Buddhist philosophers have developed a rich tradition of logic. Buddhist material on logic that forms the Buddhist tradition of logic, however, is hardly discussed or even known. This article presents some of that material in a manner that is accessible to contemporary logicians and philosophers of logic and sets agendas for global philosophy of logic.

Max Cresswell and Hilary Putnam seem to hold the view, often shared by classical logicians, that paraconsistent logic has not been made sense of, despite its well-developed mathematics. In this paper, I examine the nature of logic in order to understand what it means to make sense of logic. I then show that, just as one can make sense of non-normal modal logics (as Cresswell demonstrates), we can make `sense' of paraconsistent logic. Finally, I turn (...) the tables on classical logicians and ask what sense can be made of explosive reasoning. While I acknowledge a bias on this issue, it is not clear that even classical logicians can answer this question. (shrink)

Wittgenstein’s Tractatus construes the nature of reasoning in a manner which sharply conflicts with the conventional wisdom that logic is normative, not descriptive of thought. For although we sometimes seem to reason incorrectly, Wittgenstein denies that we can make logical mistakes (5.473). My aim in this paper is to show that the Tractatus provides us with good reasons to rethink some of the central assumptions that are standardly made in thinking about the relation between logic and thought. (...) In particular, the rejection of logical mistakes is to be understood in connection with Wittgenstein’s non-psychological approach to the thinking subject (5.641). On Wittgenstein's view, inference, understanding, and meaning are holistically related; cases of defective reasoning are to be explained in terms of a defective grasp of meaning which manifests in an indeterminate use of signs. Invalid reasoning therefore does not count for Wittgenstein as a species of reasoning, but rather as the mere illusion of reasoning. The rejection of logical mistakes thus gives voice to a radical disjunctivist approach. (shrink)

The starting point of this paper concerns the apparent difference between what we might call absolute truth and truth in a model, following Donald Davidson. The notion of absolute truth is the one familiar from Tarski’s T-schema: ‘Snow is white’ is true if and only if snow is white. Instead of being a property of sentences as absolute truth appears to be, truth in a model, that is relative truth, is evaluated in terms of the relation between sentences and models. (...) I wish to examine the apparent dual nature of logical truth (without dwelling on Davidson), and suggest that we are dealing with a distinction between a metaphysical and a linguistic interpretation of truth. I take my cue from John Etchemendy, who suggests that absolute truth could be considered as being equivalent to truth in the ‘right model’, i.e., the model that corresponds with the world. However, the notion of ‘model’ is not entirely appropriate here as it is closely associated with relative truth. Instead, I propose that the metaphysical interpretation of truth may be illustrated in modal terms, by metaphysical modality in particular. One of the tasks that I will undertake in this paper is to develop this modal interpretation, partly building on my previous work on the metaphysical interpretation of the law of non-contradiction (Tahko 2009). After an explication of the metaphysical interpretation of logical truth, a brief study of how this interpretation connects with some recent important themes in philosophical logic follows. In particular, I discuss logical pluralism and propose an understanding of pluralism from the point of view of the metaphysical interpretation. (shrink)

Work on the nature and scope of formal logic has focused unduly on the distinction between logical and extra-logical vocabulary; which argument forms a logical theory countenances depends not only on its stock of logical terms, but also on its range of grammatical categories and modes of composition. Furthermore, there is a sense in which logical terms are unnecessary. Alexandra Zinke has recently pointed out that propositional logic can be done without logical terms. By defining a logical-term-free (...) language with the full expressive power of first-order logic with identity, I show that this is true of logic more generally. Furthermore, having, in a logical theory, non-trivial valid forms that do not involve logical terms is not merely a technical possibility. As the case of adverbs shows, issues about the range of argument forms logic should countenance can quite naturally arise in such a way that they do not turn on whether we countenance certain terms as logical. (shrink)

In this paper, I argue that Goff's view that universal consciousness grounds logical laws such as the law of non-contradiction cannot be true on the grounds that we cannot guarantee the classical logic loving nature of universal consciousness that Goff desires in order to ground logical laws. I will present three arguments to show this.

The paper compares two theories of the nature of logic: Penelope Maddy's and my own. The two theories share a significant element: they both view logic as grounded not just in the mind (language, concepts, conventions, etc.), but also, and crucially, in the world. But the two theories differ in significant ways as well. Most distinctly, one is an anti-holist, "austere naturalist" theory while the other is a non-naturalist "foundational-holistic" theory. This methodological difference affects their questions, goals, (...) orientations, the scope of their investigations, their logical realism (the way they ground logic in the world), their explanation of the modal force of logic, and their approach to the relation between logic and mathematics. The paper is not polemic. One of its goal is a perspicuous description and analysis of the two theories, explaining their differences as well as commonalities. Another goal is showing that and how (i) a grounding of logic is possible, (ii) logical realism can be arrived at from different perspectives and using different methodologies, and (iii) grounding logic in the world is compatible with a central role for the human mind in logic. (shrink)

