Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of these (...) extensions are often justified only by example rather than by rigorous proof. In this paper, we provide proofs of many of these claims and present a more complete picture of the expressive landscape for such languages. (shrink)

There are many different ways to talk about the world. Some ways of talking are more expressive than others—that is, they enable us to say more things about the world. But what exactly does this mean? When is one language able to express more about the world than another? In my dissertation, I systematically investigate different ways of answering this question and develop a formal theory of expressive power, translation, and notational variance. In doing so, I show (...) how these investigations help to clarify the role that expressive power plays within debates in metaphysics, logic, and the philosophy of language. (shrink)

The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution (...) and the Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (shrink)

Paul Pietroski has developed a powerful minimalist and internalist alternative to standard compositional semantics, where meanings are identified with instructions to fetch or assemble human concepts in specific ways. In particular, there appears to be no need for Fregean Function Application, as natural language composition only involves processes of combining monadic or dyadic concepts, and Pietroski’s theory can then, allegedly, avoid both singular reference and truth conditions. He also has a negative agenda, purporting to show, roughly, that the vocabulary of (...) standard truth conditional semantics is far too powerful to plausibly describe the linguistic competence of mere human minds. In this paper, I explain some of the basics of Pietroski’s compositional semantics and argue that his major objection to standard compositionality is inconclusive, because a similar argument can be mounted against his own minimalist theory. I argue that we need a clear distinction between the language of the theorist---theoretical notation---and the language whose nature we are trying to explain. The theoretical notation should in fact be as expressively powerful as possible. It does not follow that the notation cannot be used to explain mere human linguistic competence, even if human minds are limited in various ways. (shrink)

Moss (2018) argues that rational agents are best thought of not as having degrees of belief in various propositions but as having beliefs in probabilistic contents, or probabilistic beliefs. Probabilistic contents are sets of probability functions. Probabilistic belief states, in turn, are modeled by sets of probabilistic contents, or sets of sets of probability functions. We argue that this Mossean framework is of considerable interest quite independently of its role in Moss’ account of probabilistic knowledge or her semantics for epistemic (...) modals and probability operators. It is an extremely general model of uncertainty. Indeed, it is at least as general and expressively powerful as every other current imprecise probability framework, including lower probabilities, lower previsions, sets of probabilities, sets of desirable gambles, and choice functions. In addition, we partially answer an important question that Moss leaves open, viz., why should rational agents have consistent probabilistic beliefs? We show that an important subclass of Mossean believers avoid Dutch bookability iff they have consistent probabilistic beliefs. (shrink)

When reusing existing ontologies for publishing a dataset in RDF (or developing a new ontology), preference may be given to those providing extensive subcategorization for important classes (denoted as focus classes). The subcategories may consist not only of named classes but also of compound class expressions. We define the notion of focused categorization power of a given ontology, with respect to a focus class and a concept expression language, as the (estimated) weighted count of the categories that can be (...) built from the ontology’s signature, conform to the language, and are subsumed by the focus class. For the sake of tractable initial experiments we then formulate a restricted concept expression language based on existential restrictions, and heuristically map it to syntactic patterns over ontology axioms (so-called FCE patterns). The characteristics of the chosen concept expression language and associated FCE patterns are investigated using three different empirical sources derived from ontology collections: first, the concept expression pattern frequency in class definitions; second, the occurrence of FCE patterns in the Tbox of ontologies; and last, for class expressions generated from the Tbox of ontologies (through the FCE patterns); their ‘meaningfulness’ was assessed by different groups of users, yielding a ‘quality ordering’ of the concept expression patterns. The complementary analyses are then compared and summarized. To allow for further experimentation, a web-based prototype was also implemented, which covers the whole process of ontology reuse from keyword-based ontology search through the FCP computation to the selection of ontologies and their enrichment with new concepts built from compound expressions. (shrink)

When embedding data are used to argue against semantic theory A and in favor of semantic theory B, it is important to ask whether A could make sense of those data. It is possible to ask that question on a case-by-case basis. But suppose we could show that A can make sense of all the embedding data which B can possibly make sense of. This would, on the one hand, undermine arguments in favor of B over A on the basis (...) of embedding data. And, provided that the converse does not hold—that is, that A can make sense of strictly more embedding data than B can—it would also show that there is a precise sense in which B is more constrained than A, yielding a pro tanto simplicity-based consideration in favor of B. In this paper I develop tools which allow us to make comparisons of this kind, which I call comparisons of potential expressive power. I motivate the development of these tools by way of exploration of the recent debate about epistemic modals. Prominent theories which have been developed in response to embedding data turn out to be strictly less expressive than the standard relational theory, a fact which necessitates a reorientation in how to think about the choice between these theories. (shrink)

Many contemporary artworks include active matter along with rules for conservation that are designed to either facilitate or prevent that matter’s degradation or decay. I discuss the mechanisms through which actual or potential states of material decay contribute to the work’s expressive import. Nelson Goodman and Catherine Elgin introduce the concepts of literal and metaphorical exemplification, which are critical to expression: a work literally exemplifies a property when it both possesses and highlights that property, and it metaphorically exemplifies a (...) property when the properties it literally exemplifies bring that property powerfully to mind. I argue that the literal exemplification of actual or potential states of decay enhances a work’s expressive power by stimulating our bodily and emotional responses to the physical potential of the work’s active matter. Conservation practices, by affecting the properties the work literally and metaphorically exemplifies, are key to the expressive power of works that employ states of degradation and decay. The argument is illustrated through discussion of works by Zoe Leonard, Marc Quinn, and Kara Walker that literally exemplify actually or potentially decaying materials, as contrasted with works by Ai Weiwei and Sam Taylor-Johnson that represent rather than exemplify decaying materials. (shrink)

