We consider semantic and syntactic transformations of the concept of "the logical" in the ancient philosophy in the form of crypto-logos, para-logismos, dia-logos, and syl-logismos. We interpret Heraclitus' concept of Logos as a cryptologos through which intuitive insight (epístasthai gnóomen) reveals hidden or implicit harmony (harmoníe aphanés) in nature (phýsis) as a conceptual unity of ontic opposites (tà enantía). In Pramenides' paraconsistent concept of the identity of Being and thought, we point to para-logical hypotheses about the One (...) that are carried out through antithetical deductions of thought and which maintain the dynamics of the ontic determinations of being (ón) in the statics of the conceptual determinations of Being (tò eînai). As the beginning of the explicative granulation of ''the logical'' we consider Plato's concept of the dialectical skill (dialektikè tékhne) of dividing concepts of genus into species and sub-species that logically represent ontic opposites in problem-formulated questions. Finally Aristotle's concept of lógos as a statement-making sentence / proposition (lógos apophantikós) made explicit the Being (tò eînai), or the Being as Being (tò ón hê ón), in semantic and syntactic figures and modes of syllogistic inferences in which ontological (eînai), ontic (ón), conceptual (logikôos) and linguistic (légomenon) correspondence is shown. We conclude that with these changes in the concept of lógos, the path has been taken from the hidden or implicit Truth of the phenomena of nature and the world (pân) to explicit truthfulness of propositions as the unhiddeness (alétheia) of Being trough the semantical and syntactical visibility of the logical structures of being, thought and language in scientific knowledge based on demonstration (apoódeiksis). (shrink)

This paper discusses the Uniqueness Thesis, a core thesis in the epistemology of disagreement. After presenting uniqueness and clarifying relevant terms, a novel counterexample to the thesis will be introduced. This counterexample involves logical disagreement. Several objections to the counterexample are then considered, and it is argued that the best responses to the counterexample all undermine the initial motivation for uniqueness.

This paper discusses the uniqueness thesis, a core thesis in the epistemology of disagreement. After presenting uniqueness and clarifying relevant terms, a novel counterexample to the thesis will be introduced. This counterexample involves logical disagreement. Several objections to the counterexample are then considered, and it is argued that the best responses to the counterexample all undermine the initial motivation for uniqueness.

The logos question, one of the most important among the subjects that traverse the Plato's Sophist, has in fact some different aspects: the criticism of father Parmenides' logos, that is unable to speak about the not-being, but also about the being; the relations between logos and its cognates, phantasia, doxa and dianoia; the logos’ complex structure, that is a compound with onoma and rema; the difference between naming and saying, two distinct but inseparable actions; the logical (...) and ontological conditions that make possible to say the truth, or to lie or simply to joke; the necessity of a most flexible logos that allows us to speak about the not-being, and about the being, but at the same time is a logos dangerously similar to the sophist’ one; finally, the identity between the power to produce “spoken images” and the very power to speak. The aim of the present article is giving a systematical view of the matter that grasps all these faces. (shrink)

How does logic relate to rational belief? Is logic normative for belief, as some say? What, if anything, do facts about logical consequence tell us about norms of doxastic rationality? In this paper, we consider a range of putative logic-rationality bridge principles. These purport to relate facts about logical consequence to norms that govern the rationality of our beliefs and credences. To investigate these principles, we deploy a novel approach, namely, epistemic utility theory. That is, we assume (...) that doxastic attitudes have different epistemic value depending on how accurately they represent the world. We then use the principles of decision theory to determine which of the putative logic-rationality bridge principles we can derive from considerations of epistemic utility. (shrink)

This paper introduces two new paradoxes for standard deontic logic (SDL). They are importantly related to, but distinct from Ross' paradox. These two new paradoxes for SDL are the simple weakening paradox and the complex weakening paradox. Both of these paradoxes arise in virtue of the underlaying logic of SDL and are consequences of the fact that SDL incorporates the principle known as weakening. These two paradoxes then show that SDL has counter-intuitive implications related to disjunctive obligations that (...) arise in virtue of deontic weakening and in virtue of decisions concerning how to discharge such disjunctive obligations. The main result here is then that theorem T1 is a problematic component of SDL that needs to be addressed. (shrink)

Euthyphro is a Socratic interlocutor claiming enormous religious expertise, while his portrayal in the eponymous dialogue raises questions the reliability of his beliefs. This paper closely examines how Euthyphro justifies his case against his father, identifying an argument that relies on the concept of miasma (pollution). In so far as miasma is considered in isolation, Euthyphro has a good argument. Unfortunately, there is more than miasma at stake when considering why one could prosecute one’s own parent. Introducing the other relevant (...) concepts, honor and shame, we find his case reflects a dilemma at the source of ancient Greek religious thought. It would not be possible for Euthyphro or anyone else to know what to do in his case. (shrink)

This paper presents and critically discusses the “logos approach to quantum mechanics” from the point of view of the current debates concerning the relation between metaphysics and science. Due to its alleged direct connection with quantum formalism, the logos approach presents itself as a better alternative for understanding quantum mechanics than other available views. However, we present metaphysical and methodological difficulties that seem to clearly point to a different conclusion: the logos approach is on an epistemic equal (...) footing among alternative realist approaches to quantum mechanics. (shrink)