TWENTIETH-CENTURY ETHICS. AFTER NIETZSCHE -/- Preface This book tells the story of twentieth-century ethics or, in more detail, it reconstructs the history of a discussion on the foundations of ethics which had a start with Nietzsche and Sidgwick, the leading proponents of late-nineteenth-century moral scepticism. During the first half of the century, the prevailing trends tended to exclude the possibility of normative ethics. On the Continent, the trend was to transform ethics into a philosophy of existence whose self-appointed task was (...) that of describing the human condition as consisting of choices, as unavoidable as arbitrary, without any attempt at providing criteria for making such choices. In the Anglo-Saxon countries, the heir of ethics was a philosophy of morality, that is, an analysis of the language of morality that intended to clarify valuations without trying to justify them. 1958 was the year of the normative turn that led to the Rehabilitation of practical philosophy, a turn followed by decades of controversies between distinct kinds of normative ethics: utilitarian, Kantian, virtue ethics. While the controversy was raging, a quiet revolution took place, that of applied ethics which surprisingly dissolved the controversy's very subject matter by providing methods for making convergence possible on intermediate principles even when no agreement was available about first principles. The normative turn and the revolution of applied ethics have led us, at the turn of the century, to a goal that was quite far from the starting point. Instead of scepticism and relativism that was the fashion at the beginning of the century, at the beginning of the third millennium impartial and universal moral arguments seem to hold the spot being supported, if not by a final rational foundation, at least by reasonableness, the most precious legacy of the Enlightenment. -/- ● TABLE OF CONTENTS -/- ● I Anglo-Saxon philosophy: naturalism 1. Dewey beyond evolutionism and utilitarianism 2. Dewey and anti-essentialist moral epistemology 3. Dewey and naturalist moral ontology 4. Dewey and normative ethics of conduct and function 5. Perry and semantic naturalism -/- ● II Anglo-Saxon philosophy: ideal utilitarianism and neo-intuitionism 1. Moore's critique of utilitarian empiricism 2. Moore on the naturalistic fallacy 3. Moore on the nature of intrinsic value 4. Moore on ideal utilitarianism 5. Prichard on the priority of the right over the good 6. Ross's coherentist moral epistemology 7. Ross's moral ontology: realism, pluralism, and non-naturalism 8. Ross's normative ethics of prima facie duties -/- The chapter reconstructs the background of ideas, concerns and intentions out of which Moore's early essays, the preliminary version, and then the final version of Principia Ethica originated. It stresses the role of religious concerns, as well as that of the Idealist legacy. It argues that PE is more a patchwork of somewhat diverging contributions than a unitary work, not to say the paradigm of a new school in Ethics. -/- ●III Anglo-Saxon philosophy: non-cognitivism 1. The Scandinavian School, the Vienna circle and proto-emotivism 2. Wittgenstein and the ineffability of ethics 3. Russell's and Ayer's radical emotivism 4. Stevenson and moderate emotivism 5. Stevenson and the pragmatics of moral language 6. Stevenson and the methods for solving ethical disagreement 7. Hare and prescriptivism The chapter reconstructs first the discussion after Moore. The naturalistic-fallacy argument was widely accepted but twisted to prove instead that the intuitive character of the definition of 'good', its non-cognitive meaning, in a first phase identified with 'emotive' meaning. Alfred Julius Ayer is indicated as a typical proponent of such non-cognitivist meta-ethics. More detailed discussion is dedicated to Bertrand Russell's ethics, a more nuanced and sophisticated doctrine, arguing that non-cognitivism does not condemn morality to arbitrariness and that the project of rational normative ethics is still possible, heading finally to the justification of a kind of non-hedonist utilitarianism. Stevenson's theory, another moderate version of emotivism is discussed at some length, showing how the author comes close to the discovery of the role of a pragmatic dimension of language as a basis for ethical argument. A section reconstructs the discussion from the Forties about Hume's law, mentioning Karl Popper's argument and Richard Hare's early non-cognitivist but non-emotivist doctrine named prescriptivism. -/- ●IV Anglo-Saxon philosophy: critics of non-cognitivism 1. Neo-naturalism and its objections to the naturalistic fallacy argument 2. Objections to Hume's law 3. Clarence Lewis and the pragmatic contradiction 4. Toulmin and the good reasons approach 5. Baier and moral reasons 5. Baier, social moralities and the absolute morality 6. Baier and the moral point of view 7. Baier and the contents of absolute ethics -/- ● V Continental philosophy: the philosophy of values 1. Max Weber and the polytheism of values 2. Phenomenology against psychologism and rationalism 3. Reinach and the theory of social acts 4. Scheler and the material ethics of values 5. Hartmann and the ontology of values 6. Plessner, Gehlen and the Philosophische Anthropologie -/- The chapter illustrates first the idea of phenomenology and the Husserl's project of a phenomenological ethic as illustrated in his 1908-1914 lectures. The key idea is dismissing psychology and trying to ground a new science of the apriori of action, within which a more restricted field of inquiry will be the science of right actions. Then the chapter illustrates the criticism of modern moral philosophy conducted in the 1920 lectures, where the main target is naturalism, understood in the Kantian meaning of primacy of common sense. The third point illustrate is Adolph Reinach's theory of social acts as a key the grounding of norms, a view that sketches the ideas 'discovered' later by Clarence I. Lewis, John Searle, Karl-Otto Apel and Jürgen Habermas. A final section discusses Nicolai Hartman, who always refused to define himself a phenomenologist and yet developed a more articulated and detailed theory of 'values' – with surprising affinities with George E. Moore - than philosophers such as Max Scheler, who claimed to be Husserl's legitimate heirs. -/- ● VI Continental philosophy: the critics of the philosophy of values 1. Freud, the Superego and Civilization 2. Heidegger on original ethos against ethics 3. Sartre and de Beauvoir on authenticity and ambiguity 4. Adorno and Horkheimer on emancipation and immoralism -/- ●VII Post-liberal theologians and religious thinkers 1. Barth on the autonomy of faith from ethics 2. Developments of Reformed moral theology after Barth 3. Bonhoeffer on the concrete divine command and ethics of penultimate realities 4. Developments of Reformed and Catholic moral theology after world war II 5. Baeck and the transformation of liberal Judaism 6. Rosenzweig against liberal Judaism 7. Buber and religion as the vital lymph of morality 8. Heschel and Judaism as a science of actions -/- The chapter examines the main protagonists of Christian theology and Jewish religious thinking in the twentieth century. It stresses how the main dilemmas of contemporary philosophical ethics lie at the root of the various path of inquiry taken by these thinkers. -/- ● VIII Normative ethics: neo-Utilitarianism 1. The discussion on act and rule utilitarianism 2. Hare on two-tiered preference utilitarianism 3. Harsanyi, Gauthier and rational choice ethics 4. Parfit, utilitarianism and the idea of a person 5. Brandt and indirect conscience utilitarianism -/- The chapter addresses the issue of the complex process of self-transformation Utilitarianism underwent after Sidgwick's and Moore's fatal criticism and the unexpected Phoenix-like process of rebirth of a doctrine refuted. Two examples give the reader a glimpse at this uproarious process. The first is Roy Harrod Wittgensteinian transformation of utilitarianism in pure normative ethics depurated from hedonism as well as from whatsoever theory of the good. This transformation results in preference utilitarianism combined with a 'Kantian' version of rule utilitarianism. The second is Richard Hare's two-level preference utilitarianism, where act utilitarianism plays the function of the eventual rational justification of moral judgments and rule-utilitarianism that of an action-guiding practical device. -/- ● IX Normative ethics: neo-Aristotelianism and virtue ethics 1. Hannah Arendt, action and judgement 2. Hans-Georg Gadamer and phronesis 3. Alasdair MacIntyre on practices, virtues, and traditions 5. Stuart Hampshire on deliberation 6. Bernard Williams and moral complexity 7. Feminist ethics -/- Sect 1 reconstructs the post-war rediscovery of ethics by many German thinkers and its culmination in the Sixties in the movement named 'Rehabilitation of practical philosophy' is described. Heidegger's most brilliant disciples were the promoters of this Rehabilitation. Hans-Georg Gadamer is a paradigmatic example. His reading of Aristotle's lesson I reconstructed, starting with Heidegger's lesson but then subtly subverting its outcome thanks to the recovery of the significant role of the notion of phronesis. Sect 3 discusses the three theses defended by Anscombe in 'Modern Moral Philosophy'. It argues that: a) her answer to the question "why should I be moral?" requires a solution of the problem of theodicy, and ignores any attempts to save the moral point of view without recourse to divine retribution; b) her notion of divine law is an odd one more neo-Augustinian than Biblical or Scholastic; c) her image of Kantian ethics and intuitionism is the impoverished image manufactured by consequentialist opponents for polemical purposes and that she seems strangely accept it; d) the difficulty of identifying the "relevant descriptions" of acts is not an argument in favour of an ethics of virtue and against consequentialism or Kantian ethics, and indeed the role of judgment in the latter is a response to the difficulties raised by the case of judgment concerning future action. The chapter gives a short look at further developments in the neo-naturalist current trough a reconstruction of Philippa Foot's and Peter Geach's critiques to the naturalist-fallacy argument and Alasdair MacIntyre's grand reconstruction of the origins and allegedly inevitable failure of the Enlightenment project of an autonomous ethic. -/- ● X Normative ethics: Kantian and rights-based ethics 1. Dialogical constructivism 2. Apel, Habermas and discourse ethics 3. Gewirth and rights-based ethics 4. Nagel on agent-relative reasons 5. Donagan and persons as ends in themselves Parallel to the neo-Aristotelian trend, there was in the Rehabilitation of practical philosophy a Kantian current. This current started with the discovery of the pragmatic dimension of language carried out by Charles Peirce and the Oxford linguistic philosophy. On this basis, Karl-Otto Apel singled out as the decisive proponent of the linguistic and Kantian turn in German-speaking ethics, worked out the performative-contradiction argument while claiming that this was able to provide a new rational and universal basis for normative ethics. The chapter offers an examination of his argument in some detail, followed by a more cursory reconstruction of Jürgen Habermas's elaboration on Apel's theory. -/- ● XI The applied ethics renaissance 1. Elisabeth Anscombe on the atom bomb 2. From medical ethics to bioethics 3. Rawls and public ethics 3. Nozick, Dworkin and further developments of public ethics 5. Sen and the revival of economic ethics -/- The chapter presents the revolution of applied ethics while stressing its methodological novelty, exemplified primarily by Beauchamp and Childress principles approach and then by Jonsen and Toulmin's new casuistry. The chapter argues that Rawls's distinction between a "political" and a "metaphysical" approach to the theory of justice, one central part of ethical theory, is a formulation of the same basic idea at the root of both the principles approach and the new casuistry, both discussed in the following chapter. The idea is that it is possible to reach an agreement concerning positive moral judgments even though the discussion is still open – and in Rawls' view never will be close – on the essential criteria for judgment. -/- ● XII Fin-de-siècle metaethics 1. Deontic logics 2. Anti-realism 3. External realism 4. Internal realism 5. Kantian constructivism -/- The chapter illustrates the fresh start of meta-ethical discussion in the Eighties and Nineties and the resulting new alignments: metaphysical naturalism, internal realism, anti-realism, and constructivism. (shrink)