This chapter explores a potential analogy between mereological principles and laws of nature. Against a backdrop of what Marmodoro has termed ‘power structuralism’ (and a rejection of a Humean worldview), the connection between parthood and modality may be richer than has hitherto been considered. Mereological principles delineate possibilities for parts and wholes, and putting powers at the centre of a discussion about parthood can furnish a novel conception of mereological laws, much as dispositionalism has done so for natural laws; (...) namely, these principles express connections between fundamental dispositional properties. By extending dispositionalism to comprehend mereology in this way, we can help fulfil its promise to provide a foundational, naturalistic metaphysics, as foundational mereological debates then begin to mirror those relating to dispositionalist views of laws of nature: we may treat natural and mereological laws in tandem, as holding either necessarily or contingently, with associated strategies for dealing with supposed counterexamples to one’s preferred set of mereological principles. We can thus bring new life to the debate over whether questions of composition admit of contingent or only necessary answers. (shrink)

Philosophical interest in state power has tended to focus on the state’s coercive powers rather than its expressive powers. I consider an underexplored aspect of the state’s expressive capacity: its capacity to use symbols (such as monuments, memorials, and street names) to promote political ends. In particular, I argue that the liberal state’s deployment of symbols to promote its members’ commitment to liberal ideals is in need of special justification. This is because the state’s exercise of its (...) capacity to use symbols may be in tension with respecting individual autonomy, particularly in cases in which the symbols exert influence without engaging citizens’ rational capacities. But despite the fact that the state’s deployment of symbols may circumvent citizens’ rational capacities, I argue that it may nonetheless be permissible when surrounded by certain liberal institutions and brought about via democratic procedures. (shrink)

The sociobiological and socio-political aspects of human existence have been the subject of techno-rationalistic control and manipulation. The investigation of the mutual complementarity of anthropological and ontological paradigms under these circumstances is the main purpose of present publication. The comparative conceptual analysis of the bio-power and bio-politics in the mentality of the modern technological civilization is a main method of the research. The methodological and philosophical analogy of biological and social engineering allows combining them in the nature and social (...) implications as part of a High Hume technologies class. As result of the transformation of somatic foundations of the human being and his behavior, stereotypes in the object of control and management the technogenic risk reached the existential level. The rapidly growing status of biopower and biopolitics in the conceptual field of contemporary political science becomes by phenomenological expression of these processes. (shrink)

In this article, I link Lisa Feldman Barrett's theory of constructed emotion1 to decolonial perspectives that also challenge this universality of affect in cross-cultural facial expressions. After first outlining some of the present-day political stakes of these questions, I turn to Sylvia Wynter on the "ethnoclass of Man" in Western modernity, where she asks: how were concepts of not only being, truth, power, and freedom but also affect—the intelligibility of one's feelings toward others—framed by histories of colonial violence and (...) refusals of imaginative identification?2 Wynter argues that the overrepresentation of the Western ethnoclass results in the naturalization of a limited and contingent mode of being as... (shrink)

The central claim of normative pragmatism is that intentional states can be explained in terms of participation in practices. My aim in this paper is not so much to defend this claim as to rearticulate it in a different medium: the medium of computation. I describe two computer programs in which this claim is re-expressed. The first is the latest version of THE SIMS, in which participation in practices enables the Sims to do and understand more. The second is a (...) prototype simulation of philosophical debate. In this second program, normative pragmatism is expressed at two different levels: once as the theory powering the implementation, and once as a set of claims which are debated by the simulated philosophers. Here, a philosophical theory is used to implement a system in which that very same theory is articulated, challenged, and justified. (shrink)

In this work, author expressed new R-Synthesis specifically. Good and/or correct perspective that must be behind the definitions and administration generally expressed. New perspective of the philosophy explained generally. Philosophy of GodForm is defined and expressed as connected/related with the following concepts: (a) basic principles, (b) 17 upper constructional philosophies, (c) 14 lower constructional philosophies, (d) eight basic philosophies. As special cases, Philosophy of Engineering and Technology, Philosophy of Wireless Administration and others defined as hybrid philosophies. 17 specific components/units which (...) can be considered to define the basic principles of the related formation, are proposed to be designed by GodForm and defined by the author. Philosophy of GodForm and its relation with Values and Positions specifically defined. New Era Theory and New Era Belief explained generally. Some specific religions/beliefs are defined as variants/forms of the Progressive Religion. Good and/or correct power authorities (R-Power Authority) are defined due to 29 categories. Functional position levels defined for the R-Power Authorities with a unique table. As result of the R-Synthesis, functional position levels of some philosophers, some scientists, and of Prophet Jesus, Prophet Mohamed, Prophets Mouses, Buddha, and of Confucius generally/specifically defined. Integration and past/present effects of some R-Power Authorities in 5 x 5 Ideal Political Construction specifically explained. New Era Belief, Concepts of GodX and Science relation explained with the following concepts: (1) Religion of GodForm, (2) Knowledge of GodX, (3) Nature of GodX. With this respect, some other characteristics of 7 GodX power authorities expressed with details as complementary information. Following concepts/systems defined to arrange and solve some/most/all religious problems, which are determined with R-Synthesis: (a) Religious Responsibilities and Positions, (b) Ideal Religious Administration, (c) Sustainable/Continuable Political Administration System, (d) Community Values Council/Authority for each world country, (e) Progressive Councils. 15 general religious position categories defined to express their good and/or correct meanings/values/responsibilities in the religious system. 21 general/specific cases/programs defined due to New Era Belief to solve possible past/present/future community values problems, to have continuous, judicious, and progressive administration about the 36 kinds of community values. Progressive Councils, which are related with the CUS-WW-HO, are defined. Progressive Religion Council and some of the related religious responsibilities expressed for the kind progressive religion studies due to the Philosophy of Progressive Religions. (shrink)