In this paper I argue that we can solve the interpretation problem of quantum mechanics and the question of ontology of Quantum Field Theory on the basis of simple metaphysical position: The connection of the phase space with the ancient Theory of Logi of Beings, which is, by giving ontological meaning to the entities which "live" at the phase space, the Hamiltonian or Lagrangian formalism. There is a physical subject of such functions and it is the logos of a (...) being. Therefore we can refer to the logical space as the total sum of logi of being. The result of this position is that we can attribute to the wave function a physical meaning, a special case of logos of a being and also give an ontological meaning at a quantum field. The developed metaphysical scheme can interpret the quantum paradoxes, by using the commonly accepted mathematical formalism. It can also interpret certain issues of Quantum Field Theory, although further study of this topic is necessary. (shrink)

Already in ancient philosophy, there was a transition from the implicit and hidden action of the Logical ( lógos) in nature ( phýsis) to the scientific and explicit expression of the logical structures of thought, action, the world and language. Heraclitus' heno-logic with Logos as hidden implicit principle of homologization of opposites ( tà enantía) in nature differs from Parmenides' paraconsistent logic developed in a hypothetical hemidyalectics given in the formula ''All is One'' ( hén pánta eînai). (...) Plato's concept of dia-logic (dialektikè téchne ) with a new concept of Logos as the one genus of beings ( hén tí génon toôn ontoôn) in which the word not-Being (negation) got its place enabled production of dyadic logical structure by the granulation of genera into opposite species and sub-species that it contains. Aristotle's concept of triadic-logic as syl-logistics ( syllogismós) and demonstrative science (epistéme apodeiktikê ) give a new approach by new granulation of the concept of Logos into triadic logical structure: (1) the structure of being (substratum-attributes relation), (2) the structure of thought (substance-second substances relation), and (3) the structure of propositions (subject-predicate relation). Plato's dialectic and Aristotle's syllogistic both deconstructed the implicit ontological unity of the world (pan, kosmos, sphairos ) given through the concept of Logos in Pre-Socratic philosophy in order to make that unity in explicit form given by the logical and semantical structures of the propositions about the world, about the thought and about the language. The hidden implicit of the nature, which had to be known intuitively, was transformed into unhidden explicit inferential logical structures given in the semantics and pragmatics of scientific demonstration. (shrink)

In this essay, our goal is to discover science in Martin Heidegger's Introduction to Metaphysics, lecture notes for his 1935 summer semester course, because, after all, his subject is metaphysica generalis, or ontology, and this could be construed as a theory of the human brain. Here, by means of verbatim quotes from his text, we attempt to show that indeed these lectures can be viewed as suggestion for an objective scientific theory of human perception, the human capacity for deciphering phenomena, (...) ie. hermeneutics in its broadest sense. His added notes from the 1953 edition, all of which are comments, not corrections, imply that he never abandoned these thoughts on metaphysics, despite all of his utterances about a need to overcome it, and their popular interpretations to that effect. In his presentation, he further develops the colorful and intuitive style, an hermeneutic language, that he had created in his earlier work Being and Time. Of human existence he speaks in such expressions as being-there -- ``Dasein" -- and being-in-the-world, the latter term no longer explicit in the 1935 lectures. The lectures can be read as a pre-scientific analysis of how man, being-there, perceives his environment, artfully managing to deal with the manifold challenges posed by the phenomenal structures of the universe. Man attentively recognizes and deciphers their pre-linguistic contents and, while trying to make sense of it all, puts into words his awareness. There are numerous passages in Heidegger's work where he in fairly concrete terms provides us with hints for a perceptive science that, as it turns out and is demonstrated below in this essay, can be explained in terms of recent advances in neuroscience. It would be implausible, even unthinkable, unimaginable, for there not to be found essential agreement between on one hand his philosophical insights gained by hermeneutics of Dasein, into how our brain functions to let us know what's happening & on the other hand, scientific discoveries obtained through anatomy, EEG, fMRI, TMS, electrode implants, etc, of brain structures & functions employed in perception of the momentary scene. A nexus between science and philosophy is provided in Heidegger's definitive treatment of the Logos, here interpreted as a structural version of Platonic forms (Burchard, 2014). This allows for neurolinguistic brain functions to serve as meta-context for Heidegger's being-in-the-world. The logical functions of Dasein's anatomical brain are performed by the logos machine, formerly the human soul, using top-down processing based on a global context, the noumenal cosmos which humans maintain internally. Heidegger's 1942/43 winter semester lectures Parmenides extend in unbroken fashion his 1935 work, proving that he never abandoned, as is widely claimed, his metaphysical avenue of thought. (shrink)

