The goals of this paper are two-fold: I wish to clarify the Aristotelian conception of the law of non-contradiction as a metaphysical rather than a semantic or logical principle, and to defend the truth of the principle in this sense. First I will explain what it in fact means that the law of non-contradiction is a metaphysical principle. The core idea is that the law of non-contradiction is a general principle derived from how things are in the (...) world. For example, there are certain constraints as to what kind of properties an object can have, and especially: some of these properties are mutually exclusive. Given this characterisation, I will advance to examine what kind of challenges the law of non-contradiction faces; the main opponent here is Graham Priest. I will consider these challenges and conclude that they do not threaten the truth of the law of non-contradiction understood as a metaphysical principle. (shrink)

According to some critics, Aristotle’s elenctic defence (elenchos, elenchus) of the Law of Non-Contradiction (Metaphysics IV) would be ineffective because it viciously begs the question. After briefly recalling the elenctic refutation of the denier of the Law of Non-Contradiction, I will first focus on Filippo Costantini’s objection to the elenchus, which, in turn, is based on the dialetheic account of negation developed by Graham Priest. Then, I will argue that there is at least one reading of the elenchus (...) that might not be viciously question-begging. In doing so, I will leverage, reinterpret and adjust the distinction between two senses of epistemic dependence, offered by Noah Lemos and originally based on some thoughts about George Edward Moore’s ‘proof of an external world.’ The key point of my counter-objection to recover the elenchus is to use the distinction between a necessary-condition relation between propositions (p only if q) and a grounding relation between facts (the fact that an epistemic agent S believes that p is grounded in the fact that S believes that q), where p and q are the content of S’s beliefs. (shrink)

The question of whether the Pyrrhonist adheres to certain logical principles, criteria of justification, and inference rules is of central importance for the study of Pyrrhonism. Its significance lies in that, whereas the Pyrrhonist describes his philosophical stance and argues against the Dogmatists by means of what may be considered a rational discourse, adherence to any such principles, criteria, and rules does not seem compatible with the radical character of his skepticism. Hence, if the Pyrrhonist does endorse them, one must (...) conclude that he is inconsistent in his outlook. Despite its import, the question under consideration has not received, in the vast literature on Pyrrhonism of the past three decades, all the attention it deserves. In the present paper, I do not propose to provide a full examination of the Pyrrhonist’s attitude towards rationality, but to focus on the question of whether he endorses the law of non-contradiction (LNC). However, I will also briefly tackle the question of the Pyrrhonist’s outlook on both the canons of rational justification at work in the so-called Five Modes of Agrippa and the logical rules of inference. In addition, given that the LNC is deemed a fundamental principle of rationality, determining the Pyrrhonist’s attitude towards it will allow us to understand his general attitude towards rationality. (shrink)

Abstract. As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification theory, too, with (...) its residue of existentially loaded theorems and patterns of inference, has been claimed to suffer from a defect of logical purity. The law of non-contradiction rules out certain circumstances as impossible—circumstances in which a statement is both true and false, or perhaps circumstances where something both is and is not the case. Is this to be regarded as a further ontological bias? (shrink)

There is a widespread view that Buddhist philosophy embodies logical contradictions such that there would be 'true' contradictions, This article explains that this is not the case and that Buddhist philosophy, more generally the Perennial philosophy, denies all contradictions for the sake of a doctrine of Unity.

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 Laws of Thought is an exploration of the deductive and inductive foundations of rational thought. The author here clarifies and defends Aristotle’s Three Laws of Thought, called the Laws of Identity, Non-contradiction and Exclusion of the Middle – and introduces two more, which are implicit in and crucial to them: the Fourth Law of Thought, called the Principle of Induction, and the Fifth Law of Thought, called the Principle of Deduction. This book is a thematic compilation drawn from (...) past works by the author over a period of twenty-three years (1990-2013). (shrink)

The Law of Non-Contradiction holds that both sides of a contradiction cannot be true. Dialetheism is the view that there are contradictions both sides of which are true. Crucial to the dispute, then, is the central notion of contradiction. My first step here is to work toward clarification of that simple and central notion: Just what is a contradiction?

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of (...) the Law which appears to be unquestionable, in the sense that the Priestian dialetheist is committed to accept it without also accepting something inconsistent with it, on pain of trivialism—that is to say, on pain of lapsing into the position according to which everything is the case. This will be achieved via (a) a discussion of Priest's dialetheic treatment of the notions of rejection and denial; and (b) the characterization of a negation via the primitive intuition of content exclusion. Such a result will not constitute a cheap victory for the friends of consistency. We may just learn that different things have been historically conflated under the label of 'Law of Non-Contradiction'; that dialetheists rightly attack some formulations of the Law, and orthodox logicians and philosophers have been mistaken in assimilating them to the indisputable one. (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)

Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...) Georg Cantor (1845-1918) says that between the realm of the finite and the absolute infinite, there is an intermediate realm partaking in properties in a certain sense of both the finite and the infinite: the transfinite realm. Like the finite, the transfinite realm is a realm of mathematical objects, numbers, and knowledge. Like the absolute infinite, the transfinite is a form of infinity insofar as transfinite sets and numbers transcend any finite number. Echoing Cusanus and neo-Platonism, Cantor says that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, that is, God. This paper considers how the doctrine of symbolism and the philosophers' different commitments to the laws of logic, especially the Law of Non-Contradiction (LNC), enables these thinkers to articulate a transcendental apophatic approach to divinity. (shrink)

Hume’s Treatise, with its celebrated bundle theory of the self, is a significant contribution to the embryonic Newtonian experimental philosophy of the enlightenment. But the theory is inadequate as it stands, as the appendix to the Treatise makes clear. For this account of the self, apparently, rests on contradictory principles — propositions, fortunately, that can be reconciled, according to Hume. My paper is a critical exploration of Hume’s argument for this intriguing suggestion.

A dialectical contradiction can be appropriately described within the framework of classical formal logic. It is in harmony with the law of noncontradiction. According to our definition, two theories make up a dialectical contradiction if each of them is consistent and their union is inconsistent. It can happen that each of these two theories has an intended model. Plenty of examples are to be found in the history of science.

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.

This article challenges the prevailing interpretations of Hegel's account of the concept "contradiction" in the Science of Logic by arguing that it is concerned with the principle of Hegel's method rather than with the classical law of non-contradiction. I first consider Hegel's Doctrine of Essence in view of Kant's discussion of the concepts of reflection in the first Critique. On this basis, I examine Hegel's account of the logical principles based on the concepts "identity," "opposition," and "contradiction." (...) Finally, I point out how the principle Hegel derives from the concept of contradiction actually informs his own method. (shrink)

There are two ways of understanding the notion of a contradiction: as a conjunction of a statement and its negation, or as a pair of statements one of which is the negation of the other. Correspondingly, there are two ways of understanding the Law of Non-Contradiction (LNC), i.e., the law that says that no contradictions can be true. In this paper I offer some arguments to the effect that on the first (collective) reading LNC is non-negotiable, but on (...) the second (distributive) reading it is perfectly plausible to suppose that LNC may, in some rather special and perhaps undesirable circumstances, fail to hold. (shrink)

When faced with the charge that a given concept of God is contradictory, the standard move among philosophers and theologians has been to try to explain away the contradiction and show that the concept of God in question is consistent. This has to do, of course, with the Law of Non-Contradiction (LNC). Another option, which has recently generated interest among logicians and analytic philosophers of religion, is to reject such a move as unnecessary and defend what might be (...) called the contradictory God thesis. To be sure, something close to that can be found in philosophers such as Pseudo-Dionysius, Thomas Aquinas and Nicolaus de Cusa. However, it is only recently that this approach has gained momentum, certainly driven by the contemporary advance of dialetheism and glut theoretic approaches in general, and paraconsistent logic. Needless to say, a standard move among defenders of the contradictory God thesis is to reject the LNC. The argumentation, however, is seldomly framed in conceptual terms. Instead, it is mostly framed in ontological terms, as God being a contradictory entity. From this perspective, the contradictory God thesis is the thesis that God is a contradictory object. My goal in this paper is to provide a conceptual assessment of the discussion surrounding the contradictory God thesis. To achieve this, I make use of a general and hopefully non-controversial meta-theory of concepts and adopt a semantic approach rather than a metaphysical one. Within this framework, I address the following questions: What are the different ways we can understand the contradictory God thesis? What grounds are there for rejecting a contradictory concept of God? What standard moves are available to defend oneself from such criticisms and how do they relate to the LNC? What challenges do they present? As a secondary goal, the paper introduces a novel defense of the contradictory God thesis, drawing on a specific interpretation of the theology of the 16th-century Indian thinker Jīva Gosvāmī, which does not necessitate the rejection of the LNC. I term this approach ‘non-dialetheic mystical contradictory theism.’. (shrink)

Philosophy and Phenomenological Research, EarlyView.

