my table but not of their fusion, because the first two have a kind of internal organizational coherence that their putative fusion lacks. Kolmogorov complexity theory supplies the needed rigorous sense of “internal organizational coherence”.
Karl Leonhard Reinhold (1757–1823), Austrian philosopher and first
occupant of the chair on Critical Philosophy established at the
University of Jena in 1787, first achieved fame as a proponent of
popular Enlightenment and as an early and effective popularizer of the
Kantian philosophy. During his period at the University of Jena
(1787–94), Reinhold proclaimed the need for a more
“scientific” and systematic presentation of the Critical
philosophy, one based upon a single, self-evident first principle. In
an effort to satisfy this need, he expounded his own “Elementary
Philosophy” in a series of influential works between 1789 and
In my book Understanding Scientific Progress (Maxwell 2017), I argue that fundamental philosophical problems about scientific progress, above all the problem of induction, cannot be solved granted standard empiricism (SE), a doctrine which most scientists and philosophers of science take for granted. A key tenet of SE is that no permanent thesis about the world can be accepted as a part of scientific knowledge independent of evidence. For a number of reasons, we need to adopt a rather different conception of science which I call aim-oriented empiricism (AOE). This holds that we need to construe physics as accepting, as a part of theoretical scientific knowledge, a hierarchy of metaphysical theses about the comprehensibility and knowability of the universe, these theses becoming increasingly insubstantial as we go up the hierarchy. Fundamental philosophical problems about scientific progress, including the problems of induction, theory unity, verisimilitude and scientific discovery, which cannot be solved granted SE, can be solved granted AOE.
[Editor's Note: The following new entry by Ana María
Mora-Márquez replaces the
on this topic by the previous author.] Simon of Faversham († 1306) was a thirteenth-century scholar,
mainly known as a commentator on Aristotle’s logic and natural
philosophy. He is considered a modist, among other things because of
his use of the notions of modi praedicandi and modi
essendi in his commentary on Aristotle’s
Categories (cf. Marmo 1999). Simon’s work as an
Aristotelian commentator heavily relies on Albert the Great’s
paraphrases on the Aristotelian corpus. Simon’s
question-commentaries often portray key medieval discussions in a
somewhat undeveloped state.
The central question of my paper is whether there is a coherent logical theory in which truth is construed in epistemic terms and in which also some version of the law of excluded middle is defended. Brentano in his later writings has such a theory. My first question is whether his theory is consistent. I also make a comparison between Brentano’s view and that of an intuitionist at the present day, namely Per Martin-Löf. Such a comparison might provide some insight into what is essential to a theory that understands truth in epistemic terms.
Dom Robert Desgabets (1610–1678) was an early defender and
teacher of the Cartesian philosophy at St. Maur in the region of
Lorraine, France. He was born in Ancemont and in 1636 became a monk
in the Benedictine order. He taught theology at Saint-Evre at Toul
between 1635–1655, and served as Procurer General of Mihiel to Paris
during 1648–49. Although he is little-known today, he played an
important role in the development and transmission of the Cartesian
philosophy, especially in Paris and Toulouse. He is best known for his
role in the theological controversy over the Cartesian explication of
the Eucharist (Desgabets, 1671), and for his defense of Nicolas
Malebranche against the skeptic Simon Foucher (Desgabets, 1675).
The following general attitude to mathematics seems plausible: standard claims, such as ‘there are infinitely many primes’ or ‘every consistent set of sentences has a model’, are true; nevertheless, if one rifles through the fundamental furniture of the universe, one will not find mathematical objects, such as numbers, sets or models. A natural way of making sense of this attitude is to augment it with the following thought: this is possible because such standard claims have paraphrases that make clear that their truth does not require the fundamental existence of such objects. This paper will draw out some surprising consequences of this general approach to mathematics—an approach that I call paraphrase anti-realism. These consequences concern the relationship between logical structure, on the one hand, and explanatory structure, on the other.
Constantin Brancusi. Socrates
Image © The Museum of Modern Art;
Licensed by Scala/Art Resource, NY
©2005 Artists Rights Society (ARS),
New York/ADAGP, Paris
reproduced with permission
of the Brancusi Estate
The philosopher Socrates remains, as he was in his
B.C.E. ),[ 1 ]
an enigma, an inscrutable individual who, despite having written
nothing, is considered one of the handful of philosophers who forever
changed how philosophy itself was to be conceived. All our information
about him is second-hand and most of it vigorously disputed, but his
trial and death at the hands of the Athenian democracy is nevertheless
the founding myth of the academic discipline of philosophy, and his
influence has been felt far beyond philosophy itself, and in every
My article aims to revisit the aesthetic thought of the Austrian psychologist and philosopher Joseph Wilhelm Nahlowsky (1812–1885), as expounded in his formerly famous monograph Das Gefühlsleben. I show that although Nahlowsky was a direct heir of Herbart, his ideas were in keeping with both the contemporary debate about form and content and the then-emerging paradigm of psychological aesthetics. I describe his developments on aesthetic feelings and his remarkable attempt to elaborate a general psycho-affective theory on the experience of the aesthetic object. I also discuss the importance of the notion of form, inherited from Herbart, in his psychological aesthetics. Finally, I demonstrate that, in addition to having marked an ‘affective’ turn in Herbartianism, Nahlowsky was a key actor in the evolution of ideas in psychological aesthetics in the second half of the nineteenth century.