Just started a new book. The aim is to establish a science of knowledge in the same way that we have a science of physics or a science of materials. This might appear as an overly ambitious, possibly arrogant, objective, but bear with me. On the day I am beginning to write it–June 7th, 2020–, I think I am in possession of a few things that will help me to achieve this objective. Again, bear with me. My aim is well (...) reflected in the title I chose (just now) for this book: Knowledge & Logic: Towards a science of knowledge. Its most important feature is that I shall take logic to be to knowledge science as calculus is to physics or to materials science. I do not intend to reclaim knowledge from the bosom of philosophy, in which, known as epistemology its erudite discussion has hardly progressed since Plato first defined it as true belief with logos. With only a few adjustments, it will actually provide me with the right, science-bound start. More recently, knowledge has been reclaimed by the field of BA, a reclaim that has opened the box of Pandora: Among the evils, and perhaps at the head of the list, is an overly lay, essentially naive, notion of knowledge. But the very idea that one can have something like “knowledge (management) software” puts us on the right track. (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)

The present paper deals with the ontological status of numbers and considers Frege ́s proposal in Grundlagen upon the background of the Post-Kantian semantic turn in analytical philosophy. Through a more systematic study of his philosophical premises, it comes to unearth a first level paradox that would unset earlier still than it was exposed by Russell. It then studies an alternative path, that departin1g from Frege’s initial premises, drives to a conception of numbers as synthetic a priori in a more (...) Kantian sense. On this basis, it tentatively explores a possible derivation of basic logical rules on their behalf, suggesting a more rudimentary basis to inferential thinking, which supports reconsidering the difference between logical thinking and AI. Finally, it reflects upon the contributions of this approach to the problem of the a priori. (shrink)

The concern of deductive logic is generally viewed as the systematic recognition of logical principles, i.e., of logical truths. This paper presents and analyzes different instantiations of the three main interpretations of logical principles, viz. as ontological principles, as empirical hypotheses, and as true propositions in virtue of meanings. I argue in this paper that logical principles are true propositions in virtue of the meanings of the logical terms within a certain linguistic framework. Since these principles also regulate and (...) control the process of deduction in inquiry, i.e., they are prescriptive for the use of language and thought in inquiry, I argue that logic may, and should, be seen as an instrument or as a way of proceeding (modus procedendi) in inquiry. (shrink)

We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.

It is pointed out that the different concepts of the Universe serve as an ultimate basis determining the frames of consciousness. A unified concept of the Universe is explored which includes consciousness and matter as well to the universe of existents. Some consequences of the unified concept of the Universe are derived and shown to be able to solve the paradox of the self-founding notion of the Universe. The self-contained Universe is indicated to possess a logical nature. It is shown (...) that a passage exists between consciousness and the material world and its nature is exemplified. Moreover, arguments are presented showing the simultaneous emotional nature of the Universe. A solution to the paradox of semi-finite spacetime existents, possessing finite and infinite substances simultaneously, namely eternal existents like moral values and logical validity, is obtained. (shrink)

We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.

The purpose of this paper is to explore the question of how truthmaker theorists ought to think about their subject in relation to logic. Regarding logic and truthmaking, I defend the view that considerations drawn from advances in modal logic have little bearing on the legitimacy of truthmaker theory. To do so, I respond to objections Timothy Williamson has lodged against truthmaker theory. As for the logic of truthmaking, I show how the project of understanding the (...) logical features of the truthmaking relation has led to an apparent impasse. I offer a new perspective on the logic of truthmaking that both explains the problem and offers a way out. (shrink)

This paper introduces a novel strategy for responding to skeptical arguments based on the epistemic possibility of error or lack of certainty. I show that a nonclassical logic motivated by recent work on epistemic modals can be used to render such skeptical arguments invalid. That is, one can grant that knowledge is incompatible with the possibility of error and grant that error is possible, all while avoiding the skeptic’s conclusion that we lack knowledge.

I argue that Hegel and Wittgenstein, each in their own specific way, used the idea of God at the beginning of creation as a complex analogy for other kinds of beginning, most notably the beginning of philosophical thought. Hegel’s Logic describes God’s mind before the creation of the world, i.e. God’s pure thinking. For a philosopher, beginning afresh means resolving to consider this kind of abstraction from the existence of the world. Wittgenstein, by contrast, says that the idea of (...) a creator of the world does not explain anything. It marks the terminus ad quem of asking for explanations; we must not ask further who created the creator of the world. Wittgenstein generalizes this for any kind of reasoning: “Explanations come to an end somewhere.” (Philosophical Investigations: §1) Any sort of explanation must eventually arrive at its terminus ad quem, which means only that any kind of reasoning must have its logical beginning. (shrink)

Logical reasoning is not only a component of religious faith (cf., for instance, the "Golden rule"), but, in addition, the religious faith itself can be conceived as a logical pragmatic function applied to sentences and their meanings. Pragmatic role of religious faith is shown on the examples of the analogy of seed and spoken word (e.g., Mt 13:3-23) and on the degrees of faith described in the episode about Nicodemus (John 3). Pragmatics adds (different grades of) perseverance to the correctness (...) of reasoning and to the truth-preservation of the consequence relation. Correspondingly, religious faith is described by formally defined model and satisfaction relation, which are applied to and examined on the text of John 3. (shrink)