It is widely agreed that fiction is necessarily incomplete, but some recent work postulates the existence of universal fictions—stories according to which everything is true. Building such a story is supposedly straightforward: authors can either assert that everything is true in their story, define a complement function that does the assertoric work for them, or, most compellingly, write a story combining a contradiction with the principle of explosion. The case for universal fictions thus turns on the intuitive priority we (...) assign to the law of non-contradiction. My goal in this paper is to show that our critical and reflective literary practices set constraints on story-telling which preclude universal fictions. I will raise four stumbling blocks for universal fictionalists: the gap between saying and making true, our actual interpretive reactions to story-level contradictions, the criteria we accept for what counts as a story in our literary practices, and the undesirability of the universal fictionalist’s closure principles. (shrink)

In this paper I examine what exactly is ‘Aristotelian metaphysics’. My inquiry into Aristotelian metaphysics should not be understood to be so much concerned with the details of Aristotle's metaphysics. I am are rather concerned with his methodology of metaphysics, although a lot of the details of his metaphysics survive in contemporary discussion as well. This warrants an investigation into the methodological aspects of Aristotle's metaphysics. The key works that we will be looking at are his Physics, Metaphysics, Categories and (...) De Interpretatione. Perhaps the most crucial features of the Aristotelian method of philosophising are the relationship between science and metaphysics, and his defence of the principle of non-contradiction (PNC). For Aristotle, natural science is the second philosophy, but this is so only because there is something more fundamental in the world, something that natural science – a science of movement – cannot study. Furthermore, Aristotle demonstrates that metaphysics enters the picture at a fundamental level, as he argues that PNC is a metaphysical rather than a logical principle. The upshot of all this is that the Aristotelian method and his metaphysics are not threatened by modern science, quite the opposite. Moreover, we have in our hands a methodology which is very rigorous indeed and worthwhile for any metaphysician to have a closer look at. (shrink)

Metamorphosis as it is represented by some pre-historical artists seems problematic for our occidental point of view. In fact, it seems to be strongly against identity and law of non-contradiction. Becoming in general is also viewed as an error or exception by our classic point of view. This very claim can conduct to theories of non-classical logic. Deleuze and Guattari in their monumental work had tried to offer enormous contributions in order to comprehend the becoming phenomenon. Through a pre-historical (...) representations analysis, with also an intrusion in contemporary art's field, I want to confront with possible metamorphosis representations remain theoretically founded in the deleuzian proposal in dialogue with phenomenological inquiry. New principle of individuation and analysis of expression provide new looks to arisen problems with classical logic and metamorphosis representations, which will be acceptable and comprehensible as art shows. (shrink)

Metamorphosis seems problematic for our occidental point of view. Becoming in general is viewed as an error or exception by our classic standpoint. In fact, it is strongly against identity and law of non-contradiction: A is fundamentally something different from B and for A it is impossible to be at the same time B. We need to think A as what-becomes-B in order to make metamorphosis possible. Anyway, how can A become B? As a matter of fact, this very (...) claim has been historically the most common critic opposed to becoming. Deleuze and Guattari in their monumental work had tried to offer an enormous contribution to a few related problems. Redefining the subject as an event described by movement and affect can exceed the metamorphosis’ aporia. This new principle of individuation provides a new look upon arisen questions primarily because affects and movements are constant coordinates that define how metamorphosis is experienced. The paper tries to show how the betweenness in action in the encounter with people, human beings, things, animals, plants and minerals defines the logic field of metamorphosis. This is shown in dialogue with the ontological turn in anthropology that is particularly focused on this affective and lively dimension of encounter especially among Amazonian populations. Actually this is also what happens in our – occidental and classical but live – relation with things and objects, as long as we try to think a real conceptualisation of experience. (shrink)

According to Aristotle if a universal proposition (for example: “All men are white”) is true, its contrary proposition (“All men are not white”) must be false; and, according to Aristotle, if a universal proposition (for example: “All men are white”) is true, its contradictory proposition (“Not all men are white”) must be false. I agree with what Aristotle wrote about universal propositions, but there are universal propositions which have no contrary proposition and have no contradictory proposition. The proposition X “All (...) the propositions that contradict this proposition are true” does not have the contrary proposition and does not have the contradictory proposition. In fact: FEX “All the propositions that contradict this proposition are not true” has a different subject: the subject of the proposition X is constituted by all the propositions that contradict the proposition X; by contrast, the subject of the proposition FEX is constituted by all the propositions that contradict the proposition FEX. And FOX “Not all the propositions that contradict this proposition are true” has a different subject: the subject of the proposition X is constituted by the propositions that contradict the proposition X; by contrast, the subject of the proposition FOX is constituted by the propositions that contradict the proposition FOX. According to Aristotle, a singular proposition (in his example: "Socrates is white") which is true must have its negative proposition ("Socrates is not white") which is false. I agree with Aristotle, but there are singular propositions which do not have the corresponding negative proposition. The proposition (or, rather, the pseudo-proposition) L “This same statement is not true” does not have the negative proposition because the proposition FNL “This same statement is true” has a different subject from the subject of the proposition L: the subject of the proposition L is the proposition L; by contrast, the subject of the proposition FNL is the proposition FNL. L and FNL cannot have the same subject. By contrast, the proposition M “This mount is entirely in Swiss territory” and the proposition NM “This mount is not entirely in Swiss territory” can have the same subject (for example, the Mount Eiger): in case the subject of the proposition M and the subject of the proposition NM is the same, M and NM are opposite propositions, NM is the negative proposition of M. By contrast, the proposition (or, rather, the pseudo-proposition) L "This same statement is not true" cannot have the corresponding negative proposition because FNL "This same statement is true" has a different subject: the subject of L is L ; by contrast, the subject of FNL is FNL. Then the paper continues by analyzing some variants of the liar’s paradox: L1 “The statement L1 is not true”; the so-called liar cycle; and the so-called Yablo’s paradox. (shrink)