A recent trend in Husserl scholarship takes the Logische Untersuchungen (LU) as advancing an inconsistent and confused view of the non-conceptual content of perceptual experience. Against this, I argue that there is no inconsistency about non-conceptualism in LU. Rather, LU presents a hybrid view of the conceptual nature of perceptual experience, which can easily be misread as inconsistent, since it combines a conceptualist view of perceptual content (or matter) with a non-conceptualist view of perceptual acts. I show how this (...) hybrid view is operative in Husserl’s analyses of essentially occasional expressions and categorial intuition. And I argue that it can also be deployed in relation to Husserl’s analysis of the constitution of perceptual fullness, which allows it to avoid a objection raised by Walter Hopp—that the combination of Husserl’s analysis of perceptual fullness with conceptualism about perceptual content generates a vicious regress. (shrink)

My first paper on the Is/Ought issue. The young Arthur Prior endorsed the Autonomy of Ethics, in the form of Hume’s No-Ought-From-Is (NOFI) but the later Prior developed a seemingly devastating counter-argument. I defend Prior's earlier logical thesis (albeit in a modified form) against his later self. However it is important to distinguish between three versions of the Autonomy of Ethics: Ontological, Semantic and Ontological. Ontological Autonomy is the thesis that moral judgments, to be true, must answer to a realm (...) of sui generis non-natural PROPERTIES. Semantic autonomy insists on a realm of sui generis non-natural PREDICATES which do not mean the same as any natural counterparts. Logical Autonomy maintains that moral conclusions cannot be derived from non-moral premises.-moral premises with the aid of logic alone. Logical Autonomy does not entail Semantic Autonomy and Semantic Autonomy does not entail Ontological Autonomy. But, given some plausible assumptions Ontological Autonomy entails Semantic Autonomy and given the conservativeness of logic – the idea that in a valid argument you don’t get out what you haven’t put in – Semantic Autonomy entails Logical Autonomy. So if Logical Autonomy is false – as Prior appears to prove – then Semantic and Ontological Autonomy would appear to be false too! I develop a version of Logical Autonomy (or NOFI) and vindicate it against Prior’s counterexamples, which are also counterexamples to the conservativeness of logic as traditionally conceived. The key concept here is an idea derived in part from Quine - that of INFERENCE-RELATIVE VACUITY. I prove that you cannot derive conclusions in which the moral terms appear non-vacuously from premises from which they are absent. But this is because you cannot derive conclusions in which ANY (non-logical) terms appear non-vacuously from premises from which they are absent Thus NOFI or Logical Autonomy comes out as an instance of the conservativeness of logic. This means that the reverse entailment that I have suggested turns out to be a mistake. The falsehood of Logical Autonomy would not entail either the falsehood Semantic Autonomy or the falsehood of Ontological Autonomy, since Semantic Autonomy only entails Logical Autonomy with the aid of the conservativeness of logic of which Logical Autonomy is simply an instance. Thus NOFI or Logical Autonomy is vindicated, but it turns out to be a less world-shattering thesis than some have supposed. It provides no support for either non-cognitivism or non-naturalism. (shrink)

This paper presents two systems of natural deduction for the rejection of non-tautologies of classical propositional logic. The first system is sound and complete with respect to the body of all non-tautologies, the second system is sound and complete with respect to the body of all contradictions. The second system is a subsystem of the first. Starting with Jan Łukasiewicz's work, we describe the historical development of theories of rejection for classical propositional logic. Subsequently, we present the two (...) systems of natural deduction and prove them to be sound and complete. We conclude with a ‘Theorem of Inversion’. (shrink)

The philosophy of superdeterminism is based on a single scientific fact about the universe, namely that cause and effect in physics are not real. In 2020, accomplished Swedish theoretical physicist, Dr. Johan Hansson published a physics proof using Albert Einstein’s Theory of Special Relativity that our universe is superdeterministic meaning a predetermined static block universe without cause and effect in physics. In the absence of cause and effect in physics, past, present and future events must all exist equally in logical (...) relationship. Our experience of time must be an illusion, because our experience of change in our world is not actually caused in time. Rather, the change we experience in our world is caused by the changing appearances in our static block universe in the static fourth dimension of time. We should think of time as a distance in the fourth dimension of time from our present position in the dimension of time to another position either towards or away from the beginning of the universe. Because physical reality is not actually caused to change in our static block universe, then static physical reality is actually timeless. But, because very good evidence supports the creation of timeless physical reality, then non-temporal causation of timeless physical reality outside of time is real. (shrink)

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth-conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the `logicality of language', accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter-examples consisting of acceptable tautologies and contradictions, the logicality of language is often paired (...) with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is `blind' to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non-classical---indeed quite exotic---kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis-a-vis its open class terms and employs a deductive system that is basically classical. (shrink)

According to the scientific ideal of modernity, the propositions of science are considered fundamentally fallible. On the other hand, science strives for objective knowledge. Kant saw in the apriori the precondition for objective knowledge. But with the new conception of science the apriori (if it is not to be only logic) has become problematic. With it, however, the objectivity of scientific knowledge is at stake. As long as one grants objectivity to scientific knowledge, the question of the (...) apriori remains topical. On the one hand, this volume wants to trace the historical roots as well as the different interpretations of the apriori, and on the other hand, it wants to ask for approaches for a contemporary reinterpretation of this basic concept. (shrink)

What separates the unique nature of human consciousness and that of an entity that can only perceive the world via strict logic-based structures? Rather than assume that there is some potential way in which logic-only existence is non-feasible, our species would be better served by assuming that such sentient existence is feasible. Under this assumption, artificial intelligence systems (AIS), which are creations that run solely upon logic to process data, even with self-learning architectures, should therefore not (...) face the opposition they have to gaining some legal duties and protections insofar as they are sophisticated enough to display consciousness akin to humans. Should our species enable AIS to gain a digital body to inhabit (if we have not already done so), it is more pressing than ever that solid arguments be made as to how humanity can accept AIS as being cognizant of the same degree as we ourselves claim to be. By accepting the notion that AIS can and will be able to fool our senses into believing in their claim to possessing a will or ego, we may yet have a chance to address them as equals before some unforgivable travesty occurs betwixt ourselves and these super-computing beings. (shrink)