A consequence relation is strongly classical if it has all the theorems and entailments of classical logic as well as the usual meta-rules (such as Conditional Proof). A consequence relation is weakly classical if it has all the theorems and entailments of classical logic but lacks the usual meta-rules. The most familiar example of a weakly classical consequence relation comes from a simple supervaluational approach to modelling vague language. This approach is formally equivalent to an account of logical (...) consequence according to which α1, ..., αn entails β just in case □α1, ..., □αn entails □β in the modal logic S5. This raises a natural question: If we start with a different underlying modal logic, can we generate a strongly classical logic? This paper explores this question. In particular, it discusses four related technical issues: (1) Which base modal logics generate strongly classical logics and which generate weakly classical logics? (2) Which base logics generate themselves? (3) How can we directly characterize the logic generated from a given base logic? (4) Given a logic that can be generated, which base logics generate it? The answers to these questions have philosophical interest. They can help us to determine whether there is a plausible supervaluational approach to modelling vague language that yields the usual meta-rules. They can also help us to determine the feasibility of other philosophical projects that rely on an analogous formalism, such as the project of defining logical consequence in terms of the preservation of an epistemic status. (shrink)

This chapter intervenes in recent debates in Kant scholarship about the possibility of a general logical alien. Such an alien is a thinker whose laws of thinking violate ours. She is third-personal as she is radically unlike us. Proponents of the constitutive reading of Kant’s conception of general logic accordingly suggest that Kant rules out the possibility of such an alien as unthinkable. I add to this an often-overlooked element in Kant’s thinking: there is reason to think that he (...) grants—and in fact presupposes—the possibility of a transcendental logical alien. Such an alien is a knower whose laws of experience purport to violate ours. She is first-personal as she is radically like us. In other words, she is us, insofar as we are alienated from ourselves and our experience. I go on to draw an analogy between her, a dogmatist, and another transcendental alien, an evil agent. Just as a dogmatist is alienated from her (our) experiential laws, an evil agent is alienated from her (our) moral law. These forms of theoretical and practical self-conceit require self-knowledge in the form of a critique of speculative or practical reason. In bringing this point out, I aim to shift from the question of whether logical laws constitute our thinking to the question of whether grasping our experiential and moral laws as our laws constitutes our reason. (shrink)

The suggestion of Logical Quanta (LQ) is a bidirectional synthesis of the theory of logos of Maximus the Confessor and the philosophical interpretation of quantum mechanics. The result of such a synthesis is enrichment to the ontology of classical mechanics that enable us to have a unified view and an explanatory frame of the whole cosmos. It also enables us to overcome the Cartesian duality both on biology and the interaction of body and mind. Finally, one can reconstruct a (...) new understanding of religion. (shrink)

Purpose. The author believes that the main topic of philosophical studies of Heraclitus was not nature, not dialectics, and not political philosophy; he was engaged in the development of philosophical anthropology, and all other questions raised by him were subordinated to it to one degree or another. It is anthropology that is the most "dark" part of the teachings of this philosopher, therefore the purpose of this article is to identify the hidden anthropological message of Heraclitus. In case of success, (...) it will become clear what made him "darken". Theoretical basis. The methodological basis of the article is the anthropological understanding of fragments of Heraclitus’ texts presented in a historical and philosophical context. Originality. The philosophical concept of Heraclitus is still a mystery for researchers of his work. The author of the article proposed such a variant of interpretation, within the framework of which different elements of this concept fit into a consistent model. Conclusions. The article proves that although the anthropological turn in philosophy is traditionally associated with the activities of the sophists and Socrates, the previous philosophical thought was also not devoid of anthropological ideas. Moreover, pre-Socratic philosophers posed problems, the interpretation of which brought the doctrine of man to the level of high-order abstractions, while surprisingly preserving the concreteness of the life-meaning questions that confront him. And one of the brightest representatives of pre-Socratic anthropology was Heraclitus of Ephesus. Religion was the motivator that made him study the world, man, and society. The doctrine of the Logos developed by Heraclitus had a tremendous impact on Plato and Philo of Alexandria, and through them on the author of the Fourth Gospel, who begins his story with a "Greek" rethinking of the mystery of the Incarnation. If Heraclitus claimed that a person carries a particle of the Logos, then John proclaimed that the Logos itself incorporated a particle of man. Despite all the differences between these approaches, each of them postulated the cosmic significance of human existence, which means that it brought anthropology to the ontological level. (shrink)

A report on the pioneering of a new pedagogy designed to challenge students to use and improve their memory, increase their awareness of logical fallacies and tacitly embedded contradiction(s) and sensitize them to the deeply symbolic nature of thought in all its expressions (math, logos, music, picture and motor skills), as created, by the author, from in situ research at a senior level (ESL) course in Storytelling at Hankuk University of Foreign Studies, South Korea’s premier university for foreign languages (...) and translation.in. (shrink)