Some forms of defining PNC in Aristotle’s works are as follows: a) Everything must be either affirmed or denied (φάναι ἢ ἀποφάναι). (Met., B, 996b28-29) or: it will not be possible to assert and deny the same thing truly at the same time. (Met., Γ, 1008a36-b1) In other words, ‘contradictory statements (ἀντικειμένας φάσεις) are not at the same time true. (Met., Γ, 1011b13-14) Also, ‘It is impossible that contradictories (ἀντίφασιν) should be at the same time true of the same thing.’ (...) (Met., Γ, 1011b15-16) Also, ‘Opposite statements (ἀντικειμένας φάσεις) can never be true of the same subjects.’ (Met., K, 1062a33-34; 1063b15-17) Also, ‘Of all affirmation or negation one is impossible. (PsA., A, 11, 77a22) b) A thing cannot at the same time be and not be. (Met., B, 996b30-31; Γ, 1006a3-5) This can also be extended to many other similar pairs of opposites: ‘The same thing cannot at the same time be and not be, or admit any other similar pair of opposites.’ (Met., K, 1061b34-1062a2) Also, ‘It will be possible for the same thing to be and not to be, except in virtue of an ambiguity.’ (Met., Γ, 1006b18-19) This is also asserted in another similar way: it is impossible that it should be at the same time true to say the same thing is a thing and is not a thing.’ (Met., Γ, 1006b33-34) c) ‘The same attribute cannot at the same time belong (ὑπάρχειν) and not belong to the same object in the same respect.’ (Met., Γ, 1005b19-21) d) Those positive and negative propositions are said to be contradictory which have the same subject and predicate. (OI, I, 7, 17a33-35) The opposition between an affirmation and a denial makes contradictories (ἀντίφασεως). (PsA., A, 2, 72a11-14) Based on Aristotle’s definition, ‘An affirmation is opposed to a denial in the sense which I denote by the term ‘contradictory’ (ἀντίφατικως), when, while the subject remains the same, the affirmation is of universal character and the denial is not.’ (OI., I, 7, 17b16-19) 1) Characteristics of PNC a) It is the most certain (Met., Γ, 1005b22-23 and b11) and the most indisputable (Met., Γ, 1006a5-6) of all principles. b) It is impossible: to believe its contrary (Met., Γ, 1005b24-30); to be really in that position (Met., Γ, 1008b11-13); and to defend it. (OI, I, 9, 18b17-19) Nonetheless, Aristotle thinks that many of the writers about nature assert the contrary of PNC and use a language opposite to it. (Met., Γ, 1005b35-1006a3) c) It is the starting point of all the other axioms. (Met., Γ, 1005b32-34) d) It is not hypothetical. (Met., Γ, 1005b13-17) e) Contradictories are extremely opposed to each other. (Met., Γ, 1007a1-4) f) Believing in PNC saves substance and essence and not believing in it makes all attributes accidents and there will be nothing as being essentially something. The reason is that something which essentially is a being cannot avoid being that thing. (Met., Γ, 1007a20-29 and b16-18) g) PNC supports plurality of things because otherwise all things will be one: ‘If all contradictories are true of the same subject at the same time, evidently all things will be one. For the same thing will be a trireme, a wall, and a man, if it is equally possible to affirm and deny anything of anything.’ (Met., Γ, 1007b18-22) In fact, PNC supports difference: ‘For if contradictories can be predicated alike of each subject, one thing will in no wise differ from another; for if it differs, this difference will be something true and peculiar to it.’ (Met., Γ, 1008a25-27) h) To accept truth and falsity, whether in an absolute sense (e.g. A is more true than B; or C is less true than D) entails PNC. (Met., Γ, 1008b2-7 and b31-35; 1009a2-5) In fact, PNC is entailed by accepting true affirmation. (Met., K, 1062b7-11) i) Judging and choosing between at least two things entails PNC: you cannot choose one as better than another without a previous judging that one is A and the other not A. (Met., Γ, 1008b18-24) The same is true about avoiding. (Met., Γ, 1008b24-29) j) PNC guarantees speaking and saying anything intelligible because otherwise e.g. saying ‘yes’ means both yes and no. (Met., Γ, 1008b7-13) k) Contradictories do not accept intermediates that means we must either affirm or deny a predicate on a subject and there is no third option. (Met., Γ, 1011b23-24; Met., I, 1055b1-2; PsA., A, 2, 72a11-14; Met., I, 1057a33-36) l) PNC is applicable also to the future time. (OI., I, 9, 19a28-29) m) PNC is presupposed by the least semantic of words. If we accept that each word has a meaning and, thus, signifies something definite, we cannot accept that it has the contradictory meaning and signies contradictory things and this approves PNC. Thus, Aristotle asks the opponent of PNC to say just one word, a significant word and takes this as the demonstration of PNC because by saying the word e.g. ‘man’ you have already signified man and not-man. (Met., Γ, 1005a11-13 and a18-22; 1006a28-31 and b13-15) Therefore, signification entails PNC: ‘He, then, who says this is and is not denies what he affirms, so that what the word signifies, he says it does not signify; and this is impossible. Therefore, if ‘This is’ signifies something, one cannot truly assert the contradictory.’ (Met., K, 1062a16-20) He says again: ‘If the word signifies something and this can be truly asserted of it, it necessarily is this; and it is not possible that that which is necessary should ever not be: it is not possible therefore to make the opposed assertions truly of the same subject.’ (Met., K, 1062a20-23; cf. Met., K, 1062a24-31) n) At Met., 4, 3, 1005b9-10 (check???) PNC is called as principle of things (ἀρχὰς τοῦ πράγματος). (quoted from B215, 517) . (shrink)

Truth pluralism offers the latest extension in the tradition of substantive theorizing about truth. While various forms of this thesis are available, most frameworks commit to domain reliance. According to domain reliance, various ways of being true, such as coherence and correspondence, are tied to discourse domains rather than individual sentences. From this follows that the truth of different types of sentences is accounted for by their domain membership. For example, sentences addressing ethical matters are true if they cohere and (...) those addressing extensional states of affairs if they correspond. By tying distinct truth-grounding properties to domains rather than individual sentences, truth pluralists avoid certain issues with definitional ambiguity and indeterminacy. I argue that contrary to the ideal situation, domains fail to provide the sought-after benefits of achieving definitional unambiguity and determinacy in the standard domain reliant pluralist frameworks. The reason is that, when combined with the inherently ambiguous nature of certain truth-relevant terms of sentences, fringe cases emerge, causing some of them to count as members of multiple domains. Consequently, some sentences end up being both true and false in the standard domain reliant pluralist frameworks, thus conflicting with both standard laws of non-contradiction and identity. Finally, I argue that truth pluralists should pay closer attention to the hitherto neglected question of inherent natural language ambiguity. (shrink)