Must privacy and freedom of expression conflict? To witness recent debates in Britain, you might think so. Anything other than self-regulation by the press is met by howls of anguish from journalists across the political spectrum, to the effect that efforts to protect people’s privacy will threaten press freedom, promote self-censorship and prevent the press from fulfilling its vital function of informing the public and keeping a watchful eye on the activities and antics of the powerful.[Brown, 2009, 13 January]1 Effective (...) protections for privacy, from such a perspective, inevitably pose a threat to democratic government via the constraints that they place on the press. Such concerns with privacy must be taken seriously by anyone who cares about democratic government, and the freedom, equality and wellbeing of individuals. But if it is one thing to say that privacy and freedom of expression cannot always be fully protected, it is another to suppose that protections for the one must always come at the expense of the other. After all, the economics of contemporary politics and journalism would seem to be partly responsible for our difficulties in protecting personal privacy while sustaining robust and informative forms of public discourse. [Moore, 2010, 10 -141]2 Most newspapers are loss-making businesses and the need to reduce those losses and, if possible, to turn a profit, make investigative journalism an increasingly expensive proposition as compared to both “comment” and more or less elevated forms of gossip. At the same time, politics has increasingly become the prerogative of a narrow group of people with access to the large sums of money necessary successfully to compete for high office. In those circumstances, the need for critical scrutiny is as important as it is difficult. Revising our ideas about privacy and its protection cannot alone reduce the tensions between freedom of expression and personal privacy typical of our societies, necessary though such revision may be. Moreover, this paper can only touch on some aspects of the ways in which we need to rethink our interests in privacy, in order adequately to reflect people’s diverse interests in freedom of expression, and the important role of a free press to democratic government. Nonetheless, I hope to suggest ways of thinking about people’s claims to privacy which can be generalised fairly readily, and can help us to think constructively about the nature, causes and solutions to some important social and political problems, even if, in its nature, philosophical analysis rarely tells us what to do. More specifically, this paper argues that people are entitled to keep some true facts about themselves to themselves, should they so wish, as a sign of respect for their moral and political status, and in order to protect themselves from being used as a public example in order to educate or to entertain other people. The “outing” - or non-consensual public disclosure - of people’s health records or status, or their sexual behaviour or orientation is usually unjustified, even when its consequences seem to be beneficial. Indeed, the paper claims, the reasons to reject outing, as inconsistent with democratic commitments to freedom and equality, are reasons to insist on the importance of privacy to freedom of expression. While a free press is of the utmost importance to democratic government, it is not identical with the free expression of individuals and, on occasion, the former may have to be constrained in order to protect the latter. [Barendt, 2007, 231]. Hence, the paper concludes, we should distinguish the claims of individuals to publish reports about their lives – even if this necessarily involves revealing the private lives of others – from journalistic claims to publish information about the sex lives of consenting adults. I will start by briefly situating my argument within a democratic approach to privacy, before using the “outing” of Oliver Sipple to examine people’s claims to privacy and their implications for freedom of expression and of the press. I will be assuming that some forms of privacy are legitimate, in order to focus more closely on the question of what information, if any, people may keep to themselves. (shrink)

This paper suggests the democratic direction in which the right of freedom of expression should be conceived and applied. In the first two sections it suggests some counter-examples to, and diagnoses of, the libertarian and liberal conceptions of freedom of expression, taking Scanlon (1972) and Scanlon (1979), respectively, to be their chief proponents. The paper suggests that these conceptions cannot take into account clear examples, like fraudulent propaganda, which should not be legal. The democratic conception takes it to heart that (...) the pillars upon which the right of freedom of expression is founded are individual and collective autonomy, the right to know facts of public interest and information necessary for effective democratic control of government. The paper suggests that in a time when private powers seriously threaten these pillars, it is correct for the government to step in to provide the framework in which genuine discussion geared toward fulfilling the objectives of these pillars can take place. (shrink)

Uptake is typically understood as the hearer’s recognition of the speaker’s communicative intention. According to one theory of uptake, the hearer’s role is merely as a ratifier. The speaker, by expressing a particular communicative intention, predetermines what kind of illocutionary act she might perform. Her hearer can then render this act a success or a failure. Thus the hearer has no power over which act could be performed, but she does have some power over whether it is performed. (...) Call this the ratification theory of uptake. Several philosophers have recently endorsed an alternative theory of uptake, according to which the hearer can determine the nature of the act the speaker performs. According to this theory, if the hearer regards an utterance as illocutionary act y, then it is act y, even if the speaker intended to perform act x. Call this the constitution theory of uptake. The purported advantage of this theory is that it identifies a common but underanalysed way in which speakers can be silenced. I argue that despite its initial intuitive pull, the constitution theory of uptake should be rejected. It is incompatible with ordinary intuitions about speech, it entails a conceptual impossibility, and it has unsavoury political implications, entailing that marginalised speakers barely qualify as agents. (shrink)

I here defend a theory consisting of four claims about ‘property’ and properties, and argue that they form a coherent whole that can solve various serious problems. The claims are (1): ‘property’ is defined by the principles (PR): ‘F-ness/Being F/etc. is a property of x iff F’ and (PA): ‘F-ness/Being F/etc. is a property’; (2) the function of ‘property’ is to increase the expressive power of English, roughly by mimicking quantification into predicate position; (3) property talk should be (...) understood at face value: apparent commitments are real and our apparently literal use of ‘property’ is really literal; (4) there are no properties. In virtue of (1)–(2), this is a deflationist theory and in virtue of (3)–(4), it is an error theory. (1) is fleshed out as a claim about understanding conditions, and it is argued at length, and by going through a number of examples, that it satisfies a crucial constraint on meaning claims: all facts about ‘property’ can be explained, together with auxiliary facts, on its basis. Once claim (1) has been expanded upon, I argue that the combination of (1)–(3) provides the means for handling several problems: they help giving a happy-face solution to what I call the paradox of abstraction , they form part of a plausible account of the correctness of committive sentences, and, most importantly, they help respond to various indispensability arguments against nominalism. (shrink)