The depth-bounded approach seeks to provide realistic models of reasoners. Recognizing that most useful logics are idealizations in that they are either undecidable or likely to be intractable, the approach accounts for how they can be approximated in practice by resource-bounded agents. The approach has been applied to Classical Propositional Logic (CPL), yielding a hierarchy of tractable depth-bounded approximations to that logic, which in turn has been based on a KE/KI system. -/- This Thesis shows that the approach (...) can be naturally extended to useful nonclassical logics such as First-Degree Entailment (FDE), the Logic of Paradox (LP), Strong Kleene Logic (K3 ) and Intuitionistic Propositional Logic (IPL). To do this, we introduce a KE/KI-style system for each of those logics such that: is formulated via signed formulae, consist of linear operational rules and branching structural rule(s), can be used as a direct-proof and a refutation method, and is interesting independently of the approach in that it has an exponential speed-up on its tableau system counterpart. The latter given that we introduce a new class of examples which we prove to be hard for all tableau systems sharing the V/& rules with the classical one, but easy for their analogous KE-style systems. Then we focus on showing that each of our KE/KI-style systems naturally yields a hierarchy of tractable depth-bounded approximations to the respective logic, in terms of the maximum number of allowed nested applications of the branching rule(s). The rule(s) express(es) a generalized rule of bivalence, is (are) essentially cut rule(s) and govern(s) the manipulation of virtual information, which is information that an agent does not hold but she temporarily assumes as if she held it. Intuitively, the more virtual information needs to be invoked via the branching rule(s), the harder the inference is for the agent. So, the nested application the branching rule(s) provides a sensible measure of inferential depth. We also show that each hierarchy approximating FDE, LP, and K3 , admits of a 5-valued non-deterministic semantics; whereas, paving the way for a semantical characterization of the hierarchy approximating IPL, we provide a 3-valued non-deterministic semantics for the full logic that fixes the meaning of the connectives without appealing to “structural” conditions. -/- Moreover, we show a super-polynomial lower bound for the strongest possible version of clausal tableaux on the well-known class of “truly fat” expressions (which are easy for KE), settling a problem left open in the literature. Further, we investigate a hierarchy of tractable depth-bounded approximations to CPL based only on KE. Finally, we propose a refinement of the p-simulation relation which is adequate to establish positive results about the superiority of a system over another with respect to proof-search. (shrink)

One well-known objection to the traditional Lewis-Stalnaker semantics of counterfactuals is that it delivers counterintuitive semantic verdicts for many counterpossibles (counterfactuals with necessarily false antecedents). To remedy this problem, several authors have proposed extending the set of possible worlds by impossible worlds at which necessary falsehoods may be true. Linguistic ersatz theorists often construe impossible worlds as maximal, inconsistent sets of sentences in some sufficiently expressive language. However, in a recent paper, Bjerring (2014) argues that the “extended” Lewis-Stalnaker semantics delivers (...) the wrong truth-values for many counterpossibles if impossible worlds are required to be maximal. To make room for non-maximal or partial impossible worlds, Bjerring considers two alternative world-ontologies: either (i) we construe impossible worlds as arbitrary (maximal or partial) inconsistent sets of sentences, or (ii) we construe them as (maximal or partial) inconsistent sets of sentences that are closed and consistent with respect to some non-classical logic. Bjerring raises an objection against (i), and suggests that we opt for (ii). In this paper, I argue, first, that Bjerring’s objection against (i) conflates two different conceptions of what it means for a logic to be true at a world. Second, I argue that (ii) imposes too strong constraints on what counts as an impossible world. I conclude that linguistic ersatzists should construe impossible worlds as arbitrary (maximal or partial) inconsistent sets of sentences. (shrink)

While there is considerable disagreement on the precise nature of material objecthood, it is standardly assumed that material objects must be spatial. In this paper, I provide two arguments against this assumption. The first argument is made from largely a priori considerations about modal plenitude. The possibility of non-spatial material objects follows from commitment to certain plausible principles governing material objecthood and plausible principles regarding modal plenitude. The second argument draws from current philosophical discussions regarding theories of quantum gravity (...) and the emergence of spacetime. When it is appreciated what possible worlds these current theories commit us to, the possibility of non-spatial material objects will follow. Thus, either route will lead us to the possibility of non-spatial material objects. The significance of this result is that we need to revise our accounts of material objecthood to both accommodate these possibilities and the theories that lead to them. (shrink)

Husserl’s theory of fulfilment conceives of empty acts, such as symbolic thought, and fulfilling acts, such as sensory perceptions, in a strict parallel. This parallelism is the basis for Husserl’s semantics, epistemology, and conception of truth. It also entails that any true proposition can be known in principle, which Church and Fitch have shown to explode into the claim that every proposition is _actually_ known. I assess this logical challenge and discuss a recent response by James Kinkaid. While Kinkaid’s proposal (...) saves one direction of the parallel for semantics, it gives up the parallelism for truth. I spell out a different response which meshes naturally with Husserl’s account of meaning. If the parallelism is restricted to a class of basic propositions, the truth of non-basic propositions can be defined inductively, without leading to the paradox. I then discuss objections that have been raised against a similar proposal by Dummett. The result is that exegetically plausible and popular interpretations of Husserl’s correlationism are indeed challenged by Church and Fitch. But when taking into account the ‘logical adumbration’ of propositional blindspots, truth and possible fulfilment can be connected without paradox. (shrink)

Are properties perfectly natural (or not) relative to worlds, or are they perfectly natural (or not) tout court? That is, could there be a property P that is instanti-ated at worlds w1 and w2, and is perfectly natural at w1 but not at w2? Here, we offer an original argument for the non-world-relativity of perfect naturalness. Along the way, we reply to a prima facie compelling argument for the contin-gency of perfect naturalness, based upon the connection between natural prop-erties and (...) laws of nature. (shrink)

Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices (which he called quasi-matrices), in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlev’s hierarchy, also proposing weaker six-valued systems in which the (T) axiom was replaced by the deontic (D) axiom. In this paper, we (...) propose even weaker systems, by eliminating both axioms, which are characterized by eight-valued non-deterministic matrices. In addition, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary (deterministic) logical matrices would be possible for all those Ivlev-like systems. We will show that finite deterministic matrices do not characterize any of them. (shrink)

"It is difficult not to notice a curious unrest in the philosophic atmosphere of the time, a loosening of old landmarks, a softening of oppositions, a mutual borrowing from one another on the part of systems anciently closed, and an interest in new suggestions, however vague, as if the one thing sure were the inadequacy of extant school-solutions. The dissatisfactions with these seems due for the most part to a feeling that they are too abstract and academic. Life is confused (...) and superabundant, and what the younger generation appears to crave is more of the temperament of life in its philosophy, even though it were at some cost of logical rigor and formal purity." - William James (1904). -/- Abstract: The study of model-based reasoning (MBR) is one of the most interesting recent developments at the intersection of psychology and the philosophy of science. Although a broad and eclectic area of inquiry, one central axis by which MBR connects these disciplines is anchored at one end in theories of internal reasoning (in cognitive science), and at the other, in C.S. Peirce’s semiotics (in philosophy). In this paper, we attempt to show that Peirce’s semiotics actually has more natural affinity on the psychological side with ecological psychology, as originated by James J. Gibson and especially Egon Brunswik, than it does with non-interactionist approaches to cognitive science. In particular, we highlight the strong ties we believe to exist between the triarchic structure of semiotics as conceived by Peirce, and the similar triarchic stucture of Brunswik’s lens model of organismic achievement in irreducibly uncertain ecologies. The lens model, considered as a theory of creative abduction, provides a concrete instantiation of at least one, albeit limited, interpretation of Peirce’s semiotics, one that we believe could be quite fruitful in future theoretical and empirical investigations of MBR in both science an philosophy. (shrink)