Arthur Kaufmann is one of the most prominent figures among the contemporary philosophers of law in German speaking countries. For many years he was a director of the Institute of Philosophy of Law and Computer Sciences for Law at the University in Munich. Presently, he is a retired professor of this university. Rare in the contemporary legal thought, Arthur Kaufmann's philosophy of law is one with the highest ambitions — it aspires to pinpoint the ultimate foundations of law by explicitly (...) proposing an ontology, a general theory of knowledge and concept of a person. Kaufmann's work derives, first of all, from the thinking of Gustav Radburch, his teacher, and then from ideas of Karl Engish and Hans-Georg Gadamer. The philosophy undertakes to pursue the ultimate foundation of law, law which is understood by Kaufmann, first of all, as a "concrete judgement" that is, what is right in a concrete situation. Justice belongs to the essence of law and "unjust law" is contradictio in adiectio. Kaufmann opposes all those theories, which as the only foundation for establishing just law (Recht) adopt legal norms (Gesetz). In Kaufmann's opinion , such theories are powerless in the face of all types of distortions of law rendered by political forces. He suggests that the basic phenomenon which needs to be explained and which cannot be disregarded by a philosopher of law is so-called "legal lawlessness" ("Gestzliches Unrecht"). "Legal lawlessness" which forms a part of life experience for the people of twentieth century totalitarian states. It proved "with the accuracy of scientific experiment" that the reality of law consists of something more than bare conformity with legal norms. The existence of lex corrupta indicates that law contains something "non-dispositive" which requires acknowledgment of both law-maker and judge. Kaufmann, accepting the convergent concept of truth and cognition, assumes that "non-dispositive" content, emerging as the conformity of a number of cognitive acts of different subjects (inter-subjective communicativeness and verifiability), indicates the presence of being in this cognition. The questions "What is law?" and "What are the principles of a just solution?" lead straight to the ontology of law, to the question about the ontological foundations of law. Kaufmann discerns the ontological foundations of law in the specifically understood "nature of things" and, ultimately, in a "person". He proposes a procedural theory of justice, founded on a "person". In my work, I undertake to reconstruct the train of thought which led Kaufmann to the recognition of a "person" as the ontological foundation of law. In the first part, the conception of philosophy adopted by Kaufmann, initial characteristics of law — of reality which is the subject of analysis, as well as, the requirements for proper philosophical explanation of law posed by Kaufmann are introduced. In the second, Kaufmann's reconstruction of the process of the realisation of law is presented. Next, the conception of analogy which Kaufmann uses when explaining law is analyzed. In the fourth part, Kaufmann's conception of ontological foundations of law is discussed. A critical analysis is carried out in which I demonstrate that the theory of the ontological foundation of law proposed by Kaufmann and the concept of a person included in it do not allow a satisfac¬tory explanation of the phenomenon of "legal lawlessness" and lead to a number of difficulties in the philosophical explanation of law. Finally, the perspectives of a proper formulation of the issue of the ontological foundations of law are drafted in the context of the analyzed theory. My interest is centered on the conception of philosophy adopted by Kaufmann, according to which the existence of the reality is inferred on the basis of a certain configuration of the content of consciousness, whereas at the point of departure of philosophy of law, the data to be explained is a certain process, which is, basically, a process of cognition, while the reality appears only as a condition for the possibility of the occurrence of the process. I wish to argue that the difficulties which appear in the explanation of law are a consequence of the assumed fundamental philosophical solu¬tions, which seem to be characteristic, though usually not assumed explicitly, in philoso¬phy and theory of law dominant at present in continental Europe. Thereby, I wish to show the significance of ontological and epistemological solutions to the possibility of a proper formulation of the problems posed by philosophy and theory of law. Kaufmann proclaims himself in favour of a philosophy which poses questions about the ultimate foundations of understanding of the reality. In epistemology, he assumes that answers to the questions "What is reality like?" and ultimately "What is real?" are inferred on the basis of uniformity of a cognitive acts of different subjects. Cognition of the reality is accomplished exclusively through the content of conceptual material. The two fundamental questions posed by philosophy of law are "What is just law?" and "How is the just law enacted?" The latter is a question about the process of achieving a solution to a concrete case. Since, in Kaufmann's opinion, law does not exist apart from the process of its realisation, an answer to the question about the manner of realisation of law is of fundamental significance to answering the question: "What is law?" and to the explanation of the question about the ontological grounding of law, which is, as well, the foundation of justice. The proper solution has to take into account the moment of "non-dispositive" content of law; its positiveness understood as the reality and, at the same time, it has to point to the principles of the historical transformation of the content. Law, in the primary meaning of the word, always pertains, in Kaufmann's opinion, to a concrete case. A legal norm is solely the "possibility" of law and the entirely real law is ipsa res iusta, that which is just in a given situation. Determination of what is just takes place in a certain type of process performed by a judge (or by man confronted with a choice). Kaufmann aims to reconstruct this process. A question about the ontological foundation of law is a question about the ontological foundations of this process. In the analyzed theory it is formulated as a question about the transcendental conditions, necessary for the possibility of the occurrence of the process: how the reality should be thought to make possible the reconstructed process of the realisation of law. Kaufmann rejects the model for finding a concrete solution based on simple subsump¬tion and proposes a model in which concrete law ensues, based on inference by analogy, through the process of "bringing to conformity" that which is normative with that which is factual. Kaufmann distinguishes three levels in the process of the realisation of law. On the highest level, there are the fundamental legal principles, on the second legal norms, on the third — concrete solutions. The fundamental principles of law are general inasmuch as they cannot be "applied" directly to concrete conditions of life, however, they play an important part in establishing norms. A judge encounters a concrete situation and a system of legal norms. A life situation and norms are situated on inherently different levels of factuality and normativeness. In order to acquire a definite law both a norm (system of norms) and a life situation (Lebenssachverhalt) should undergo a kind of "treatment" which would allow a mutual conformity to be brought to them. Legal norms and definite conditions of life come together in the process of analogical inference in which the "factual state" ("Tatbestand") — which represents a norm, and in the "state of things" ("Sachverhalt") — which represents a specific situation are constructed. A "factual state" is a sense interpreted from a norm with respect to specific conditions of life. The "state of things" is a sense constructed on the basis of concrete conditions of life with respect to norms (system of norms). Legal norms and concrete conditions of life meet in one common sense established during the process of realisation of law. Mutatis mutandis the same refers to the process of composition of legal norms: as the acquisition of concrete law consists in a mutual "synchronization" of norms and concrete conditions of life, so acquisition of legal norms consists of bringing to conformity fundamental principles and possible conditions of life. According to Kaufmann, both of these processes are based on inference through analogy. As this inference is the heart of these processes it is simultaneously a foundation finding just law and justice. How does Kaufmann understand such an inference? As the basis for all justice he assumes a specifically interpreted distributive justice grounded on proportionality. Equality of relations is required between life conditions and their normative qualification. Concrete conditions of life are ascribed normative qualification not through simple application of a general norm. More likely, when we look for a solution we go from one concrete normative qualified case to another, through already known "applications" of norms to a new "application". The relation between life conditions and their normative qualifica¬tion has to be proportional to other, earlier or possible (thought of) assignments of that which is factual to that which is normative. Law as a whole does not consist of a set of norms, but only of a unity of relations. Since law is a, based on proportion, relative unity of a norm and conditions of life, in order to explain law in philosophical manner, the question about ontological base of this unity has to be asked. What is it that makes the relation between a norm and conditions of life "non-dispositive"? What is the basis for such an interpretation of a norm and case which makes it possible to bring a norm and conditions of life into mutual "conformity"? This is a question about a third thing (next to norms and conditions of life), with respect to which the relative identity between a norm and conditions of life occurs, about the intermediary between that which is normative and that which is factual and which provides for the process of establishing of norms, as well as, finding solutions. It is the "sense" in which the idea of law or legal norm and conditions of life have to be identical to be brought to mutual "conformity". In Kaufmann's opinion such a sense is nothing else but the "nature of things" which determines the normative qualification of the reality. Since establishment of this "sense" appears to be "non-dispositive" and controlled inter-subjectively (namely, other subjects will reach a similar result) so, in conformity with the convergent concept of truth, the "nature of things" must be assigned a certain ontological status. According to Kaufmann this is a real relation which occurs between being and obligation, between the conditions of life and normative quality. However, it should be underlined that from the point of view of the analyzed system the "nature of things" is a correlate of constructed sense, a result of a construction which is based on the principle of consistent understanding of senses ("non-normative" and "normative") and is not a reality which is transcendent against the arrangement of senses. In Kaufmann's theory, inference from analogy appears to be a process of reshaping the concepts (senses) governed by tendency to understand the contents appearing in relations between that which is factual and that which is normative in a consistent way. The analogical structure of language (concepts) and recognition of being as composed of an essence and existence is an indispensable requirement for the possibility of the realisation of law, based on specifically understood inference from analogy. It is necessary to assume a moment of existence without content which ensures unity of cognition. Existence emerges thus as a condition of the possibility of cognition. According to Kaufmann, the "nature of things" is the heart of inference through analogy and the basis for establishment of finding of law. Inference from the "state of things" to a norm or from a norm to the "state of things" always means inference through the "nature of things". The "nature of things" is the proper medium of objective legal sense sought in every cognition of law. In Kaufmann's view, the question whether the "nature of things" is ultima ratio of interpretation of law or is only a means of supplement gaps in law or whether it is one of the sources of law, is posed wrongly. The "nature of things" serves neither to supplement the gaps nor is it a source of law as, for example, a legal norm may be. It is a certain kind of "catalyst" necessary in every act of making law and solving a concrete case. Owing to "nature of things" it is possible to bring to a mutual conformity the idea of law and possible conditions of life or legal norms and concrete conditions of life. In Kaufmann's conception the "nature of things" is not yet the ultimate basis for understanding the "non-dispositiveness" of law. The relation between obligation and being is determined in the process of the realisation of law. Both the process itself and that which is transformed in this process are given. A question about the ontological bases of "material" contents undergoing "treatment" in the process of the realisation of law and about being which is the basis of regularity of the occurrence of the process arises. Only this will allow an explanation that the result of the process is not optional. Thus, a question about reality to which law refers and about the subject realising the law has to be formed. To this, Kaufmann gives the following answer: that which is missing is man but not "empirical man" but man as a "person". A "person" understood as a set of relations between man and other people and things. A "person" is the intermediary between those things which