This book offers a detailed study of the political philosophies of Thomas Hobbes and Benedict de Spinoza, focussing on their concept of power as potentia, concrete power, rather than power as potestas, authorised power. The focus on power as potentia generates a new conception of popular power. Radical democrats–whether drawing on Hobbes's 'sleeping sovereign' or on Spinoza's 'multitude'–understand popular power as something that transcends ordinary institutional politics, as for instance popular plebsites or mass (...) movements. However, the book argues that these understandings reflect a residual scholasticism which Hobbes and Spinoza ultimately repudiate. Instead, on the book's revisionist conception, a political phenomenon should be said to express popular power when it is both popular (it eliminates oligarchy and encompasses the whole polity), and also powerful (it robustly determines political and social outcomes). Two possible institutional forms that this popular power might take are distinguished: Hobbesian repressive egalitarianism, or Spinozist civic strengthening. But despite divergent institutional proposals, the book argues that both Hobbes and Spinoza share the conviction that there is nothing spontaneously egalitarian or good about human collective existence. From this point of view, the book accuses radical democrats of pernicious romanticism; the slow, meticulous work of organizational design and maintenance is the true centre of popular power. Three minute video summary available via HPBin3. Extended discussion on The Political Theory Review podcast. First chapter open access available via Oxford Scholarship Online. Videos of book talks at National University of Singapore (Centre for Legal Theory) and Universidad de Buenos Aires (Instituto de Investigaciones Gino Germani) available via YouTube. (See links below.). (shrink)

In this paper I argue that, in Leibniz’s mature metaphysics, primary matter is not a positive constituent which must be added to the form in order to have a substance. Primary matter is merely a way to express the negation of some further perfection. It does not have a positive ontological status and merely indicates the limitation or imperfection of a substance. To be sure, Leibniz is less than explicit on this point, and in many texts he writes as if (...) primary matter were a positive constituent of a substance. It seems to me, however, that the view most in keeping with the thrust of his mature philosophical system is that captured by a striking remark of 1695: “Materia rerum est nihilum: id est limitatio [The matter of things is nothing: that is, limitation].” This becomes especially apparent in texts showing that Leibniz’s conception of primary matter corresponds to his conception of creaturely limitation. I start by discussing the notion of primary matter in the scholastic tradition. I then show that although Leibniz places the scholastic terminology of primary matter at a crucial juncture of his metaphysics, he thinks of primary matter in a way which significantly deviates from earlier scholastic views. I conclude that despite his adoption of distinctive terminology of Aristotelian scholasticism, instead of holding a broadly Aristotelian concept of primary matter as the ultimate subject of inherence, Leibniz thinks of primary matter according to a Neoplatonic blue-print in which matter is non-being, privation, mere absence of perfection. (shrink)

● Any given placement (e.g. Sun in Taurus; Mars in Capricorn; Mercury in the third house) is necessarily common to tens of thousands of people. Saturn in the ninth house, for example, will not behave the same or produce the same effects in the twenty or one hundred charts in which we find it there. In each case Saturn will behave in accordance with the rest of the astrographic/chart composition (as if we stayed in the same hotel in different epochs (...) or different people contracted the same disease; our stay will be different each time, according to the epoch, and each person’s symptoms will too, be different, according to their individual biochemistry; not to mention that each chart or astrography, like each genetic code or sequence, is unrepeatable). Certainly, “no planet can produce, on its own, what only the combined or concerted action of all can” (BUSTAMANTE, 2023, SPICA magazine, pp. 93-111). Hence the synergistic nature of the interpretative exercise (i.e., the whole is greater than all its parts). The fundamental component of the mathematical expression of the interpretive exercise is: astrological triangulation, the functional denomination for what we know as synthesis (WEISS, 1946; LEO, 1983, HAND, 1981). In order to demonstrate its usefulness, as well as the convenience of its mathematical expression, we have chosen two individuals (JEFFREY DAHMER, STEVEN SPIELBERG) whose astrographies do not—according to the community—explain their lives. The rest of the astrographies correspond to those of serial killers JOHN WAYNE GACY, DAVID CARPENTER, and TED BUNDY. ● We explain, by means of algebraic notations, the synthesis and the functional values that make up the synthesis. ● We take the Moon and Neptune as relevant bodies for the purpose of diagnosing or studying endocrine or neurohormonal issues, and Mars, Pluto, and Saturn as relevant planets for the purpose of inferring violence or sinister behaviour, upon the case, and quadratures or oppositions—and conjunctions—between Venus and the Moon, the Moon and Neptune, and the Sun or Venus and Neptune or Uranus as indicators of neurohormonal disorders and/or sexual deviance (APA definition) . ● We consider quadratures (90º) or oppositions (180º)—and conjunctions—between Mercury or the Moon and Saturn, or between Mars or the Moon and Saturn, Uranus, Neptune, and/or Pluto as powerful indications of violence or mental disorders, upon the case. ● We have also regarded Sagittarius as a sign as expansive and abundant as its ruler, Jupiter, according to the best of its characterisations (or as an exceptionally swift and wild sign, according to other characterisations), and the fifth region of a natal chart as one closely related to fortune in a broad sense (material and immaterial). ● Because we advocate the idea that orbs should be predicated of the planet (size, speed), not the aspect itself, the gas giants (Jupiter, Saturn, Uranus, and Neptune) and the Sun have been granted up to 10º of orb (or 12º, in the case of broad influence ). We understand aspectual relationships as angular relationships held between two or more celestial bodies placed in signs with at least one property in common (according to our molecular theory of the ecliptic, compatible with the optical theory of the aspects from the Hellenistic tradition). (shrink)