The world is awake. That can stand as a slogan for panpsychism: the view that I will understand here as holding that consciousness is fundamental and ubiquitous in nature. This does not mean that everything is conscious. Whether a particular non-fundamental entity is conscious will depend upon the arrangement of its fundamental constituents given some presumed laws of ‘mental chemistry’ which govern the emergence of complex forms of consciousness. So in bare outline panpsychism presents a familiar picture of fundamental features interacting in ways to generate more complex forms. Nor does panpsychism entail that sophisticated, high level consciousness is ubiquitous. The term ‘consciousness’ is notoriously hard to define and the victim of multitudes of more or less well motivated (re)definitions. I aim for a minimal conception. For contrast, compare this expansive notion of consciousness, plucked merely for illustrative purposes from Aaronson (2016): ‘displaying intelligent behavior (by passing the Turing Test or some other means) might be thought a necessary condition for consciousness’. On the minimal conception, consciousness does not at all require that ability to pass the Turing test. Feeling pain (or any other sensation) alone is sufficient for consciousness. It’s worth noting this because there is a somewhat pernicious ambiguity lurking here, that between a property and the evidence we have for ascribing it. Although still inaccurate, Aaronson’s dictum is closer to the truth if we change the final phrase to ‘a necessary condition for the ascription of consciousness’. But note that we can have theoretical reasons for ascribing a property without there being any direct observational evidence for the ascription. So, the kind of minimal consciousness in question is not ‘self-consciousness’ or ‘transcendental subjectivity’, or awareness of the self as a subject, or awareness of one’s own mental states, or the ability to conceptualize one’s own mental states as such. Consciousness is simply sentience, or the way things are present (to the mind).
Øystein Linnebo and Richard Pettigrew () have recently developed a version of noneliminative mathematical structuralism based on Fregean abstraction principles. They argue that their theory of abstract structures proves a consistent version of the structuralist thesis that positions in abstract structures only have structural properties. They do this by defining a subset of the properties of positions in structures, so-called fundamental properties, and argue that all fundamental properties of positions are structural. In this paper, we argue that the structuralist thesis, even when restricted to fundamental properties, does not follow from the theory of structures that Linnebo and Pettigrew have developed. To make their account work, we propose a formal framework in terms of Kripke models that makes structural abstraction precise. The formal framework allows us to articulate a revised definition of fundamental properties, understood as intensional properties. Based on this revised definition, we show that the restricted version of the structuralist thesis holds.
Fictions evoke imagery, and their value consists partly in that achievement. This paper offers analysis of this neglected topic. Section I identifies relevant philosophical background. II offers a working definition of imagery. III identifies empirical work on visual imagery. IV and V criticize imagery essentialism, through the lens of genuine fictional narratives. This outcome, though, is not wholly critical. The expressed spirit of imagery essentialism is to encourage philosophers to "put the image back into the imagination." The weakened conclusion is that while an image is not essential to imagining, it should be returned to our theories of imagination.
A Comment in a Letter by John Dewey to Charles Strong, Quoted by Louis Menand in the Metaphysical Club, has Become Well Known. Dewey Wrote in 1905 That "the Chief Service of Pragmatism, as Regards Epistemology" Will Be "to Give the Coup de Grace to Representationalism” (Menand 2001, 361). The Passage is Quoted with Approval by Huw Price (2009), Drawing on Menand, and in Macarthur and Price (2007) It is Used to Support a Statement of What Pragmatism Itself Should Be Taken to Be, a View in Which Opposition to Representationalism is Central: Pragmatism = Linguistic Priority Without Representationalism. Whether or Not They Would Agree with the "=", Quite a Few Others Would Agree That "Representationalism" is a Philosophical Error, and Dewey Helps Us Get Past It – Rorty is a Further Example (1982).
In this work I argue for the existence of an ontological state in which no entity in it can be more basic than the others in such a state. This is used to provide conceptual justification for a method that is applied to obtain the Schr ödinger equation, the Klein-Gordon equation, and the Klein-Gordon equation for a particle in an electromagnetic field. Additionally, it is argued that the existence of such state is incompatible with indirect realism; and the discussion suggests that a panexeperientialist view is a straightforward means to embrace it.