are different — norm and case are brought to conformity. A "person" is that which is given and permanent in the process of the realisation of law. It determines the content of law, is "subject" of law; this aspect is described by Kaufmann as the "what" of the process of realisation of law. A "person" consists of precisely just these relations which undergo "treatment" in the process. On the other hand, a "person" is "a place" in which the processes of realisation of law occur, it is the "how" of normative discourse, a "person" is that which determines the procedure of the process, being "outside" of it. This aspect of a "person" is connected with the formal moment of law. A "person" being, at the same time, the "how" and the "what" of the process of the realisation of law, is also, to put it differently, a structural unity of relation and that which constitutes this relation (unity of relatio and relata). According to this approach a "person" is neither an object nor a subject. It exists only "in between". It is not substance. Law is the relation between being and obligation. That which is obligatory is connected with that which is general. That which is general does not exist on its own, it is not completely real. Accordingly, a "person" as such is also not real. It is relational, dynamic and historical. A "person" is not a state but an event. In Kaufmann's opinion, such a concept of a "person" helps to avoid the difficulties connected with the fungibility of law in classical legal positivism. A "person" is that which is given, which is not at free disposal and secures the moment of "non-dispositiveness" of law. Kaufmann concludes: "The idea (»nature«) of law is either the idea of a personal man or is nothing". Theory points at the structure of realising law and explains the process of adoption of general legal norms for a concrete situation. The analysis has shown however, that in this theory a satisfactory answer to the question about the ultimate foundations of law is not given. It seems that in the analyzed theory the understanding of human being takes place through understanding of law. What is good for man as a "person", what is just, what a "person" deserves may be determined only against the existing system of law. A "per¬son" adopted as a basis of law is the reality postulated in the analysis of the process of the realisation of law. It is a condition of possibility of this process ( explaining, on one hand, its unity and, on the other hand, the non-dispositive moments stated in this process). A "person" in the discussed theory is entirely defined by the structure of law, it can be nothing more than that which is given in law, what law refers to, what law is about. Being, which is a "person", is constituted by relations between people and objects, the relations which are based on fundamental links between norms and conditions of life established in a process of bringing them to conformity. It has to be assumed that man as a "person" is a subject of law only as far as realising law "treats" given senses according to their current configuration. The system of law is a starting point and it describes in content what man is as a "person". Moreover, being a "person" is the condition for entering legal relations. Consistently, Kaufmann writes that "empirical man" is not the subject of law, man is not "out of nature" a "person". People become "persons" due to the fact that they acknowledge each other as "persons" — acknowledging, at the same time, law. This acknowledgement is a con¬dition of existence, of the possibility of the occurrence of process of realisation of law and of constituting legal relations which ultimately constitute a "person". Kaufmann assumes, that law tends towards a moral aim: it may and must create an external freedom, without which the internal freedom to fulfil moral obligations cannot develop. However, this postulate is not based on the necessary structure of human being. From the point of view of his system, it is nothing more than only a condition for the possibility of the occurrence of the process of the realisation of law — lack of freedom would destroy the "how" of this process. Thus, the postulate to protect the freedom of personal acts has to be interpreted, in accordance with the analyzed theory, as a postulate, the fulfilment of which aims ultimately at the accomplishment of the very same process of realisation of law itself and not the realisation of a given man. Kaufmann considers a "person" to be an element which unites the system of law as a whole. Law is a structure of relations, which are interdependent and inter-contingent. Consequently, a "person" which is to form the ontological basis of law has to be entity consisting of all relations. Being also the "how" of the process of realisation of law, if a "person" is to warrant its unity, it has to be a common source for all procedures. Hence, a single "person" would constitute a subject of law. Man appears to be only a moment of a certain entirety, realisation of which should be an aim of his actions. Law, creating a "person" as an object and subject of law becomes a primary entity. In the analyzed theory, the basis for determination of aims which law sets to man is not the allocation of man-subject to something which improves him but rather, such relation is only just constituted by law. A question appears, why should aims set in law also be the aims of "empirical man"? Why is this "empirical man" to be punished in the name of a "person" understood in such a way? If, however, it is assumed that what is man is determined by a system which is superior to him, then man has to be understood only as a part of a whole and there are no grounds to prohibit istrumental treatment of man and so the road to all aspects of totalitarianism might be opened. A problem of the application of created theory to the reality arises, the reality which the theory pretends to explain. Ultimately in his theory Kaufmann does not give any systemic grounds for a radical questioning of the validity of any legal norms. Every new norm becomes an equal part of system of norms. It is only its interpretation and application to given conditions of life that may be disputable, however, this refers to all norms without exception. Cohesive inter-pretation of norms and applications is necessary and sufficient for the acquisition of just law. New norms have to be interpreted in the light of others, correspondingly, the other norms require reinterpretation in the light of the new ones. Contradiction in interpretation of a norm does not form a basis for questioning norms but may serve only to question the manner of their interpretation (understanding). Therefore, no grounds exist to assume any legal norm as criminal or unjust, and in consequence, to question any consistently realised system based on formally, properly established norms, as "legal lawlessness". As law and a "person" do not exist without the process of realisation of law, the role of legal safety becomes crucial as the condition for the possibility of the occurrence of the process of realisation of law. Denying legal safety would be tantamount to negation of law in general (also of moral law) as negation of safety takes away, at the same time, the basis for occurrence of the process of realisation of law. Moreover, any lack of legal safety would also mean lack of a basis for the existence of man as a "person". Kaufmann's thesis, that civil disobedience is legalized only when it has a chance to lead to success, consistent with his concept of the foundations of law, seems to point directly to conclusions which deny the facts taken under consideration and doubtlessly Kaufmann's own intentions, since it would have to be assumed that accordingly there are no grounds to question a legal system in force based on violence which secures its operation. Force finally seems to determine which one of the mutually irreconcilable normative systems constitute law and which does not. A legitimate position is one which leads to success, it is the weaker system which is negated. If so, then basically violent imposition of law is not an act directed against the law in force but, to the contrary, realisation of law. In the context of the new system the former system of law may be talked about as unjust solely in the sense of being incapable of being consistently united with the new. However, at the base, ultimately, lies force which reaffirms differences and excludes from the process of realisation of law certain norms and their interpretations. Kaufmann was aiming at grounding of that which is "non-dispositive" in a certain given framework of interpretation. Nevertheless, he does not provide foundations for the understanding of phenomena, which he undertakes to explain at a point of departure. Instead of explaining them the theory negates the possibility of their existence. The reality postulated in regard to "non-dispositive" moments of the reconstructed process of acquiring law consist of a specifically understood "person", which appears in Kaufmann's conceptions as a condition of the possibility of the realisation of law. According to this approach understanding of a "person" may be only a function of law. To understand "legal lawlessness" and foundations of justice it is necessary to look for such theory of law in which understanding of man as a "person" and being is not a function of understanding of law (in which a "person" is not only a condition for possibility of reconstructed process of realisation of law; for possibility of cognition processes). It seems necessary to start from theory of being and a "person" based on broader experience than the one assumed by Kaufmann and reconstruct the ontological foundations of the process of realisation of law only in such perspective. Kaufmann points out that that to which law refers is ipsa res iusta a concrete relation of man to other people and things. This relation, in his theory, appears to be basically only just constituted by law (normative senses "applied" to conditions of life). Therefore, understanding the relation between a given man and other people and things which constitute the aim of his actions, that is understanding of good, is enacted against the background of constitution of senses; constitution which is a result of a process aiming towards consistent understanding of particular contents (of nor¬mative and non-normative senses). "Being" is secondary towards constructed senses it is only their correlate. The primary relation consists of relation of a man to law (system of norms), while the secondary relation is one of man to something which is the aim of his action (relation between man and good). Considering such approach it is difficult to envision a satisfying answer to the fundamental question: why does law put concrete man under any obligation to obey it? The source of this problem can be seen in reduction of the base for understanding good to content of obligation formulated in auto-reflection. Such reduction seems to be a consequence of Kaufmann's adoption of "convergent concept of truth" and in con¬sequence his recognition of indirect, essentialistic grasp of reality formulated in concepts as the basic and only foundation of theory of being and of law. In view of such an approach, analogy of law, concepts and being is the condition for the possibility of the process of transformation of senses which aims at consistent interpretation of all law. Existence is postulated with respect to the possibility of unity of experience and cognition. However, also a different approach to understanding of the problem of being and good is possible. In spontaneous cognition being is affirmed, first of all, not as a certain, non-contradictory, determined content, but as something existing. Together with a cer¬tain content (passed indirectly through notions) existence of being is co-given. The basis for unity of being is not formed by the consistence of content, as it is in the case of the theories departing from the analysis of cognition processes, but by an act of existence realising content (essence). Such an approach makes it also possible to go beyond the convergent concept of truth. It is worth mentioning that allocation of an agent to good is realised not only by the content of duty. A statement that something is good is primary with respect to determination of this good in content. The recognised good always bears some content, however, there are no reasons to base the concept of good exclusively on indirect, formulated in concepts cognition. As primary, can be adopted the relation of man to good and not of man to law. Determination in content appears to be only an articulation of aspectual cognition of being, as an object of action. In such a case the basis for relative unity of norm and conditions of life is not the "nature of things" understood as correlate of sense but it is relation to good based on internal constitution of man as potential, not self-sufficient being. It does not mean, that the moments of the process of realisation of law singled out by Kaufmann are not important to determination of what is just. He, quite rightly, points to significant role played by norms in the evaluation of concrete situations, in man's search for closer specification in content of good innate to him. The structure of process of determining law for a concrete situation, to a great degree corresponds to the processes of determining law which take place not only in the legal sciences. Kaufmann's analyses of the process of realisation of law show the complexity of the structure of these processes and point towards important moments allowing a better understanding of law and man. Nevertheless, these analyses cannot be a basis for construction of philosophical theory of law, theory which hopes to point out the ultimate, ontological foundations for understanding law. Kaufmann's results may become fully valid only in a more general perspective including broader experience at the point of departure. (shrink)