Almost any mainstream reading about the nature of Kant's 'content of cognition' in both non-conceptualist and conceptualist camps agree that 'singular representations' (sensible intuitions) are, at least in some weak sense, objectdependent because they supervene on a manifold of sensations that are given through the disposition of our sensibility and parallel thus the real and physical components of the world (cf. McDowell 1996, Allison 1983, Ginsborg 2008, Allais 2009). The relevant class of sensible intuitions should refer, as they argue, (...) only to empirical and not to pure ones. Kant's transcendental argument creates, however, no implications as to the metaphysics of properties. Neither does he consider the world to be consisted of sensory content simpliciter nor do sensations refer to objects per se. Instead, he provides an all-encompassing pattern for sensible intuitions of any kind through the representation of space as a cognitive map in that an object can be represented if spatial properties are attributed to it. Sensible intuitions of any kind could be referring, that is to say, and can be conceptualized if they are spatial. Consequently and unlike the contemporary philosophy of perception, Kant contrasts sensible intuitions and pure concepts of understanding 'altogether' against one single experience, from which the justification of objects should proceed. In other words, what stands at the core of exposing the content of cognition concerns not the phenomenological status and actuality of sensible intuitions in the sense of 'bits of experiential intake', but the logical structure of possibility of sensible intuitions of any (external or internal) causal background. The aim of this discussion is to clarify that Kant's transcendental idealism mutatis mutandis reviews multiple and diverse kinds of 'data of mind' and cognition in the background, without reducing the content of cognition to metaphysically determined referents as 'matters of fact' and to pure concepts of understanding. Sensible intuitions in the sense of content of cognition vary, most importantly, from unstructured and unjustifiable data of mind including (physical) contents of perception and stuff of mind and also from reflective and intellectual intuitions that are the cognates of the structured complex singular representations. Put it in simple terms, Kant advocates the thesis that 'facts' are objects for concepts if they are already well-founded trough the cognitive map of the representation of space. -/- . (shrink)

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. (...) Specifically, a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

Cultural landscapes represent a complex category where the nature-culture dichotomy seem to not be able to unfold the main features and the profound relations that humans have with the environment. Drawing on ethnographic data collected in the saltpans of Se-ovlje (Slovene Istria) and Janubio (Lanzarote--Canary Islands) this article examines informant`s perceptions about the awareness of the importance and the enhancement of the holistic values of both saltpans, as well as the impacts and benefits of tourism. Comparing these perceptions about (...) both cultural landscapes, I try to suggest that the complex fruitfully relations between humans and nature in these saltpans are at odds with the neoliberal logic of nature which exploit and commoditize its resources depriving them of their respective agency. A sustainability to contrast the harmful activities of the market ought to be understood not as a simply isolation and fencing of nature for the sake of conservation, but as a preservation that need to foster the continuity of the deep interactions between human culture and non-human nature which are the core of the cultural landscapes. (shrink)

Abstract McDowell's contributions to epistemology and philosophy of mind turn centrally on his defense of the Aristotelian concept of a ?rational animal?. I argue here that a clarification of how McDowell uses this concept can make more explicit his distance from Davidson regarding the nature of the minds of non-rational animals. Close examination of his responses to Davidson and to Dennett shows that McDowell is implicitly committed to avoiding the following ?false trichotomy?: that animals are not bearers of semantic (...) content at all, that they are bearers of content in the same sense we are, and that they are bearer of "as if" content. Avoiding the false trichotomy requires that we understand non-rational animals as having concepts but not as making judgments. Furthermore, we need to supplement McDowell's distinction between the logical spaces of reasons and of the realm of law with what Finkelstein calls ?the logical space of animate life?. Though McDowell has taken some recent steps to embrace a view like this, I urge a more demanding conception than what McDowell has thus far suggested. (shrink)

The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of Language Signs and the (...) Problem of Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)

When we see or hear a spontaneous emotional expression, we usually immediately, effortlessly, and often correctly interpret it to mean happiness, sadness, or some other emotion as well as what this emotion is about. How do we do that? In this article, I evaluate how useful the concepts of natural meaning and probabilistic meaning are when it comes to explaining how we and other animals interpret emotional signs displayed without communicative intentions. I argue that Grice’s notion of natural meaning, because (...) it is a factive relation, is too restrictive for this purpose. I then present the notion of probabilistic meaning. The latter seems adequate for analyzing our ability to interpret non-communicative emotional signs, but it faces several difficulties when it comes to analyzing how we and other animals interpret emotional _signals_, i.e. signs that have the function to communicate emotional information. I present three of these difficulties. En passant, I suggest that a teleosemantic notion may be better suited for these challenges. (shrink)

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory (...) validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities. (shrink)

Foundations of Relational Realism presents an intuitive interpretation of quantum mechanics, based on a revised decoherent histories interpretation, structured within a category theoretic topological formalism. -/- If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed the limits of intuitive (...) vision, if not intuitive comprehension. For many physicists and philosophers, however, the currently fashionable tendency toward exotic interpretation of the theoretical formalism is recognized not as a mark of ascent for the tower of physics, but rather an indicator of sway—one that must be dampened rather than encouraged if practical progress is to continue. -/- In this unique two-part volume, designed to be comprehensible to both specialists and non-specialists, the authors chart out a pathway forward by identifying the central deficiency in most interpretations of quantum mechanics: That in its conventional, metrical depiction of extension, inherited from the Enlightenment, objects are characterized as fundamental to relations—i.e., such that relations presuppose objects but objects do not presuppose relations. The authors, by contrast, argue that quantum mechanics exemplifies the fact that physical extensiveness is fundamentally topological rather than metrical, with its proper logico-mathematical framework being category theoretic rather than set theoretic. -/- By this thesis, extensiveness fundamentally entails not only relations of objects, but also relations of relations. Thus, the fundamental quanta of quantum physics are properly defined as units of logico-physical relation rather than merely units of physical relata as is the current convention. Objects are always understood as relata, and likewise relations are always understood objectively. In this way, objects and relations are coherently defined as mutually implicative. The conventional notion of a history as “a story about fundamental objects” is thereby reversed, such that the classical “objects” become the story by which we understand physical systems that are fundamentally histories of quantum events. -/- These are just a few of the novel critical claims explored in this volume—claims whose exemplification in quantum mechanics will, the authors argue, serve more broadly as foundational principles for the philosophy of nature as it evolves through the twenty-first century and beyond. (shrink)

Contemporary natural-language semantics began with the assumption that the meaning of a sentence could be modeled by a single truth condition, or by an entity with a truth-condition. But with the recent explosion of dynamic semantics and pragmatics and of work on non- truth-conditional dimensions of linguistic meaning, we are now in the midst of a shift away from a truth-condition-centric view and toward the idea that a sentence’s meaning must be spelled out in terms of its various roles in (...) conversation. This communicative turn in semantics raises historical questions: Why was truth-conditional semantics dominant in the first place, and why were the phenomena now driving the communicative turn initially ignored or misunderstood by truth-conditional semanticists? I offer a historical answer to both questions. The history of natural-language semantics—springing from the work of Donald Davidson and Richard Montague—began with a methodological toolkit that Frege, Tarski, Carnap, and others had created to better understand artificial languages. For them, the study of linguistic meaning was subservient to other explanatory goals in logic, philosophy, and the foundations of mathematics, and this subservience was reflected in the fact that they idealized away from all aspects of meaning that get in the way of a one-to-one correspondence between sentences and truth-conditions. The truth-conditional beginnings of natural- language semantics are best explained by the fact that, upon turning their attention to the empirical study of natural language, Davidson and Montague adopted the methodological toolkit assembled by Frege, Tarski, and Carnap and, along with it, their idealization away from non-truth-conditional semantic phenomena. But this pivot in explana- tory priorities toward natural language itself rendered the adoption of the truth-conditional idealization inappropriate. Lifting the truth-conditional idealization has forced semanticists to upend the conception of linguistic meaning that was originally embodied in their methodology. (shrink)

It is often assumed that theorizing in terms of natural properties is more objectively valuable than theorizing in terms of non-natural properties. But this assumption faces an explanatory challenge: explain the greater objective value of theorizing in terms of natural properties. In this paper, I answer that challenge by proposing and exploring three different accounts of the objective value of naturalness. Two appeal to constitutive natures: it is part of the constitutive nature of explanation, or of objective value, that (...) theorizing in terms of natural properties is more objectively valuable. The third appeals to the theoretical role that naturalness plays. (shrink)