Presentism is the view that only present things exist (Hinchliff 1996:
123; Crisp 2004: 15; Markosian 2004: 47–48). So understood, presentism is an ontological doctrine; it’s a
view about what exists (what there is), absolutely and unrestrictedly. The view is the subject of extensive discussion in the literature,
with much of it focused on the problems that presentism allegedly
faces. Thus, much of the literature that frames the development of
presentism has grown up either in formulating objections to the view
(e.g., Sider 2001: 11–52), or in response to such objections
(e.g., Bigelow 1996; Markosian 2004), with exceptions to this largely
coming via the ways in which presentism is motivated.
I present an argument against a relational theory of spacetime that regards spacetime as a ‘structural quality of the field’. The argument takes the form of a trilemma. To make the argument, I focus on relativistic worlds in which there exist just two fields, an electromagnetic field and a gravitational field. Then there are three options: either spacetime is a structural quality of each field separately, both fields together, or one field but not the other. I argue that the first option founders on a problem of geometric coordination and that the second and third options collapse into substantivalism. In particular, on the third option it becomes clear that the relationalist’s path to Leibniz equivalence is no simpler or more straightforward than the substantivalist’s.
Although the theory of the assertoric syllogism was Aristotle’s great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was that a syllogism is a conditional proposition deduced from a set of axioms. There is even unclarity about what the basis of syllogistic validity consists in. Returning to Aristotle’s text, and reading it in the light of commentary from late antiquity and the middle ages, we find a coherent and precise theory which shows all these claims to be based on a misunderstanding and misreading.
My aim is to defend a counterfactual analysis of causation against purportedly decisive difficulties raised recently, many rehearsed and developed further in this volume. Although some of the moves I will make are available to any counterfactual theory, my principal aim is to explain how a theory I outlined elsewhere can, with some adjustment and simplification for the purposes of discussion, deal with a range of problems (see Noordhof (1999) for original presentation of the theory). Specifically, I will be concerned with the issue of whether the semantics of counterfactuals can be characterised independently of causation (raised by Dorothy Edgington (XXXX)), the proper way to deal with the nontransitivity of causation (raised by Michael McDermott (1995) and Murali Ramachandran (XXXX)), and a range of counterexamples to the idea that causation involves, at its heart, chance raising (discussed by Helen Beebee (XXXX); Phil Dowe (XXXX); Doug Ehring (XXXX); Chris Hitchcock (XXXX), Jonathan Schaffer (2000a, 2000b) and Michael Tooley (XXXX)). Obviously, in defending my own counterfactual theory, I am also implicitly arguing that counterfactual approaches to causation in general have the resources to capture its important features. The ambiguity in the title thus accurately reflects the content of the present paper.
The exceptional Lie group E8 plays a prominent role both in mathematics and theoretical physics. It is the largest symmetry group connected to the most general possible normed division algebra, that of the non-associative real octonions, which — thanks to their non-associativity — form the only possible closed set of spinors that can parallelize the 7-sphere. By contrast, here we show how a similar 7-sphere also arises naturally from the algebraic interplay of the graded Euclidean primitives, such as points, lines, planes, and volumes, characterizing the three-dimensional conformal geometry of the physical space, set within its eight-dimensional Clifford-algebraic representation. Remarkably, the resulting algebra remains associative, and allows us to understand the origins and strengths of all quantum correlations locally, in terms of the geometry of the compactified physical space, namely that of a quaternionic 3-sphere, S , with S being the corresponding algebraic representation space.
We often express our emotions. Indeed, we may often find it very hard to avoid expressing our emotions. We also often find ourselves aware of others' emotions - our friend's anger, their rival's joy. How is it that we become aware of these states? What is the relationship between our emotions, their expression, and others’ knowledge of how we feel? Certainly we sometimes have to infer how people are feeling - from the tear-stained letter or the unexpected hanging up of the 'phone. We may find ourselves reflecting on what these signs mean; find ourselves piecing together various strands of what we know of the person. But that is not always how things unfold. Our sensitivity to each other’s mental lives often lacks that cerebral or effortful character of conscious reasoning. Our awareness may be psychologically spontaneous; immediate. In greeting your friend you find yourself unreflectively realising that she is angry. Or even without attending to it you realise later that in your interactions with her you displayed a certain sensitivity to her anger. Even when your sensitivity is just in the background it can play a central role in guiding how you interact.
We discuss some recent work by Tim Maudlin concerning Black Hole Information Loss. We argue, contra Maudlin, that there is a paradox, in the straightforward sense that there are propositions that appear true, but which are incompatible with one another. We discuss the significance of the paradox and Maudlin’s response to it.
There is a subjective way you experience the world. This is way it is like for you to listen to Jazz, to look around curiously, or to taste dark chocolate. It is hard to know about what it is like for you to experience these things simply by observing your behavior. …