I show that standard dynamic approaches to the semantics of epistemic modals invalidate the classical laws of excluded middle and non-contradiction, as well as the law of epistemic non-contradiction. I argue that these facts pose a serious challenge.

The purpose of this paper is to examine the status of logic from a metaphysical point of view – what is logic grounded in and what is its relationship with metaphysics. There are three general lines that we can take. 1) Logic and metaphysics are not continuous, neither discipline has no bearing on the other one. This seems to be a rather popular approach, at least implicitly, as philosophers often skip the question altogether and go about their business, be it (...) logic or metaphysics. However, it is not a particularly plausible view and it is very hard to maintain consistently, as we will see. 2) Logic is prior to metaphysics and has metaphysical implications. The extreme example of this kind of approach is the Dummettian one, according to which metaphysical questions are reducible to the question of which logic to adopt. 3) Metaphysics is prior to logic, and your logic should be compatible with your metaphysics. This approach suggests an answer to the question of what logic is grounded in, namely, metaphysics. Here I will defend the third option. (shrink)

The purpose of this thesis is to demonstrate that metaphysics is a necessary discipline -- necessary in the sense that all areas of philosophy, all areas of science, and in fact any type of rational activity at all would be impossible without a metaphysical background or metaphysical presuppositions. Because of the extremely strong nature of this claim, it is not possible to put forward a very simple argument, although I will attempt to construct one. A crucial issue here is what (...) metaphysics in fact is -- the nature of metaphysics. The conception of metaphysics which I support could be called Aristotelian, as opposed to Kantian: metaphysics is the first philosophy and the basis of all other philosophical and scientific inquiry. I will argue that this is indeed the most plausible conception of metaphysics. (shrink)

The thesis that the two-valued system of classical logic is insufficient to explanation the various intermediate situations in the entity, has led to the development of many-valued and fuzzy logic systems. These systems suggest that this limitation is incorrect. They oppose the law of excluded middle (tertium non datur) which is one of the basic principles of classical logic, and even principle of non-contradiction and argue that is not an obstacle for things both to exist and to not exist (...) at the same time. However, contrary to these claims, there is no inadequacy in the two-valued system of classical logic in explanation the intermediate situations in existence. The law of exclusion and the intermediate situations in the external world are separate things. The law of excluded middle has been inevitably accepted by other logic systems which are considered to reject this principle. The many-valued and the fuzzy logic systems do not transcend the classical logic. Misconceptions from incomplete information and incomplete research are effective in these criticisms. In addition, it is also effective to move the discussion about the intellectual conception (tasawwur) into the field of judgmental assent (tasdiq) and confusion of the mawhum (imaginable) with the ma‘kûl (intellegible). (shrink)

This chapter defends a single, fixed, definite answer to the question: Is there a logic that governs the unsayable? The proposed answer is: “Yes, and no. Or yes-but-not-yes. And/or yes-no.” Each component of this answer is examined and used to generate three laws of what I call “synthetic logic”, which correspond directly to the laws of classical (Aristotelian) logic: the law of contradiction (“A=-A”), the law of non-identity (“A≠A”), and the law of the included middle (“-(Av-A)”). We can talk (...) about the unsayable only by assuming that propositions constructed in accordance with these three alternative logical laws can be meaningful. (shrink)

Spinoza ’s letter of June 2, 1674 to his friend Jarig Jelles addresses several distinct and important issues in Spinoza ’s philosophy. It explains briefly the core of Spinoza ’s disagreement with Hobbes’ political theory, develops his innovative understanding of numbers, and elaborates on Spinoza ’s refusal to describe God as one or single. Then, toward the end of the letter, Spinoza writes: With regard to the statement that figure is a negation and not anything positive, it is obvious that (...) matter in its totality, considered without limitation [indefinitè consideratam], can have no figure, and that figure applies only to finite and determinate bodies. For he who says that he apprehends a figure, thereby means to indicate simply this, that he apprehends a determinate thing and the manner of its determination. This determination therefore does not pertain to the thing in regard to its being [esse]; on the contrary, it is its non-being [non-esse]. So since figure is nothing but determination, and determination is negation [Quia ergo figura non aliud, quam determinatio, et determinatio negatio est], figure can be nothing other than negation, as has been said. Arguably, what is most notable about this letter is the fate of a single subordinate clause which appears in the last sentence of this passage: et determinatio negatio est. That clause was to be adopted by Hegel and transformed into the slogan of his own dialectical method: Omnis determinatio est negatio. Of further significance is the fact that, while Hegel does credit Spinoza with the discovery of this most fundamental insight, he believes Spinoza failed to appreciate the importance of his discovery. The issue of negation and the possibility of self-negation stand at the very center of the philosophical dialogue between the systems of Spinoza and Hegel, and in this paper I will attempt to provide a preliminary explication of this foundational debate between the two systems. In the first part of the paper I will argue that the “determination is negation” formula has been understood in at least three distinct senses among the German Idealists, and as a result many of the participants in the discussion of this formula were actually talking past each other. The clarification of the three distinct senses of the formula will lead, in the second part of the paper, to a more precise evaluation of the fundamental debate between Spinoza and Hegel regarding the possibility of self-negation. In this part I will evaluate the validity of each interpretation of the determination formula, and motivate the positions of the various participants in the debate. (shrink)

outrageous remarks about contradictions. Perhaps the most striking remark he makes is that they are not false. This claim first appears in his early notebooks (Wittgenstein 1960, p.108). In the Tractatus, Wittgenstein argued that contradictions (like tautologies) are not statements (Sätze) and hence are not false (or true). This is a consequence of his theory that genuine statements are pictures.

*North American Society for Social Philosophy (NASSP) Book Award 2019.* -/- *International Studies Association (ISA) - International Ethics Section Book Award 2021.* -/- Although military mores have relied primarily on just war theory, the ethic of cooperation in warfare (ECW)—between enemies even as they are trying to kill each other—is as central to the practice of warfare and to conceptualization of its morality. Neither game theory nor unilateral moral duties (God-given or otherwise) can explain the explicit language of cooperation in (...) developing and enforcing principles of military ethics and the law of armed conflict. -/- The ethic of cooperation is borne of various motivations: reciprocity, self-preservation, and efficiency, to be sure, but also a sense of warrior honor and concern with human rights. This shared morality can persist despite making it more difficult for one side or the other to win and, unfortunately, its well-meaning motivations often lead to unintended tragic consequences. -/- This book explores three manifestations of this significant yet overlooked ethic of cooperation in warfare: (1) for a “fair fight,” (2) to protect classes of individuals (e.g., non-combatants or prisoners of war), and (3) to end the war quickly. Such cooperation can take unexpected forms, from ad hoc decisions on the battlefield to institutionalization in international law, and is the source of some critical tensions in one of the most significant developments in warfare in recent years: namely, how to handle terrorism or other forms of warfare that lie outside the purview of international law. -/- Each type of ECW raises questions internal to that ethic, such as inconsistencies in the concept of “parity” across different weapons bans, contradictions within the warrior ethic that heavily influence—and therefore confuse—notions of the “fair fight,” the disconnect between what protections a person receives and his responsibility for the war (e.g., political leaders), or the limited decisiveness of outcomes generated by very short wars. -/- Their simultaneous application also generates significant tensions and raises questions about the proper relationship of ECW to the immediate goal of war itself, which is to win, and thus yield either a political settlement or a justicial decision. For example, the ECWs for a “fair fight” and to protect classes of individuals can make it harder to win the war, but even more concerning is that they can also kill more people, which in the latter case contravenes its very purpose. -/- Human history is in some ways the story of trying to concurrently wage and tame war, and the architecture of warfare itself is informed by the ECW, in particular: (a) the political nature of war, (b) the abdication from jus ad bellum judgments in order to concentrate on justice within war (jus in bello), and (c) the ways in which modern nation-states collude to define “legitimacy” in war. -/- The combination of these three features leave questions of justicial right and responsibility for war disturbingly unresolved, it also generates new challenges in a geopolitical context in which cooperative and non-cooperative (e.g. contemporary terrorism) forms of warfare clash. (shrink)

The Swiss psychologist Jean Piaget contends that children below the age of 12 see no necessity for the logical law of non-contradiction. I argue this view is problematic. First of all, Piaget's dialogues with children which are considered supportive of this position are not clearly so. Secondly, Piaget underestimates the necessary nature of following the logical law of non-contradiction in everyday discourse. The mere possibility of saying something significant and informative at all presupposes that the law of non- (...) class='Hi'>contradiction is enforced. (shrink)

This article reviews John Wood’s Truth in Fiction: Rethinking its Logic.