In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its deductions include both (...) the direct and the indirect deductions constructed with the three traditional rules. IL3 is a hybrid of IL1 and IL2: its deductions are all direct as in IL1 but it deals with identities and inidentities as in IL2. IL1 and IL2 have a high degree of naturalness. Although the hybrid system IL3 was constructed as an artifact useful in the mathematical study of IL1 and IL2, it nevertheless has some intrinsically interesting aspects. The main motivation for describing and studying such simple systems is pedagogical. In teaching beginning logic one would like to present a system of logic which has the following properties. First, it exemplifies the main ideas of logic: implication, deduction, non-implication, counterargument(or countermodel), logical truth, self-contradiction, consistency,satisfiability, etc. Second, it exemplifies the usual general metaprinciples of logic: contraposition and transitivity of implication, cut laws, completeness,soundness, etc. Third, it is simple enough to be thoroughly grasped by beginners. Fourth, it is obvious enough so that its rules do not appear to be arbitrary or purely conventional. Fifth, it does not invite confusions which must be unlearned later. Sixth, it involves a minimum of presuppositions which are no longer accepted in mainstream contemporary logic. (shrink)

This is a thesis in support of the conceptual yoking of analytic truth to a priori knowledge. My approach is a semantic one; the primary subject matter throughout the thesis is linguistic objects, such as propositions or sentences. I evaluate arguments, and also forward my own, about how such linguistic objects’ truth is determined, how their meaning is fixed and how we, respectively, know the conditions under which their truth and meaning are obtained. The strategy is to make explicit what (...) is distinctive about analytic truths. The objective is to show that truths, known a priori, are trivial in a highly circumscribed way. My arguments are premised on a language-relative account of analytic truth. The language relative account which underwrites much of what I do has two central tenets: 1. Conventionalism about truth and, 2. Non-factualism about meaning. I argue that one decisive way of establishing conventionalism and non-factualism is to prioritise epistemological questions. Once it is established that some truths are not known empirically an account of truth must follow which precludes factual truths being known non-empirically. The function of Part 1 is, chiefly, to render Carnap’s language-relative account of analytic truth. I do not offer arguments in support of Carnap at this stage, but throughout Parts 2 and 3, by looking at more current literature on a priori knowledge and analytic truth, it becomes quickly evident that I take Carnap to be correct, and why. In order to illustrate the extent to which Carnap’s account is conventionalist and non-factualist I pose his arguments against those of his predecessors, Kant and Frege. Part 1 is a lightly retrospective background to the concepts of ‘analytic’ and ‘a priori’. The strategy therein is more mercenary than exegetical: I select the parts from Kant and Frege most relevant to Carnap’s eventual reaction to them. Hereby I give the reasons why Carnap foregoes a factual and objective basis for logical truth. The upshot of this is an account of analytic truth (i.e. logical truth, to him) which ensures its trivial nature. In opposition to accounts of a priori knowledge, which describe it as knowledge gained from rational apprehension, I argue that it is either knowledge from logical deduction or knowledge of stipulations. I therefore reject, in Part 2, three epistemologies for knowing linguistic conventions (e.g. implicit definitions): 1. intuition, 2. inferential a priori knowledge and, 3. a posteriori knowledge. At base, all three epistemologies are rejected because they are incompatible with conventionalism and non-factualism. I argue this point by signalling that such accounts of knowledge yield unsubstantiated second-order claims and/or they render the relevant linguistic conventions epistemically arrogant. For a convention to be arrogant it must be stipulated to be true. The stipulation is then considered arrogant when its meaning cannot be fixed, and its truth cannot be determined without empirical ‘work’. Once a working explication of ‘a priori’ has been given, partially in Part 1 (as inferential) and then in Part 2 (as non-inferential) I look, in Part 3, at an apriorist account of analytic truth, which, I argue, renders analytic truth non-trivial. The particular subject matter here is the implicit definitions of logical terms. The opposition’s argument holds that logical truths are known a priori (this is part of their identification criteria) and that their meaning is factually based. From here it follows that analytic truth, being determined by factually based meaning, is also factual. I oppose these arguments by exposing the internal inconsistencies; that implicit definition is premised on the arbitrary stipulation of truth which is inconsistent with saying that there are facts which determine the same truth. In doing so, I endorse the standard irrealist position about implicit definition and analytic truth (along with the “early friends of implicit definition” such as Wittgenstein and Carnap). What is it that I am trying to get at by doing all of the abovementioned? Here is a very abstracted explanation. The unmitigated realism of the rationalists of old, e.g. Plato, Descartes, Kant, have stoically borne the brunt of the allegation of yielding ‘synthetic a priori’ claims. The anti-rationalist phase of this accusation I am most interested in is that forwarded by the semantically driven empiricism of the early 20th century. It is here that the charge of the ‘synthetic a priori’ really takes hold. Since then new methods and accusatory terms are employed by, chiefly, non-realist positions. I plan to give these proper attention in due course. However, it seems to me that the reframing of the debate in these new terms has also created the illusion that current philosophical realism, whether naturalistic realism, realism in science, realism in logic and mathematics, is somehow not guilty of the same epistemological and semantic charges levelled against Plato, Descartes and Kant. It is of interest to me that in, particularly, current analytic philosophy (given its rationale) realism in many areas seems to escape the accusation of yielding synthetic priori claims. Yet yielding synthetic a priori claims is something which realism so easily falls prey to. Perhaps this is a function of the fact that the phrase, ‘synthetic a priori’, used as an allegation, is now outmoded. This thesis is nothing other than an indictment of metaphysics, or speculative philosophy (this being the crime), brought against a specific selection of realist arguments. I, therefore, ask of my reader to see my explicit, and perhaps outmoded, charge of the ‘synthetic a priori’ levelled against respective theorists as an attempt to draw a direct comparison with the speculative metaphysics so many analytic philosophers now love to hate. I think the phrase ‘synthetic a priori’ still does a lot of work in this regard, precisely because so many current theorists wrongly think they are immune to this charge. Consequently, I shall say much about what is not permitted. Such is, I suppose, the nature of arguing ‘against’ something. I’ll argue that it is not permitted to be a factualist about logical principles and say that they are known a priori. I’ll argue that it is not permitted to say linguistic conventions are a posteriori, when there is a complete failure in locating such a posteriori conventions. Both such philosophical claims are candidates for the synthetic a priori, for unmitigated rationalism. But on the positive side, we now have these two assets: Firstly, I do not ask us to abandon any of the linguistic practises discussed; merely to adopt the correct attitude towards them. For instance, where we use the laws of logic, let us remember that there are no known/knowable facts about logic. These laws are therefore, to the best of our knowledge, conventions not dissimilar to the rules of a game. And, secondly, once we pass sentence on knowing, a priori, anything but trivial truths we shall have at our disposal the sharpest of philosophical tools. A tool which can only proffer a better brand of empiricism. (shrink)

The obscure and punctuated history of symmetry is compared with the history of the celebrated and exalting notion of infinitesimal; some considerations about them are derived. A long list of odd and hidden events concerning symmetry in theoretical physics is offered. The last event is the discovery of the nature of the same word “symmetry” which pertains to non-classical logic, and it is linked to the principle of sufficient reason. A comparison of the roles played by the two (...) mathematical techniques within a classical physical theory is performed. It leads to recognize the different roles played by the two mathematical tools as a manifestation of an incommensurability phenomenon caused by two foundational dichotomies. (shrink)