Although Hannah Arendt is not known as an advocate of nonviolence per se, her analysis of power dynamics within and between groups closely parallels Gandhi’s. The paper shows the extent to which her insights are compatible with Gandhi’s and also defends her against charges that her description of the world is overly normative and unrealistic. Both Arendt and Gandhi insist that nonviolence is the paradigm of power in situations where people freely consent to and engage in concerted action, (...) and both argue that power structures based on violence and coercion will ultimately fail, because the resort to violence implies an inability to gain free consent or cooperation. Any gains from violence are temporary, since agents will express themselves freely as soon as force is withdrawn. Arendt argues that dominating powers know this, and therefore rely on manipulation, propaganda, and outright lies to win people’s consent, an analysis which can be used to explain some current social dynamics. (shrink)

Some philosophers think that the challenge of justifying punishment can be met by a theory that emphasizes the expressive character of punishment. A particular type of theories of this sort - call it Expressive Retributivism [ER] - combines retributivist and expressivist considerations. These theories are retributivist since they justify punishment as an intrinsically appropriate response to wrongdoing, as something wrongdoers deserve, but the expressivist element in these theories seeks to correct for the traditional obscurity of retributivism. Retributivists often (...) rely on appeals to controversial intuitions involving obscure concepts. While retributive intuitions can be compelling, some worry that the justificatory challenge cannot be met merely by appealing to them. ER tries to enhance the clarity and justificatory power of these intuitions and the concepts they invoke by appealing to an expressive conception of punishment. I argue that these theories fail to justify punishment and that there is reason to think that they cannot, in principle, justify punishment. (shrink)

This article offers a Nietzschean theory of digital will to power to conceptualize the temporality of social media feeds run by algorithms. Stylistic and methodological temporalities of Nietzsche are discussed as well as their influence in subsequent social theory of political technologies. The paradox of heavy investment in both subjective expression and nonhuman temporalization in social media milieus is addressed with the concept of an event-without-witness drawn from Nietzsche’s account of himself as the solitary thinker of catastrophe of nihilism (...) and psychoanalytical and deconstructive literatures on the catastrophes of the 20th century. Nietzsche’s fundamental resistance to and fascination with the philosophical and cultural modes of mummyfication, i.e. eternalization as an expression of the will to power is used to think the will to power in the creative algorithmic temporalization of social interactions through the selection, distribution and serialization of data for social media feeds. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Plato on Knowledge as a Power1Nicholas D. SmithAt 471C4 in Plato’s Republic, the argument takes a sudden turn when Glaucon becomes impatient with all of the specific prescriptions Socrates has been making, and asks to return to the issue Socrates had earlier set aside—whether or not the city he was describing could ever be brought into being. In response to Glaucon’s impatient question, Socrates articulates his “third wave of (...) paradox” (472ag–7), namely, that the ills of the cities will never be ended until either philosophers become rulers or rulers become philosophers (473c11–d6). Glaucon immediately responds that such a view is likely to be greeted with violence and scorn (473e6–474a4), and so Socrates must hasten to explain his odd claim. His explanation, it turns out, is that true philosophers have an enormous cognitive advantage over non-philosophers—philosophers have and use knowledge (ἐπιστήμη), whereas non-philosophers have and use only opinion (δόξα).2 This distinction, between επιστήμη and δόξα, turns out: to be a distinction between two different cognitive powers (δυνάμεις—477d7–e3). And different powers, Plato clearly tells us, apply to or take as their objects (Plato says they are “ἐπί”) different things (477dl).In this paper, I shall argue that the relationship between the cognitive powers and their various objects has been fundamentally misunderstood, which has led scholars into one or more misinterpretations of important and explicit features of the text. At the heart of these misunderstandings, I claim, is [End Page 145] their shared misconception of the relation between the cognitive power and its objects as interpretable in terms of the relationship between a cognitive stale and what the content of that state is of or about.3 One consequence of the view for which I shall argue is that what has come to be known as the “two-worlds theory”4 of Plato’s epistemology is seriously mistaken, but no less mistaken than the alternatives given by its recent critics. Another consequence that I shall draw from my argument is that Plato should be understood neither as a kind of foundationalist with regard to knowledge and warrant, as some have supposed him to be,5 nor as a coherentist, as others have supposed,6 but, rather, as a kind of causal reliabilist. [End Page 146]1. KNOWLEDGE AS A POWERScholarly interpretations of Plato’s epistemology have routinely sought to understand the relationships between each cognitive power of Republic Book V and the objects of the ἐφ’ ᾦ (“what it is related to”) condition by which it is differentiated from other δυνάμεις as Plato’s way of telling us what each sort of cognition is of or aboul. 7 So, for example, we find Gail Fine using the expressions “belief [δόξα] is set over [Fine’s translation of Plato’s ἐπί] …” and “knowledge is set over …” interchangeably with “belief is of …” or “belief is about…” and “knowledge is of …” or “knowledge is about …”8 Against the “two-worlds theory,” Fine argues that, for Plato, there can be knowledge of sensibles and beliefs about Forms. Accordingly, since she assimilates the power-ἐπί-object set of relations to the cognilion-of/about-object relation, she concludes—in order to account for knowledge of sensibles and beliefs about Forms—that the objects of knowledge and opinion must be propositions. Plato’s claims that knowledge is ἐπί what is, whereas opinion is ἐπί what is and is not, Fine understands as, “One can only know true propositions; one can believe both true and false propositions.”9 We shall see later that this “veridical” understanding of what Plato means to identify as “what is,” and “what is and is not” fails to account for important and explicit elements of Plato’s exposition of the epistemological and metaphysical distinctions he is making. For now, it is enough to note that Fine understands the ἐφ’ᾦ) relation in terms of our cognition-of/about-object relation. One finds the same assimilation made by those who advance existential readings of Plato’s “is” and “is not,”10 as [End Page 147] well as those who have urged that we adopt predicative readings of “is” and “is not.”11But I think there are very serious problems with this assimilation. Plato is very... (shrink)