In this paper, I argue that Kantian ethics is not inclusive, and his formulation of CI fails. It excludes some intuitive moral actions. I show that Kant’s formulation of categorical imperative fails in some important category of moral actions, due to the fact that its first formula (i.e., the formula of universal law ) is contingent, and doesn't necessarily obtain in all categories of moral actions. Wood in 1999 shows that the formula of universal law is incomplete, however, I argue (...) that it is not a necessary condition for moral action; and this entails the failure of CI. There are some exceptional moral maxims (and relevant actions), which are both permissible and moral, but they cannot be thought as universal one, without practical contradiction. (shrink)

In his Groundwork of the Metaphysics of Morals, Kant’s desiderata for a supreme principle of practical reasoning and morality require that the subjective conditions under which some action is thought of as justified via some maxim be sufficient for judging the same action as justified by any agent in those conditions. This describes the kind of universalization conditions now known as moral supervenience. But when he specifies his “formula of universal law” (FUL) Kant replaces this condition with a quite different (...) kind of universality: the judgment that some agent could rationally (i.e., without willing the frustration of his own valued ends) will his adoption of some maxim under the condition that this would cause all agents in his world to adopt it as well. Our wills typically lack this efficacy, so requiring that our wills conform to what would be rational for a hypothetical agent in this situation to will is a heteronomous requirement. Several intuitively wrong maxims pass Kant’s test but fail the test of supervenience, because they generate no contradiction in a world of universal compliance but do so in non-ideal worlds, demonstrating the inadequacy of the FUL and the logical superiority of moral supervenience. -/- Note that in the published version the title of this article incorrectly had the word "become" instead "became.". (shrink)

Philosophy and Phenomenological Research, EarlyView.

The contrast between the strategies of research employed in reductionism and holism masks a radical contradiction between two different scientific philosophies. We concentrate in particular on an analysis of the key philosophical issues which give structure to holistic thought. A first (non-exhaustive) analysis of the philosophical tradition will dwell upon: a) the theory of emergence: each level of organisation is characterised by properties whose laws cannot be deduced from the laws of the inferior levels of organisation (Engels, Morgan); b) (...) clarification of the relations between the “whole” and the “parts” (Woodger, Needham); c) the ontological or epistemological nature of the emergent properties; are they a phenomenological reality or solely an artefact of the state of our knowledge? (Pepper, Henle, Hempel and Oppenheim); d) the proposition of the holistic theoretical and methodological model ( Novikoff, Feibleman). I then go on to examine the differences that exist between the reductionist and the holistic approaches at various levels of analysis: that is to say, the differences which affect their ontologies, methodologies and epistemologies respectively. I attempt to understand the spirit of a holistic approach to ecology by analyzing the major work of E.P. Odum Fundamentals of ecology (1953, 1959, 1971). I set forward what might be meant by the “holistic approach”, which is implicated in all the different levels of organisation at which the problem of “complexity” is debated. Ecology presents itself as an “holistic science” and Odum’s book offers a vision of the world which dates far back in the history of philosophy. By looking at the three different editions of this fundamental text on ecology, we may become aware of the evolution of Odum’s thought. In fact, only in the third and last edition is there a conscious appropriation of the holistic approach (by using the theoretical models of Feibleman who, for his part, refers to Novikoff). However, even when formally referring to the theory of emergence (that is to say the ontological nucleus of every holistic approach), Odum’s systemic analysis presents the same logical errors, which push him back into the reductionist domain. Above all, in his examination of the main concepts of “population”, “community” and “ecosystem”, there is a misunderstanding of the profound difference between “collective properties” and “emergent properties”. Moreover, the cybernetic models of Odum’s systemic analysis (introduced into ecology by Margalef), allowed him to vastly oversimplify his methodological task: in fact, neither how many levels nor which levels of organization are fundamental for the study of each individual level is clearly marked. Finally, Odum analyses the ecosystem as composed of energetic flux and cycles of matter, referring to the trophic-dynamic vision of Lindeman. That is to say, in my opinion, he juxtaposes a reductionistic methodology and epistemology to an holistic ontology. (shrink)

When this article was first planned, writing was going to be exclusively about two things - the origin of life and human evolution. But it turned out to be out of the question for the author to restrict himself to these biological and anthropological topics. A proper understanding of them required answering questions like “What is the nature of the universe – the home of life – and how did it originate?”, “How can time travel be removed from fantasy and (...) science fiction, to be made scientific and practical?”, and “How can the proposed young age of genus Homo be made to actually be reasonable – when simply stating it would be solid ground for instant rejection and dismissal?” The result is that the article also talks about subjects like Artificial Intelligence, General Relativity, and cosmology. -/- From where did life originate? God? Evolution? Panspermia? If the tendency of humans and scientists to regard undiscovered science as pseudoscience can be overcome, Einstein gave another alternative to consider when he introduced General Relativity. Time isn’t linear – progressing in a straight line from past to present to future. That assumption ignores Relativity which states that space AND TIME are curved. Where did life and the genetic code come from? Can the answer build AI? -/- The first question can be answered by the section of this article titled SETI, Evolution, and Time which says life (possibly multicellular and intelligent) and the genetic code came from humans acquiring knowledge of these things over the centuries, then applying that knowledge – via terraforming, accumulation of raw materials like amino acids and nucleic acids, genetic engineering - to a time in the past when life didn’t exist. From that origin, life evolved through innumerable mutations and adaptations, with humans once again acquiring knowledge of it in cyclic (nonlinear) time. -/- The second question is answered by saying artificial intelligence (AI) as the product of life is only half of the equation. The other half refers to Relativity’s curved space-time and violation of the notion that time always travels from past to future. We have always lived in an artificially intelligent, non-probabilistic universe where everything in time and space is connected into one thing by quantum entanglement – making the brain and genes products of binary-digit activity or artificial intelligence (life is not merely dependent on biology’s “lock and key” mechanisms but also possesses AI). -/- The earliest documented representative of the genus Homo is Homo habilis, which evolved around 2.8 million years ago. Scientists used to believe there was a straight line from H. habilis to us, Homo sapiens. This article will use the “advanced” waves loved by Physics Nobel laureate Richard Feynman, view the history of science through the lens of Conic Sections applied to Relativity’s curved space-time, and incorporate the necessity of so-called imaginary time * – popularized by Prof. Stephen Hawking. While the evolutionary proposals are more in agreement with this early straight line than with modern theories, Albert Einstein’s General Relativity is used to transform the straight line into a curved line, ultimately concluding that Homo habilis (H. habilis) originated only (and unbelievably, as far as today’s science and technology is concerned) ~250,000 years ago. Other branches and dead ends of Homo – e.g. Neanderthals – are the result of mutations and adaptations, with the resultant modifications to anatomy and physiology. The surprisingly young age of H. habilis allows nearly 200,000 years for habilis, or one of its descendants, to reach Australia … if this country’s indigenous Aboriginal population did, as claimed, reach this “island continent” 60,000 years ago. -/- * The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, is a failure of classical physics to predict observed phenomena: it can be shown that a blackbody - a hypothetical perfect absorber and radiator of energy - would release an infinite amount of energy, contradicting the principles of conservation of energy and indicating that a new model for the behaviour of blackbodies was needed. At the start of the 20th century, physicist Max Planck derived the correct solution by making some strange (for the time) assumptions. In particular, Planck assumed that electromagnetic radiation can only be emitted or absorbed in discrete packets, called quanta. Albert Einstein postulated that Planck's quanta were real physical particles (what we now call photons), not just a mathematical fiction. From there, Einstein developed his explanation of the photoelectric effect (when quanta or photons of light shine on certain metals, electrons are released and can form an electric current). So it appears entirely possible that another supposed mathematical trickery (imaginary time and the y-axis of Wick rotation) will find practical application in the future. -/- The article includes mathematical references to cosmology (spoiler alert – you’ll read about things like Vector-Tensor-Scalar Geometry, topology, the “eternal present”, Einstein’s Unified Field, the inverse-square law, and there being no Big Bang and no multiverse - but there will also be no equations). -/- The other subheadings in this essay are – -/- NONLINEAR TIME AND ELECTRICAL ENGINEERING (about a 2009 electrical engineering experiment at America’s Yale University, and cosmic wormholes) -/- BITS AND TOPOLOGY (base-2 maths aka Binary digiTS, Mobius strips, and figure-8 Klein bottles) -/- WICK ROTATION, CAUSALITY, AND UNITING TIME (do past, present and future co-exist in an “eternal present”?) -/- DIGITAL BRAIN, DIGITAL UNIVERSE (if the brain and the universe are ultimately composed of binary digits, we'll someday be able to do the same things with the brain and universe that we now do with computers) -/- PROPOSAL: HUMAN AND ANIMAL INSTINCTS ARE THE RESULT OF THE UNIVERSE BEING UNIFIED BY BINARY DIGITS (AND TOPOLOGY) (If everything in the universe is ultimately composed of electronic BITS, then the universe must possess Artificial Intelligence - some prefer the term Cosmic Consciousness) -/- INFORMATION THEORY CONQUERS A RED GIANT (preserving Earth by keeping the Sun near today’s level of activity forever). 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Vitoria’s 1537 lecture On the American Indians asserts moral equality and fundamental rights for all humans but is contradicted by the significant inequalities between Spanish conquistadores and indigenous peoples of Mexico and Peru. Despite recognizing these rights, Vitoria’s vision supports an unequal Euro-American relationship regarding territorial sovereignty, self-defense, self-determination, and religious freedom. His insights have implications for contemporary international law concerning indigenous rights. However, his theological framework limits this potential. To better address indigenous issues today, I advocate reframing Vitoria’s perspective (...) by replacing his natural law-based human-rights essentialism with a naturalistic approach that views human rights as social constructs. This shift can help develop international law to prevent violent interactions and promote equality between indigenous and non-indigenous peoples, reducing reliance on nation states to safeguard indigenous rights. Received: 03 August 2023 Accepted: 18 April 2024. (shrink)