A close reading of Socrates’ arguments against the proposed definition of knowledge as true opinion together with a logos (“account”). I examine the orienting implications of his apparently destructive dilemma defeating the so-called dream theory and of his apparently decisive arguments rejecting the notions of “account” as verbalization, as working through the parts of the whole of the definiendum, and as identifying what differentiates the definiendum from all else. Whereas the dilemma implies of the object of knowledge that it (...) must be both simple and complex, the last two notions of “account” point to the kinds of discursive analysis that can do justice to its complexity; together the refutations suggest the relation between noesis, that is, eidetic intuition of the object in its simplicity, and discursive analysis of the object in its complexity that knowledge requires. (shrink)

In his “Noesis and Logos in the Eleatic Trilogy, with a Focus on the Visitor’s Jokes at Statesman 266a-d,” Mitchell Miller explores the interplay of intuition and discourse in the Statesman. He prepares by considering the orienting provocations provided by Socrates’ refutations of the proposed definition of knowledge — namely, “true judgment and a logos” — in the closing pages of the Theaetetus, by the Eleatic Visitor’s obscure schematization at Sophist 253d-e of the kinds of eidetic field discerned (...) by dialectic, and by his discussion at Statesman 277a-278e of the use of paradigms. Miller then seeks to show how the Visitor’s odd medley of geometrical and Homeric jokes at Statesman 266a-d aims, in the language of the Seventh Letter, to “spark” an intuition of the nature of statesmanship, an intuition whose “self-nourishing” motivates the subsequent rejection of the initial definition of the statesman as shepherd of the human herd, the turn to the paradigm of the weaver, and the rejection of bifurcatory division in favor of the non-bifurcatory account of the kinds of art that function as the “limbs” of a well-formed city. (shrink)

In “Belief in the Face of Controversy,” Hilary Kornblith argues for a radical form of epistemic modesty: given that there has been no demonstrable cumulativeprogress in the history of philosophy – as there has been in formal logic, math, and science – Kornblith concludes that philosophers do not have the epistemic credibility to be trusted as authorities on the questions they attempt to answer. After reconstructing Kornblith's position, I will suggest that it requires us to adopt a different conception (...) of philosophy's epistemic value. First, I will argue that ‘progress’ has a different meaning in logic, science and philosophy, and that to judge one of these disciplines by the standards appropriate to one of the others obscures the unique epistemic functions of all. Second, I will argue that philosophy is epistemically unique in that it is a non-relativistic but historically determined excavation of foundations. Finally, drawing on Frank Herbert's Dune, I will suggest that Kornblith leaves us with a choice between two epistemic ideals: the hyper-logical ‘Mentat,’ or the historically informed ‘pre-born.’. (shrink)

This paper attempts to demonstrate that in Emmanuel Levinas’ thinking, justice is the necessary opening – and dissolution- of the “I” which makes fecundity – procreation – possible, and that in that same measure makes possible that the Logos transforms into a “desire to say” and the world into a “among us”. At the same time it wants to demonstrate that this notion of justice is directly related to the ideas of expression and nudity. Due to which the “Other” (...) imposes itself in front of the “same” , as man, singular and vulnerable, and that in the same measure it is linked to the notion of the Face and its particular mode of manifestation. In this respect, we propose that justice. As long as necessary condition, can fund an ethically constituted world, where an “erotic order” mandates over logic orderings. (shrink)

A close reading of Socrates' refutation of the final proposed definition of knowledge, "true opinion with an account." I examine the provocations to further thinking Socrates poses with his dilemma of simplicity and complexity and then by his rejections of the three senses of "account," and I argue that these provocations guide the responsive reader to that rich and determinate understanding of the sort of 'object' which knowledge requires that the Parmenides and the Eleatic dialogues will go on to explicate.

Semantic externalism in the style of McDowell and Evans faces a puzzle formulated by Pryor: to explain that a sentence such as 'Jack exists' is only a posteriori knowable, despite being logically entailed by the seemingly logical truth 'Jack is self-identical', and hence being itself a logical truth and therefore a priori knowable. Free logics can dissolve the puzzle. Moreover, Pryor has argued that the existentially hedged 'If Jack exists, then Jack is self-identical', when properly formalised, is a logical truth (...) in a system of neutral free logic and therefore a priori knowable, while it does not entail that Jack exists. The latter holds also for negative free logic. In response, Yeakel has argued that on any system of neutral free logic existence hedges will either entail some unwanted existence claims or they will not entail some wanted existence claims. The dilemma also holds for any non-positive free logic. It will be shown that the extension of one of the systems of neutral free logic with a truth operator escapes Yeakel's dilemma, whereas no other non-positive free logic when extended with the truth operator does the same (or it breaks quantifier exchangeability). (shrink)

Parmenides plays an important role in the first section of Hegel’s Science of Logic due to his definition of being as a pure thought-determination. This article investigates, first, how Hegel conceives the Parmenidean being. Secondly, by discussing Hegel's logical analysis of pure being and pure nothing, it aims to show why and how such conception of being, according to Hegel, provides a crucial insight into the function of the understanding.