Nietzsche sometimes praises the drive to order—to simplify, organize, and draw clear boundaries—as expressive of a vital "classical" style, or an Apollonian artistic drive to calmly contemplate forms displaying "epic definiteness and clarity." But he also sometimes harshly criticizes order, as in the pathological dialectics or "logical schematism" that he associates paradigmatically with Socrates. I challenge a tradition that interprets Socratism as an especially one-sided expression of, or restricted form of attention to, the Apollonian: they are more radically disparate. (...) Beyond strengthening the case for this basic point, I develop a distinctive account of what, exactly, distinguishes the Apollonian-classical and Socratic forms of order. To this end, I advance interrelated interpretations of Apollonian-classical simplicity and the "cold" calm that it elicits, by contrast to superficially similar Socratic phenomena. This illuminates Nietzsche's broader ambivalence toward science, in part by clarifying the nature and value of an idealized Apollonian science. (shrink)

Avoiding partisan diatribe, Left Wing, Right Wing, People, and Power traces the historical development of the left wing and the right wing to reveal that the core of politics is the conflict over power. Despite specific differences of time and place, political actions are consistently efforts to preserve or change the structure and dynamics of power. With this insight, we can better understand political positions and actions. -/- Written in an accessible style, this book will inform readers (...) regardless of where they see themselves on the political spectrum. With clear but nuanced definitions of political ideologies and movements, the author shows how politics is people seeking to express and expand their power in the social space around them. Thus, the clash of the left and right wings is not about grand ideologies but instead is about power relations and the flow of power among people. (shrink)

ArgumentThe sixteenth-century physician and philosopher Julius Caesar Scaliger suggests that in particular cases plants can come into being that belong to a plant species that did not exist before. At the same time, he holds that God could not have created a more perfect world. However, does the occurrence of new species not imply that the world was not the best possible world from the beginning? In this article, I explore a set of metaphysical ideas that could provide Scaliger with (...) the means of solving this problem: His version of the notion of a plurality of substantial forms in every living being, and his version of the notion of the ordained divine power. As it turns out, Scaliger analyzes the generation of new species in terms of a development of subordinate substantial forms into dominant substantial forms. Thereby, previously existing essences of plant parts become essences of plants. These plants, thus, possess essences that no previously existing plant possessed and, in this sense, belong to a new species. In this way, Scaliger avoids positing the occurrence of new essences, thus saving the best possible world thesis. Moreover, he believes that all substantial forms stand in a relationship of mutual existential dependence by means of which God safeguards the persistence and unity of the world. This is why the agency of subordinate forms turned dominant can be understood as an expression of the ordained power of God. (shrink)

I present an image of humanity as the will to power expressed in context of affirmationand danger in the eternal return. Nietzsche argues the death of God not as a theological argument but as an existential challenge for humanity to be re-experienced. It is read in light of the eternal return: without ontological references or quasi-transcendentals, how is life to be lived? Deleuze contextualizes Nietzsche’s critique of nihilism qua a typology of active and reactive modes of being, however I (...) go beyond to provide what I consider an anthropological account. I do this by differentiating the will to power from individual willing and present the danger that an affirmation of life entails. Nietzsche challenges us with the eternal return. With this, one is led to realize that she is her own destruction (Untergehen) at the same time as her overture (Übergehen). She has the ability, power, capacity to overcome and self-create. With this realization one ought to remain truthful to this in form of truth-telling (Redlichkeit). Nietzsche projects humanity as a perilous crossing over from nihilism to affirmation with an embrace of an ethics of danger. This crossing over is a mark of life as the will to power. It is an overcoming of nihilism and the assurance amidst nihilism’s farce that the godhead is dead and that the eternal return is a daunting challenge we cannot escape from. With these, we are afforded an image of humanity as the will to power. (shrink)

This paper aims to provide a roadmap to AI governance. In contrast to the reigning paradigms, we argue that AI governance should not be merely a reactive, punitive, status-quo-defending enterprise, but rather the expression of an expansive, proactive vision for technology—to advance human flourishing. Advancing human flourishing in turn requires democratic/political stability and economic empowerment. Our overarching point is that answering questions of how we should govern this emerging technology is a chance not merely to categorize and manage narrow risk (...) but also to construe the risks and opportunities much more broadly, and to make correspondingly large investments in public goods, personnel, and democracy itself. To lay out this vision, we take four steps. First, we define some central concepts in the field, disambiguating between forms of technological harms and risks. Second, we review normative frameworks governing emerging technology that are currently in use around the globe. Third, we outline an alternative normative framework based in power-sharing liberalism. Fourth, we walk through a series of governance tasks that ought to be accomplished by any policy framework guided by our model of power-sharing liberalism. We follow these with proposals for implementation vehicles. (shrink)

This paper has four parts. First outline seven several questions concerning the relation between God, his goodness, and other philosophically interesting things, especially between attributes of almightiness, goodness, and faith in God, questions different from the main question of this article. The second part presents Aquinas’s account of God’s goodness, with three ways to understand it, as God’s excellence in being, with respect of His creative activity and with respect of the morality of God’s acting. The third part of the (...) article critically examines Nelson Pike’s classical account of the Aquinas-Anselm view of the problem of the possibility of God’s sin and the paradox of omnipotence and goodness. Last part contains argumentation that Pike’s argument is not sound. He shouldn’t so easily reconstruct Aquinas account of absolutely possible as concerning only the result of God’s creative action - some consistent state of affairs, second, the assessment of some agent’s decision/choice/possibility of acting in particular (morally wrong) way should be included in assessment of his power, and Pike's paper doesn’t support enough his conclusion, that Aquinas confused second and third sense of “God cannot sin.” Alternatively, to Pike’s account, I distinguish the fourth sense of the expression in question, present arguments that this meaning is coherent with Aquinas account of omnipotence and goodness of God as well as arguments that this is the concept of divine omnipotent goodness which is the condition of real faith in God. (shrink)