L’analyse des juristes médiévaux nous montre comment la manipulation des contradictions déontiques prima facie est associée, dans l’argumentation interprétative, à la théorie de la légitimité de la hiérarchie normative, entendue non seulement comme instrument politique mais aussi et essentiellement comme un instrument de rationalité au sein d’une science juridique orientée vers une théologie politique. La notion de droit naturel telle qu’elle apparaît dans certains documents emblématiques dont le Decretum de Gratien du XIIe s., ne peut être réduite au modèle intellectualiste (...) aristotélo-thomiste du XIIIe s. Il y a plusieurs façons de penser le droit naturel dans le monde médiéval chrétien et latin ; elles se maintiennent sur plusieurs siècles et l’une d’elles au moins a des points de contacts et de désaccord avec les traditions juives et musulmanes. Ces courants de pensée qui s’écartent du modèle intellectualiste aristotélo-thomiste peuvent être regroupés au sein d’une famille (au sens wittgensteinien) de modèles volontaristes : les contradictions déontiques peuvent être plus fortes que des contradictions prima facie, elles peuvent être d’authentiques contradictions renvoyant à un nouvel acte de volonté comme la seule façon d’éliminer la contradiction déontique. La théorie de Duns Scot peut être utilisée comme illustrant le problème d’une approche ontologique volontariste extrême. | Une autre version de cette contribution a été publiée dans Parisoli (2008d : 124–141). (shrink)

The Great Divide in metaphysical debates about laws of nature is between Humeans, who think that laws merely describe the distribution of matter, and non-Humeans, who think that laws govern it. The metaphysics can place demands on the proper formulations of physical theories. It is sometimes assumed that the governing view requires a fundamental / intrinsic direction of time: to govern, laws must be dynamical, producing later states of the world from earlier ones, in accord with the fundamental direction of (...) time in the universe. In this paper, we propose a minimal primitivism about laws of nature (MinP) according to which there is no such requirement. On our view, laws govern by constraining the physical possibilities. Our view captures the essence of the governing view without taking on extraneous commitments about the direction of time or dynamic production. Moreover, as a version of primitivism, our view requires no reduction / analysis of laws in terms of universals, powers, or dispositions. Our view accommodates several potential candidates for fundamental laws, including the principle of least action, the Past Hypothesis, the Einstein equation of general relativity, and even controversial examples found in the Wheeler-Feynman theory of electrodynamics and retrocausal theories of quantum mechanics. By understanding governing as constraining, non-Humeans who accept MinP have the same freedom to contemplate a wide variety of candidate fundamental laws as Humeans do. (shrink)

Buddhist Illogic. The 2nd Century CE Indian philosopher Nagarjuna founded the Madhyamika (Middle Way) school of Mahayana Buddhism, which strongly influenced Chinese, Korean and Japanese (Ch’an or Zen) Buddhism, as well as Tibetan Buddhism. Nagarjuna is regarded by many Buddhist writers to this day as a very important philosopher, who they claim definitively proved the futility of ordinary human cognitive means. His writings include a series of arguments purporting to show the illogic of logic, the absurdity of reason. He considers (...) this the way to verbalize and justify the Buddhist doctrine of “emptiness” (Shunyata). These arguments attack some of the basic tenets and techniques of reasoning, such as the laws of thought (identity, non-contradiction and the excluded middle), conceptualization and predication, our common assumptions of self, entities and essences, as well as our beliefs in motion and causation. The present essay demonstrates the many sophistries involved in Nagarjuna’s arguments. He uses double standards, applying or ignoring the laws of thought and other norms as convenient to his goals; he manipulates his readers, by giving seemingly logical form (like the dilemma) to his discourse, while in fact engaged in non-sequiturs or appealing to doubtful premises; he plays with words, relying on unclear terminology, misleading equivocations and unfair fixations of meaning; and he ‘steals concepts’, using them to deny the very percepts on which they are based. Although a critique of the Madhyamika philosophical interpretation and defense of “emptiness”, Buddhist Illogic is not intended to dissuade readers from Buddhism. On the contrary, its aim to enhance personal awareness of actual cognitive processes, and so improve meditation. It is also an excellent primer on phenomenological epistemology. (shrink)

This article is an inquiry into how the relationship between the principle of non-contradiction and the limits of thought has been understood by thinkers as diverse as Hegel, Heidegger, Levinas, and Graham Priest. While Heidegger and Levinas focus on the question of temporality and Priest takes a formal approach, all these philosophers effectively maintain that the principle of non-contradiction imposes a restriction on thought that disables it from adequately accounting for its own limits and thus what lies beyond (...) those limits, the implication being that the violation of the principle is necessary for such an accounting to take place. However, the ultimate argument here is that, contrary to Priest’s interpretation, Hegel’s philosophy can be convincingly read as supporting the idea that the mind’s ability to go beyond any particular limit of thought can actually be said to involve an adherence to a normative demand to locate and dispel the contradictions that emerge through the very setting of determinative limits. This is a non-formal consistency that evinces a “logic” that is unknowingly followed by the Heideggerian and Levinasian phenomenological philosophies of transcendence. (shrink)

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual (...) operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations. (shrink)

In this paper, I set out some basic elements of a deontic logic with an implementation appropriate for handling conflicting legal obligations for purposes of programming autonomous machine agents. Kantian justice demands that the prescriptive system of enforceable public laws be consistent, yet statutes or case holdings may often describe legal obligations that contradict; moreover, even fundamental constitutional rights may come into conflict. I argue that a deontic logic of the law should not try to work around such conflicts but, (...) instead, identify and expose them so that the rights and duties that generate inconsistencies in public law can be explicitly qualified and the conflicts resolved. I then argue that a credulous, non-monotonic deontic logic can describe inconsistent legal obligations while meeting Kant’s demand for consistency in the prescriptive system of public law. Finally, I propose an implementation of this logic via a modified form of “answer set programming,” which I demonstrate with some simple examples. (shrink)