In this paper I will develop a view about the semantics of imperatives, which I term Modal Noncognitivism, on which imperatives might be said to have truth conditions (dispositionally, anyway), but on which it does not make sense to see them as expressing propositions (hence does not make sense to ascribe to them truth or falsity). This view stands against “Cognitivist” accounts of the semantics of imperatives, on which imperatives are claimed to express propositions, which are then enlisted in explanations (...) of the relevant logico-semantic phenomena. It also stands against the major competitors to Cognitivist accounts—all of which are non-truth-conditional and, as a result, fail to provide satisfying explanations of the fundamental semantic characteristics of imperatives (or so I argue). The view of imperatives I defend here improves on various treatments of imperatives on the market in giving an empirically and theoretically adequate account of their semantics and logic. It yields explanations of a wide range of semantic and logical phenomena about imperatives—explanations that are, I argue, at least as satisfying as the sorts of explanations of semantic and logical phenomena familiar from truth-conditional semantics. But it accomplishes this while defending the notion—which is, I argue, substantially correct—that imperatives could not have propositions, or truth conditions, as their meanings. (shrink)

Imagine an equilateral triangle “pointing upward”—its horizontal base under its apex angle. A semiotic triangle has the following three “vertexes”: (apex) an expression, (lower-left) one of the expression’s conceptual meanings or senses, and (lower-right) the referent or denotation determined by the sense [1, pp. 88ff]. One example: the eight-letter string ‘coleslaw’ (apex), the concept “coleslaw” (lower-left), and the salad coleslaw (lower-right) [1, p. 84f]. Using Church’s terminology [2, pp. 6, 41]—modifying Frege’s—the word ‘coleslaw’ expresses the concept “coleslaw”, the word ‘coleslaw’ (...) denotes or names the salad coleslaw, and the concept “coleslaw” determines the salad coleslaw—recalling Frege’s principle that sense determines denotation. Church [2, p. 6] wrote: -/- We shall say that a name denotes or names its denotation and expresses its sense. […] Of the sense we say that it determines its denotation, or is a concept of the denotation. -/- Aristotle seems cognizant of distinctions going beyond those in semiotic triangles. The expression Aristotle’s semiotic pyramids seem warranted by Aristotle’s Categories, 1a1: -/- When [two] things have a name (onoma) in common and the concept (logos) of being (ousia) which corresponds to the name in each case is different, they are called same-named (homonuma). Thus, for example, both a man and a picture [of an animal] are called animals. These have only a name in common. In each case the name’s concept of being [an animal] is different; for if one says what being an animal is for each of them, one will give two distinct concepts. -/- Semiotic triangles and pyramids in Aristotle’s logic are compared to those in Church’s [2]. [1] JOHN CORCORAN, Sentence, proposition, judgment, statement, and fact, Many Sides of Logic, College Publications, 2009. [2] ALONZO CHURCH, Introduction to Mathematical Logic, Princeton, 1956. -/- The semiotic pyramid in Categories, 1a1 has a square base under the vertex ‘animal’. On the corners of the square are: the concept “animal”, the concept “animal picture”, the animals, and the animal pictures. The animals are homonymous with the animal pictures. People find Aristotle’s example far-fetched or inept even if the experience of pointing to a picture while saying “That is Tarski” is familiar. Imagine looking at a painting while thinking “That is an animal”. Without putting too fine a point on this, notice that in Aristotle’s sense it is individual things that are homonymous, not words. It would be natural to say also in his sense that two things are homonyms if one is homonymous with the other. In contrast, we use the words homonym and homonymous to relate words that are spelled the same and pronounced the same but have different meaning. Consider the noun ‘center’ and the verb ‘center’. Consider the noun ‘smell’ and the verb ‘smell’. The spelling of two homonyms is an ambiguity, or an ambiguous spelling. We need appropriate adjectives to distinguish the Categorical senses of ‘homonym’ and ‘homonymous’ from the current English sense just mentioned. I propose ‘ontological’ for the sense relating things and ‘linguistic’ for that relating words. Given that all words are things but not all things are words, we ask are words that are linguistically homonymous also ontologically homonymous? END OF POST ABSTRACT. (shrink)

We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one- and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply general (...) propositions. We consider and reinterpret some ancient texts that have been neglected in the context of Stoic universal and existential propositions and offer new explanations of some puzzling features in Stoic logic. Our results confirm that Stoic logic surpasses Aristotle’s with regard to multiple generality, and are a reminder that focusing on multiple generality through the lens of Frege-inspired variable-binding quantifier theory may hamper our understanding and appreciation of pre-Fregean theories of multiple generality. (shrink)

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems (...) to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

What is a logical constant? The question is addressed in the tradition of Tarski's definition of logical operations as operations which are invariant under permutation. The paper introduces a general setting in which invariance criteria for logical operations can be compared and argues for invariance under potential isomorphism as the most natural characterization of logical operations.

The goal of this paper is to present a new reconstruction of Aristotle's assertoric logic as he develops it in Prior Analytics, A1-7. This reconstruction will be much closer to Aristotle's original...