Standard responses to the question of the nature of logic can be broadly classified into two, namely: logical monists that privilege traditional logic above non-traditional logic and logical pluralists who recognize the legitimacy of many-valued logic and use same to argue for some form of logical relativity. The line of distinction appears to be fairly clear as traditional, Aristotelian, two-valued and standard logic maintains fidelity with the principle of bivalence and the traditional laws of (...) thought while non-traditional, non-Aristotelian, many-valued, non-standard or alternative logics somehow break their fidelity to the principle of bivalence and the traditional laws of thought. It appears to be settled that relativity typically belongs only to non-traditional logics. Contrary to this understanding, this paper argued that some level of relativity Is presupposed in traditional logic by the legitimacy enjoyed by syllogistic, propositional and predicate logics as a body of systems that make up traditional logic. This paper called for the revision of monistic approaches to traditional logic. Since there is some measure of relativity among traditional systems of logic, de-emphasizing the differences among syllogistic, propositional and predicate logics while stressing their unity as 'traditional logic' leads to the fallacy of accent. This fallacy occurs when theorists place vocal emphasis on the unity among traditional logical systems while ignoring their differences. (shrink)

In a possible world framework, an agent can be said to know a proposition just in case the proposition is true at all worlds that are epistemically possible for the agent. Roughly, a world is epistemically possible for an agent just in case the world is not ruled out by anything the agent knows. If a proposition is true at some epistemically possible world for an agent, the proposition is epistemically possible for the agent. If a proposition is true at (...) all epistemically possible worlds for an agent, the proposition is epistemically necessary for the agent, and as such, the agent knows the proposition. -/- This framework presupposes an underlying space of worlds that we can call epistemic space. Traditionally, worlds in epistemic space are identified with possible worlds, where possible worlds are the kinds of entities that at least verify all logical truths. If so, given that epistemic space consists solely of possible worlds, it follows that any world that may remain epistemically possible for an agent verifies all logical truths. As a result, all logical truths are epistemically necessary for any agent, and the corresponding framework only allows us to model logically omniscient agents. This is a well-known consequence of the standard possible world framework, and it is generally taken to imply that the framework cannot be used to model non-ideal agents that fall short of logical omniscience. -/- A familiar attempt to model non-ideal agents within a broadly world involving framework centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in epistemic space, it is easy to avoid logical omniscience. If any logical falsehood is true at some impossible world, then any logical falsehood may remain epistemically possible for some agent. As a result, we can use an impossible world involving framework to model extremely non-ideal agents that do not know any logical truths. -/- A much harder, and considerably less investigated challenge is to ensure that the resulting epistemic space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out impossible worlds that verify obvious logical falsehoods. To model such agents, we need a construction of a non-trivial epistemic space that partly consists of impossible worlds where not "anything goes". This involves imposing substantive constraints on impossible worlds to eliminate from epistemic space, say, trivially impossible worlds that verify obvious logical falsehoods. -/- The central aim of this dissertation is to investigate the nature of such non-trivially impossible worlds and the corresponding epistemic spaces. To flag my conclusions, I argue that successful constructions of epistemic spaces that can safely navigate between the Charybdis of logical omniscience and the Scylla of of “anything goes” are hard, if not impossible to find. (shrink)

This paper presents the unification of all knowledge and the framework of all sciences, so it goes the theory of consciousness, the method to measure consciousness, and the three keys of the Strong AI. “Logicality and non-absoluteness” is found out to be the intrinsicality of nature, so the “Fundamental Law of Nature” is discovered. Then, the “general methodology of research” and the “model system of nature” are developed to explain everything, especially consciousness. The Coupling Theory of Consciousness (...) tells that nature has the MFEs (More Fundamental Element) that couple to show as material and consciousness, and the brain has a CNS (central nervous system)-independent consciousness system that couples to give off the consciousness signals, with their three excitation levels to show as memory, sub-consciousness, and subjective consciousness. As consciousness is not from neurons, the method to measure consciousness via NCC (neural correlates of consciousness) is to find out participants with the same kinds of consciousness systems. And make them to produce paralleled “conscious information processes” to filtrate out the “noise” neural activities, to obtain the “real” NCC data. Examining the property of consciousness may advance not only neuroscience and physics, but also cognitive science and AI technology. First, the “conscious information processing” model has shown that the Strong AI should process the beyond-domain concepts with a self-controlled intention, second, as the “general methodology of research” is just the other name of the “principle of cognition”, we have already known the running style of the Strong AI. Hopefully, we could develop the Strong AI technology to upgrade human civilization very soon. (shrink)

It is well known the harmful effects that savage capitalism has been causing to the environment since its introduction in a sphere in which a different logic and approach to nature are the essential conditions for the maintenance of the ecosystem and its complex relations between humans and non-human organisms. The amazon rainforest is a portion of the planet in which for thousands of years its human dwellers have been interacting with nature that it is understood beyond (...) its physical condition. Thus, to what extent Amazonian’s approaches to nature could be considered as a moral philosophy through which the way of conceptualizing nature and its non-human denizens enhances the continuity of life and the intimate relations between entities? To answer this question, I will explore the cosmological system of the Shuar of the Ecuadorian Amazon with whom I lived for 5 months between July and November 2018, and thereby elucidate the spiritual relations that this society has with the metaphysical domain of nature. (shrink)

It was something of a dogma for much of the twentieth century that one cannot validly derive an ought from an is. More generally, it was held that non-normative propositions do not entail normative propositions. Call this thesis about the relation between the natural and the normative Natural-Normative Autonomy. The denial of Autonomy involves the entanglement of the natural with the normative. Naturalism entails entanglement—in fact it entails the most extreme form of entanglement—but entanglement does not entail naturalism. In a (...) ground-breaking paper “The autonomy of ethics” Arthur Prior constructed some intriguing counterexamples to Autonomy. While his counterexamples have convinced few, there is little agreement on what is wrong with them. I present a new analysis of Autonomy, one which is grounded in a general and independently plausible account of subject matters. While Prior’s arguments do establish shallow natural-normative entanglement, this is a consequence of simple logical relationships that hold between just about any two subject matters. It has nothing special to do with the logical structure of normativity or its relation to the natural. Prior’s arguments leave the fundamental idea behind natural-normative Autonomy intact. I offer a new argument for deep entanglement. I show that in any framework adequate for dealing with the natural and the normative spheres, a purely natural proposition entails a purely normative proposition, and vice-versa. But this is no threat to non-naturalist moral realism. In fact it helps ameliorate the excesses of an extreme non-naturalism, delivering a more palatable and plausible position. (shrink)

The article reviews some analyses of temporal language in logical approaches to natural language semantics. It considers some asymmetries between past and future, manifested in language, which motivate the “standard view” of the non-reversibility of time and the persistence of the past. It concludes with a puzzle about the changing past which challenges the standard view.