Can music be considered a language of the emotions? The most common view today is that this is nothing but a Romantic cliché. Mainstream philosophy seems to view the claim that 'Music is the language of the emotions' as a slogan that was once vaguely defended by Rousseau, Goethe, or Kant, but that cannot be understood literally when one takes into consideration last century’s theories of language, such as Chomsky's on syntax or Tarski's on semantics (Scruton 1997: ch. 7, see (...) also Davies 2003: ch. 8, and Kania 2012). In this chapter, I will show why this common view is unwarranted, and thus go against nowadays philosophical mainstream by defending what I call the musicalanguage hypothesis. In Section 1, I will introduce the musicalanguage hypothesis and present, based on empirical evidence, some of the many similarities between language and music and explain why we should take them seriously. I will introduce a framework that aims to explain the communicative power of music using what we already know about linguistic communication (1.1). I will then outline several working hypotheses about musical grammar, musical meaning, and affective meaning (1.2), and thus defend that music is indeed very close to literally be a language of the emotions. In Section 2, I will detail some of the methodology, expectations, and preliminary results of a cross-cultural study on musical grammar that I am presently conducting between South India (Chennai) and Switzerland (Geneva and Lausanne)4. This empirical study focuses on two musical idioms and their grammatical features: Western classical music of the Common Period (ca. 1600-1900) and South Indian classical music (also know as Carnatic music). The main hypothesis of this study is that you need to master the grammar of a musical idiom in order to properly understand its musical meanings. (shrink)

While standard first-order modal logic is quite powerful, it cannot express even very simple sentences like “I could have been taller than I actually am” or “Everyone could have been smarter than they actually are”. These are examples of cross-world predication, whereby objects in one world are related to objects in another world. Extending first-order modal logic to allow for cross-world predication in a motivated way has proven to be notoriously difficult. In this paper, I argue that the standard accounts (...) of cross-world predication all leave something to be desired. I then propose an account of cross-world predication based on quantified hybrid logic and show how it overcomes the limitations of these previous accounts. I will conclude by discussing various philosophical consequences and applications of such an account. (shrink)

The controversy that accompanied the publication and reprinting of cartoons depicting the Prophet Muhammed as part of a 2005 editorial in the Danish newspaper Jyllands-Posten has been widely interpreted as yet another illustration of an ineliminable tension between multiculturalism and liberalism. Such an interpretation would have us believe that what is at issue in defending the cartoons is our commitment to civil liberties as a mainstay of liberal democracy. But is this really what is at issue? A closer examination suggests (...) that what is actually being defended in this case is not civil liberty but civil privilege. In particular, what is at issue is the privilege to exclude and define Muslims. (shrink)

Je suis très habitué à des livres étranges et des gens spéciaux, mais Hawkins se distingue par son utilisation d’une technique simple pour tester la tension musculaire comme une clé de la «vérité» de tout type de déclaration que ce soit, c’est-à-dire pas seulement à savoir si la personne testée croit, mais si c’est vraiment vrai! Ce que l’on sait bien, c’est que les gens montreront des réponses physiologiques et psychologiques automatiques, inconscientes à peu près tout ce à quoi ils (...) sont exposés : images, sons, toucher, odeurs, idées, personnes. Donc, la lecture musculaire pour découvrir leurs vrais sentiments n’est pas radicale du tout, contrairement à l’utiliser comme un bâton dousing (plus de lecture musculaire) pour faire "science paranormale". Hawkins décrit l’utilisation de la tension décroissante dans les muscles d’un bras en réponse à l’augmentation de la charge cognitive provoquant ainsi le bras à baisser en réponse à la pression constante des doigts de quelqu’un. Il semble ignorer qu’il existe un vaste effort de recherche en psychologie sociale, longtemps établi et vaste, appelé par des expressions telles que la « cognition implicite », l'« automaticité », etc., et que son utilisation de la « kinésiologie » est une petite section. En plus du tonus musculaire (rarement utilisé), les psychologues sociaux mesurent l’EEG, la réponse cutanée galvanique et le plus souvent les réponses verbales aux mots, aux phrases, aux images ou à des situations qui varient parfois de quelques secondes à des mois après le stimulus. Beaucoup, tels que Bargh et Wegner, prennent les résultats pour signifier que nous sommes des automates qui apprennent et agissent en grande partie sans sensibilisation via S1 (système automatisé 1) et beaucoup d’autres tels que Kihlstrom et Shanks disent que ces études sont imparfaites et nous sommes des créatures de S2 (système délibératif 2). Bien que Hawkins ne semble pas avoir d’idée, comme dans d’autres domaines de la psychologie descriptive de la pensée de l’ordre supérieur, la situation concernant «l’automaticité» est toujours aussi chaotique qu’elle l’était quand Wittgenstein décrit les raisons de la stérilité et la stérilité de la psychologie dans les années 30. Néanmoins, ce livre est une lecture facile et certains thérapeutes et les enseignants spirituels peuvent le trouver utile. Ceux qui souhaitent un cadre complet à jour pour le comportement humain de la vue moderne de deux systeme peuvent consulter mon livre 'The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle' 2nd ed (2019). Ceux qui s’intéressent à plus de mes écrits peuvent voir «Talking Monkeys --Philosophie, Psychologie, Science, Religion et Politique sur une planète condamnée --Articles et revues 2006-2019 3e ed (2019) et Suicidal Utopian Delusions in the 21st Century 4th ed (2019) et autres. (shrink)

Human culture seeks to transcend and replace the uncertainties of nature with a controllable human world. The quest for the Ideal has led to the creation of artificial environments, both material and intellectual—a second nature. New technologies express ancient dreams of immortality, freedom from embodiment and pain, and unlimited control of matter in man-made environments. But nature is not an artifact and may never be fully understood or controlled. While post-humanism may be delusional, its dreams could defeat the reasoned use (...) of technology to improve human life. Globalist economics is the latest expression of the mechanist metaphor. The basal gender imbalance of modern social values must be rectified to guide society sanely into the future. (shrink)

We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, (...) Kamp's and Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions. (shrink)

This paper examines two alleged limitations in the use of formal languages: on the one hand, the trade-offs between expressive and inferential power, and on the other, the phenomenon of system imprisonment. After reconceptualizing the issue, we consider the role played by modality in the understanding of certain aspects of mathematical structures and argue for its centrality.

Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between (...) this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic's applications than has been given thus far. Questions about the correct logic of plurals play a central role in the final chapters, where traditional plural logic is rejected in favor of a "critical" alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes. (shrink)

This paper draws on the 'Fitting Attitudes' analysis of value to argue that we should take the concept of fittingness (rather than value) as our normative primitive. I will argue that the fittingness framework enhances the clarity and expressive power of our normative theorising. Along the way, we will see how the fittingness framework illuminates our understanding of various moral theories, and why it casts doubt on the Global Consequentialist idea that acts and (say) eye colours are normatively (...) on a par. We will see why even consequentialists, in taking rightness to be in some sense determined by goodness, should not think that rightness is conceptually reducible to goodness. Finally, I will use the fittingness framework to explicate the distinction between consequentialist and deontological theories, with particular attention to the contentious case of Rule Consequentialism. (shrink)

In recent years, metaphysics has undergone what some describe as a revolution: it has become standard to understand a vast array of questions as questions about grounding, a metaphysical notion of determination. Why should we believe in grounding, though? Supporters of the revolution often gesture at what I call the Argument from Explanatoriness: the notion of grounding is somehow indispensable to a metaphysical type of explanation. I challenge this argument and along the way develop a “reactionary” view, according to which (...) there is no interesting sense in which the notion of grounding is explanatorily indispensable. I begin with a distinction between two conceptions of grounding, a distinction which extant critiques of the revolution have usually failed to take into consideration: grounding qua that which underlies metaphysical explanation and grounding qua metaphysical explanation itself. Accordingly, I distinguish between two versions of the Argument from Explanatoriness: the Unexplained Explanations Version for the first conception of grounding, and the Expressive Power Version for the second. The paper’s conclusion is that no version of the Argument from Explanatoriness is successful. (shrink)

Expressivists have a problem with negation. The problem is that they have not, to date, been able to explain why ‘murdering is wrong’ and ‘murdering is not wrong’ are inconsistent sentences. In this paper, I explain the nature of the problem, and why the best efforts of Gibbard, Dreier, and Horgan and Timmons don’t solve it. Then I show how to diagnose where the problem comes from, and consequently how it is possible for expressivists to solve it. Expressivists should accept (...) this solution, I argue, because it is demonstrably the only way of avoiding the problem, and because it generalizes. Once we see how to solve the negation problem, I show, it becomes easy to state a constructive, compositional expressivist semantics for a purely normative language with the expressive power of propositional logic, in which we can for the first time give explanatory, formally adequate expressivist accounts of logical inconsistency, logical entailment, and logical validity. As a corollary, I give what I take to be the first real expressivist explanation of why Geach’s original moral modus ponens argument is genuinely logically valid. This proves that the problem with expressivism cannot be that it can’t account for the logical properties of complex normative sentences. But it does not show that the same solution can work for a language with both normative and descriptive predicates, let alone that expressivists are able to deal with more complex linguistic constructions like tense, modals, or even quantifiers. In the final section, I show what kind of constraints the solution offered here would place expressivists under, in answering these further questions. (shrink)

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

We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x (...) ⊧ ⍯φ iff Vy(y ≠ x → y ⊧ φ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in ℒ $_{c}$ . Strong completeness of the normal ℒ $_{c}$ logics is proved with respect to models in which all worlds are named. Every ℒ $_{c}$ -logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from ℒ to ℒ $_{c}$ are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched. (shrink)

"A Special Case of Logical Contradiction – Content Implication Approach" The difference between so-called performative/pragmatic and logical contradiction seems to be one of the most firmly established philosophical distinctions. There are, however, some utterances, which fall outside this classification in its current form. Moreover, they reveal that the expressive power of the language of classical logic is too weak to express some form of the logical contradiction. The main aim of this paper is to characterize this special case (...) of the contradiction. By extending classical logic with a new connective, i.e. content implication, it also provides tools needed for adequate formal representation of this phenomenon. (shrink)

Quine taught us the difference between a theory’s ontology and its ideology. Ontology is the things a theory’s quantifiers must range over if it is true, Ideology is the primitive concepts that must be used to state the theory. This allows us to split the theoretical virtue of parsimony into two kinds: ontological parsimony and ideological parsimony. My goal is help illuminate the virtue of ideological parsimony by giving a criterion for ideological innocence—a rule for when additional ideology does not (...) count against parsimony. I propose the expressive power innocence criterion: if the ideology of theory one is expressively equivalent to that of theory two, then neither is ideologically simpler than the other. In its favor I offer the argument from accuracy, showing that any account of a theoretical virtue that is supposed to make theories that have it more likely to be true than theories that do not must respect it. Next I consider its ramifications, eliminating rival views and passing judgment on some arguments from parsimony that can be found in the literature. Finally, I consider two objections. First: I address an objection arising from the possibility of languages with a ‘primitive’ operator that allows us to list a theory’s primitives in the object-language. Second: I address an objection raised by Nelson Goodman against attempts to reckon simplicity by expressive power. Both objections fail. (shrink)

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive (...) power and meta-theoretic properties when comparing first-order and second-order logic. (shrink)

According to the cliché a picture is worth a thousand words. But this is a canard, for it vastly underestimates the expressive power of many pictures and diagrams. In this note we show that even a simple map such as the outline of Manhattan Island, accompanied by a pointer marking North, implies a vast infinity of statements—including a vast infinity of true statements.

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using (...) analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning. (shrink)

Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions (...) on the scope of quantifiers reveals a natural way out. (shrink)