The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted (...) that in order to specify the truth conditions of certain sentences involving constants or variables that don’t denote, one has to apparently quantify over things that are not identical to anything. In this paper I defend a contingentist, non-Meinongian metaphysics within a positive free logic. I argue that although certain names and free variables do not actually refer to anything, in each case there might have been something they actually refer to, allowing one to interpret the contingentist claims without quantifying over mere possibilia. (shrink)

This article takes off from Johan van Benthem’s ruminations on the interface between logic and cognitive science in his position paper “Logic and reasoning: Do the facts matter?”. When trying to answer Van Benthem’s question whether logic can be fruitfully combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social cognition, including attributions such as “Bob knows that Alice knows that he wrote a novel under pseudonym”. For intelligent interaction, it is (...) important that the participants recursively model the mental states of other agents. Otherwise, an international negotiation may fail, even when it has potential for a win-win solution, and in a time-critical rescue mission, a software agent may depend on a teammate’s action that never materializes. First a survey is presented of past and current research on higher-order social cognition, from the various viewpoints of logic, artificial intelligence, and psychology. Do people actually reason about each other’s knowledge in the way proscribed by epistemic logic? And if not, how can logic and cognitive science productively work together to construct more realistic models of human reasoning about other minds? The paper ends with a delineation of possible avenues for future research, aiming to provide a better understanding of higher-order social reasoning. The methodology is based on a combination of experimental research, logic, computational cognitive models, and agent-based evolutionary models. (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)

ABSTRACT: A report on the pioneering of a new pedagogy designed to challenge students to use and improve their memory, increase their awareness of logical fallacies and tacitly embedded contradiction(s) and sensitize them to the deeply symbolic nature of thought in all its expressions (math, logos, music, picture and motor skills), as created, by the author, from in situ research at a senior level (ESL) course in Storytelling at one of East Asia’s premiere second languages university, and from teaching (...) children in several university summer programs. -/- As a Visiting Professor of Foreign Languages, I recently had a glorious opportunity to innovate curriculum and teaching techniques in an East Asian university classroom. Under the auspices of teaching senior level thematic courses in English as a Foreign Language, or more specifically, “storytelling,” I was blessed with the opportunity to innovate both on the level of curriculum and pedagogy. -/- But let me backtrack to set up my story from the start. All of this began in a children’s ESL class at a private language institute where I was given some newly formed intermediate level English classes for middle school students on a new campus that had yet to form a library. While waiting for my standard textbooks to arrive I began innovating with one of my own childrens’ stories titled The Tale of the Purple People Eater (a three page mythic story written in the late 90s. Please see appendix). In working with this story, because I envisioned presenting it orally (from memory) at first as a way to introduce students to memory arts exercises, I was compelled to read it over many times, which, to my surprise revealed a troubling feature: it was riddled with contradictions in every paragraph. At any rate, with the middle school aged students I only touched on this feature very briefly and focused more on language acquisition exercises. The tale nevertheless impressed upon me this bizarre aspect of language where a story can appear naturally cogent on the surface, but can also come apart at the seems if taken “literally.” Hence, later while teaching Storytelling in university with a rather dry textbook, I was invited to supplement the class with exercises of my own. Here I was curious to try work shopping the ‘Tale of The Purple People Eater’ with young adults. This involved three stages: 1) Memory work — or engaging with the unpublished story orally; 2) Exploring the contradictory nature of language and thought; 3) Probing the “deeply-symbolic” nature of meaning. -/- Of course, all of these levels have a long history of precedence in our civilization. Memory arts — though defunct now — had been highly developed in the ancient world, not least among bards who performed oral recitations from memory of the entire Illiad and Odyssey. Dialectics — now transmuted into the debate for show and prizes — had a deeper epistemological mission to discover truth and achieve enlightenment (i.e. Socrates, Boethius and St-Augustine). And if it could not be done via contradictory-prone rationality, it would do it by re-attaching or re-membering broken meanings via the sym-bol (“throwing together”), as per our lineage of platonic poets who created a world compelling enough to make us ask where Jesus went during his (underworld journey) three days in the crypt? Or, and, on what terrain did Dante travel? -/- Lets look at all three: Memory work can be very simple: it amounts to an oral recitation of the story in class followed by a homework assignment wherein the students are asked to reproduce the story (in writing) from memory. They can then compare ‘notes’ in class and by working in groups attempt to produce one version per group of the story in question. In this way we invite them to engage with ‘live’ stories as did our oral-history ancestors. Likewise, by writing it down (“for the first time”) they are re-living the act of our first bardic writer(s) who wove together a collection of competing versions of a popular legend to produce a standard. Very primal work! If Plato thought that writing meant the end of memory in his time, imagine what smart phones are doing to memory now. Contradictions too are easy to work with. It suffices to project a written version of the teacher’s story on the classroom screen — no note taking! — and let students have ample time to read it over and over, at first to check with their own memorized version, and later to seek out logical contradictions in the prose. Any way to ‘repair’ the story? Does it lose credibility because of contradictions? Can it be real without being true? Can it be true without being real? Do reality (L. res = matter) and truth (Gk. a-leithea = un-forgetting) etymologically speaking, share the same domain? -/- Further, if below the surface-meaning the story falls apart, its apparent mythical meaning immediately is called into question. This is a good time to ask the students to propose a (deeper) interpretation. On the surface, the obvious meaning of the Tale of the Purple People Eater, a world in which a purple ogre predatorily feasted on the purple race of the United Peoples of Benetton (a multi-racial nation representing every “skin colour of the rainbow”), revolves around racism, and indeed everyone save for one, thought the story was about racism. -/- I, the author, had the challenge of discovering the deeper meaning of my own story. Because it was written inspirationally one morning, the way we might record the memory of a dream from the night before in a journal, I also was ignorant of the story’s meaning. As luck would have it, a few days before I was to give my class feedback on their interpretations, a meditation on the color “purple” led to the book “The Color Purple” which I first heard of from a friend who, in my reply to a question about the book she was reading (in 1985), summarized it succinctly in one sentence about a black woman’s sexual awakening and liberation. I quickly got the book from the university library as well as the film which I viewed several times before my next class. -/- To my utter amazement, after reading the Tale of the Purple People Eater in light of the Color Purple and adjusting the meaning of color in the tale from the color of people’s complexion to the “color of people’s souls” (to commensurate with the film) as depicted in their clothing and other accoutrements (e.g. automobiles) as reflective of the “health of their souls” (white for revolt, purple for majesty, etc…) where the enslaved Celie is surrounded by drab lifeless colors in the beginning of the film in contrast to the liberated woman she has become in the end of the story symbolized by the extraordinary intensity of the purple shawl that bedecks her like an African queen, the tale can be considered, in part, as a kind of back story of the inner evolution of the book’s and film’s protagonist. -/- Many other cross-polenised metaphors come to the fore: Hippocrates in the tale is the mail man in the film; St-Yves anti-ageing gel is a metaphor for remaining in “childhood (sexual) slavery”; the Ex-Thrax vaccine is the spiritual laxative in the form of letters from Africa (from Ex-Lax and Thrace, a “wild place”) that eases Celie out of her yoke; the egg-shaped conference table with the pointy end in the tale is the kitchen table in the last meeting where Celie threatens her husband with the pointy end of the knife in the film… -/- Of course, the students could not be expected to decode the meaning of a story of this nature whose collective unconscious connotations the author himself had to go to great lengths to excavate almost like a detective of the subconscious. What was important here was the shared engagement between mind and narrative and how it acted as a vehicle for 1) re-membering, 2) becoming aware that all language is a metaphorical cover and 3) that the deep symbol and fused metaphor are divided not by external time and space but by external reality (in the Latin sense, res) and internal truth (in the Greek sense, aleithea). Myth then, in its highest meaning is a hybrid form (of these two) of narrative. Hence both parts real and true. (shrink)

Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on (...) in our field—a book would be needed for that. Instead, we have tried to select material that is of interest in its own right or exemplifies noteworthy features in interesting ways. Here are some themes that have guided us throughout the writing: • The back-and-forth between philosophy and modal logic. There has been a good deal of give-and-take in the past. Carnap tried to use his modal logic to throw light on old philosophical questions, thereby inspiring others to continue his work and still others to criticise it. He certainly provoked Quine, who in his turn provided—and continues to provide—a healthy challenge to modal logicians. And Kripke’s and David Lewis’s philosophies are connected, in interesting ways, with their modal logic. Analytic philosophy would have been a lot different without modal logic! • The interpretation problem. The problem of providing a certain modal logic with an intuitive interpretation should not be conflated with the problem of providing a formal system with a model-theoretic semantics. An intuitively appealing model-theoretic semantics may be an important step towards solving the interpretation problem, but only a step. One may compare this situation with that in probability theory, where definitions of concepts like ‘outcome space’ and ‘random variable’ are orthogonal to questions about “interpretations” of the concept of probability. • The value of formalisation. Modal logic sets standards of precision, which are a challenge to—and sometimes a model for—philosophy. Classical philosophical questions can be sharpened and seen from a new perspective when formulated in a framework of modal logic. On the other hand, representing old questions in a formal garb has its dangers, such as simplification and distortion. • Why modal logic rather than classical (first or higher order) logic? The idioms of modal logic—today there are many!—seem better to correspond to human ways of thinking than ordinary extensional logic. (Cf. Chomsky’s conjecture that the NP + VP pattern is wired into the human brain.) In his An Essay in Modal Logic (1951) von Wright distinguished between four kinds of modalities: alethic (modes of truth: necessity, possibility and impossibility), epistemic (modes of being known: known to be true, known to be false, undecided), deontic (modes of obligation: obligatory, permitted, forbidden) and existential (modes of existence: universality, existence, emptiness). The existential modalities are not usually counted as modalities, but the other three categories are exemplified in three sections into which this chapter is divided. Section 1 is devoted to alethic modal logic and reviews some main themes at the heart of philosophical modal logic. Sections 2 and 3 deal with topics in epistemic logic and deontic logic, respectively, and are meant to illustrate two different uses that modal logic or indeed any logic can have: it may be applied to already existing (non-logical) theory, or it can be used to develop new theory. (shrink)

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient (...) class='Hi'>logic texts. A renaissance in ancient logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)