In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories (...) of the “syllogism” in the Aristotelian and Stoic traditions. However, because the context in which these theories were developed and discussed were deeply epistemological in nature, we will also include references to the areas of epistemological theorizing that bear directly on theories of the syllogism, particularly concerning “demonstration.” Similarly, we will include literature that discusses the principles governing logic and the components that make up arguments, which are topics that might now fall under the headings of philosophy of logic or non-classical logic. This includes discussions of problems and paradoxes that connect to contemporary logic and which historically spurred developments of logical method. For example, there is great interest among ancient philosophers in the question of whether all statements have truth-values. Relevant themes here include future contingents, paradoxes of vagueness, and semantic paradoxes like the liar. We also include discussion of the paradoxes of the infinite for similar reasons, since solutions have introduced sophisticated tools of logical analysis and there are a range of related, modern philosophical concerns about the application of some logical principles in infinite domains. Our criterion excludes, however, many of the themes that Hellenistic philosophers consider part of logic, in particular, it excludes epistemology and metaphysical questions about truth. Ancient philosophers do not write treatises “On Logic,” where the topic would be what today counts as logic. Instead, arguments and theories that count as “logic” by our criterion are found in a wide range of texts. For the most part, our entry follows chronology, tracing ancient logic from its beginnings to Late Antiquity. However, some themes are discussed in several eras of ancient logic; ancient logicians engage closely with each other’s views. Accordingly, relevant publications address several authors and periods in conjunction. These contributions are listed in three thematic sections at the end of our entry. (shrink)

Kant's arguments for the synthetic a priori status of geometry are generally taken to have been refuted by the development of non-Euclidean geometries. Recently, however, some philosophers have argued that, on the contrary, the development of non-Euclidean geometry has confirmed Kant's views, for since a demonstration of the consistency of non-Euclidean geometry depends on a demonstration of its equi-consistency with Euclidean geometry, one need only show that the axioms of Euclidean geometry have 'intuitive content' in order to show that both (...) Euclidean and non-Euclidean geometry are bodies of synthetic a priori truths. Michael Friedman has argued that this defence presumes a polyadic conception of logic that was foreign to Kant. According to Friedman, Kant held that geometrical reasoning itself relies essentially on intuition, and that this precludes the very possibility of non-Euclidean geometry. While Friedman's characterization of Kant's views on geometrical reasoning is correct, I argue that Friedman's conclusion that non-Euclidean geometries are logically impossible for Kant is not. I argue that Kant is best understood as a proto-constructivist and that modern constructive axiomatizations (unlike Hilbert-style axiomatizations) of both Euclidean and non-Euclidean geometry capture Kant's views on the essentially constructive nature of geometrical reasoning well. (shrink)

The incompleteness of set theory ZFC leads one to look for natural extensions of ZFC in which one can prove statements independent of ZFC which appear to be "true". One approach has been to add large cardinal axioms. Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski- Grothendieck set theory TG [1]-[3] It is a non-conservative extension of ZFC and is obtaineed from other axiomatic set theories by the inclusion of Tarski's axiom which implies the existence (...) of inaccessible cardinals [1].Non-conservative extension of ZFC based on an generalized quantifiers considered in [4]. In this paper we look at a set theory NC_{∞^{#}}^{#},based on bivalent gyper infinitary logic with restricted Modus Ponens Rule [5]-[8]. In this paper we deal with set theory NC_{∞^{#}}^{#} based on gyper infinitary logic with Restricted Modus Ponens Rule. Set theory NC_{∞^{}}^{} contains Aczel's anti-foundation axiom [9]. We present a new approach to the invariant subspace problem for Hilbert spaces. Our main result will be that: if T is a bounded linear operator on an infinite-dimensional complex separable Hilbert space H,it follow that T has a non-trivial closed invariant subspace. Non-conservative extension based on set theory NC_{∞}^{#} of the model theoretical nonstandard analysis [10]-[12] also is considered. (shrink)

Deontic logic is standardly conceived as the logic of true statements about the existence of obligations and permissions. In his last writings on the subject, G. H. von Wright criticized this view of deontic logic, stressing the rationality of norm imposition as the proper foundation of deontic logic. The present paper is an attempt to advance such an account of deontic logic using the formal apparatus of update semantics and dynamic logic. That is, we (...) first define norm systems and a semantics of norm performatives as transformations of the norm system. Then a static modal logic for norm propositions is defined on that basis. In the course of this exposition we stress the performative nature of (i) free choice permission, (ii) the sealing legal principle and (iii) the social nature of permission. That is, (i) granting a disjunctive permission means granting permission for both disjuncts; (ii) non-prohibition does not entail permission, but the authority can declare that whatever he does not forbid is thereby permitted; and (iii) granting permission to one person means that all others are committed to not prevent the invocation of that permission. (shrink)

In this paper, I argue that the temporal connective prima (‘before’) is a comparative adverb. The argument is based on a number of grammatical facts from Italian, showing that there is an asymmetry between prima and dopo (‘after’). On the ground of their divergent behaviour, I suggest that dopo has a different grammatical status from prima. I propose a semantic treatment for prima that is based on an independently motivated analysis of comparatives which can be traced back to Seuren (in: (...) Kiefer and Ruwet (eds.) Generative grammar in Europe, 1973). Dopo is analyzed instead as an atomic two-place predicate which contributes a binary relation over events to the sentence meaning. The different semantic treatments of the two connectives provide an explanation for the grammatical asymmetries considered at the outset; interestingly, they also shed some light on other asymmetries between prima and dopo, which are known to hold for the English temporal connectives before and after as well: these asymmetries are related to the veridicality properties, the distribution of NPIs, and the logical properties of these connectives first described in Anscombe (Philos Rev 73:3–24, 1964). (shrink)

I argue that No-Ought-From-Is (in the sense that I believe it) is a relatively trivial affair. Of course, when people try to derive substantive or non-vacuous moral conclusions from non-moral premises, they are making a mistake. But No-Non-Vacuous-Ought-From-Is is meta-ethically inert. It tells us nothing about the nature of the moral concepts. It neither refutes naturalism nor supports non-cognitivism. And this is not very surprising since it is merely an instance of an updated version of the conservativeness of (...) class='Hi'>logic (in a logically valid inference you don’t get out what you haven’t put in): so long as the expressions F are non-logical, you cannot get non-vacuous F-conclusions from non-F premises. However, the triviality of No-Non-Vacuous-Ought-From-Is is important and its non-profundity profound. No-Ought-From-Is is widely supposed to tell us something significant about the nature of the moral concepts. If, in fact, it tells us nothing, this is a point well worth shouting from the housetops. This brings me to my dispute with Gerhard Schurz who has proved a related version of No-Ought-From-Is, No-Ought-Relevant-Ought-From-Is, a proof which relaxes my assumption that ‘ought’ should not be treated as a logical constant. But if ought is not a logical expression then it does not really matter much that No-Ought-From-Is would be salvageable even if it were. Furthermore, Schurz’s proof depends on special features of the moral concepts and this might afford the basis for an abductive argument to something like non-cognitivism. As an error theorist, and therefore a cognitivist, I object. Finally I take a dim view of deontic logic. Many of its leading principles are false, bordering on the nonsensical, and even the reasonably plausible ones are subject to devastating counter-examples. (shrink)

Dynamic semantics violates numerous classical laws, including Non-Contradiction. Proponents of dynamic semantics have offered no explanation for this behavior, and some critics consider this result to be strong evidence against the tenability of the dynamic program. I defend and explain failures of Non-Contradiction by comparing dynamic semantics and classical, truth conditional semantics in terms of their idealizing assumptions. I demonstrate that dynamic semantics rejects context fixity, an idealizing assumption that truth-conditional semantics typically adopts. I then argue that any semantics which (...) rejects context fixity should, by the classical semanticist’s own lights, violate Non-Contradiction under certain circumstances. I then demonstrate that dynamic semantics violates Non-Contradiction in all and only those circumstances. I subsequently appeal to this insight to vindicate some of dynamic semantics’ more controversial predictions. I close by suggesting that discussion of idealizing assumptions, common in the sciences, is similarly crucial to fruitful discussion in natural language semantics. (shrink)

The Fregean tradition promotes a conception of logic as being independent from all psychological acts of the knowing subject. Without questioning logic's status as a paradigm of objectivity the present essay rejects this conception, both on logical grounds and in light of the scholastic theory of intentionality. Finding fault with two key doctrines of the analytic movement, the linguistic turn and anti-psychologism, it reinterprets them to exclude only psychological acts that engender subjective interpretive variability. It then describes (...) class='Hi'>logic's dependence on non-interpretive psychological acts that ensue as a natural result of objects being apprehended by the intellect. These acts, which Hervaeus Natalis and the scholastic tradition thematize as the imposition of second intentional relations of reason, dictate the logically coherent parameters of logical objectivity. (shrink)