An introductory logic textbook where the central concept is not deduction but search and logical form. (Deduction - logical consequence - drops out as a special case. TIt is meant for a class-based rather than a lecture-based course, and for students with general interests.

Textbook for students in mathematical logic. Part 1. Total formalization is possible! Formal theories. First order languages. Axioms of constructive and classical logic. Proving formulas in propositional and predicate logic. Glivenko's theorem and constructive embedding. Axiom independence. Interpretations, models and completeness theorems. Normal forms. Tableaux method. Resolution method. Herbrand's theorem.

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of (...) Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

In §12 of his 1837 magnum opus, the Wissenschaftslehre, Bolzano remarks that “In the new logic textbooks one reads almost constantly that ‘in logic one must consider not the material of thought but the mere form of thought, for which reason logic deserves the title of a purely formal science’” (WL §12, 46).1 The sentence Bolzano quotes is his own summary of others’ philosophical views; he goes on to cite Jakob, Hoffbauer, Metz, and Krug as examples of thinkers who (...) held that logic abstracts from the matter of thought and considers only its form. Although Bolzano does not mention Kant by name here, Kant does of course hold that “pure general logic”, what Bolzano would consider logic in the traditional sense (the theory of propositions, representations, inferences, etc.), is formal. As Kant remarks in the Introduction to the 2nd edition of Kritik der reinen Vernunft , (pure general) logic is “justified in abstracting – is indeed obliged to abstract – from all objects of cognition and all of their differences; and in logic, therefore, the understanding has to do with nothing further than itself and its own form” (KrV, Bix).2. (shrink)

Peer Review Book Description - Maria Seykora (female, published age 28) -/- -/- Classical Logic will attempt to give a comprehensive and rigorous introduction and more advanced overview of the area of logic widely known as “classical logic,” as distinguished from modern-day “non-classical logic,” for undergraduate students in general. It will cover the topics of Informal Logic (including logical fallacies, deduction, induction, and abductive reasoning) and Formal Logic. (Because it aims to cover these two topics, the title may change (...) to Informal and Classical Logic for the first edition.) Within the category of Formal Logic, it will cover Syllogistic or Categorical Logic and Symbolic Logic. Furthermore, within Symbolic Logic, it will cover Propositional Logic, Predicate Logic, and Modal Logic. The Formal Logic component is currently unfinished, and the Informal Logic component is somewhat unfinished. The unique selling proposition is “the first comprehensive Classical Logic textbook.” It seems that many textbooks for college students today, including Patrick J. Hurley’s, are loosely organized around Classical Logic and other various areas of logic, yet there is not a clear-cut, comprehensive summation of Classical Logic in textbook form. For instance, Hurley’s textbook does not have a section on Modal Logic, and does not address some fallacies such as Hypothesis Contrary to Fact, the Genetic Fallacy, Appeal to Nature, No True Scotsman Fallacy, Emotionally Loaded Language fallacies, etc. Stan Baronett’s Logic textbook also does not include discussions of Modal Logic or these additional fallacies and others like them, and Siu-Fan Lee’s textbook does not include Modal Logic either. Additionally, abductive reasoning, which involves making an inference to the best explanation, is important in real life, yet it seems absent from most logic textbooks. (shrink)

The verifiability principle was the characteristic claim of a group of thinkers who called themselves the Vienna Circle and who formed the philosophical movement now known as logical positivism. The verifiability principle is an empiricist criterion of meaning which declares that only statements that are verifiable by —i.e., logically deducible from— observational statements are cognitively meaningful. -/- This essay is a short introduction to the philosophical movement of logical positivism and its formulation of the verifiability principle. Its primary (...) aim is to provide students of philosophy with an accessible first overview of this philosophical movement. -/- After pointing out some aspects of the philosophical background of logical positivism (section 1), I will comment on the reasoning that lead these authors to formulate the verifiability principle (section 2), and I will analyse the debate about how to understand observational language and how observational statements (the so-called ‘protocol statements’) are verified (section 3). I will also comment on the two main consequences of accepting the verifiability principle: the conception of philosophy as the task of logical analysis and the project of unified science (section 4), and I will explain the different views on ethical language defended by logical positivists (section 5). I will end this essay by identifying the main problems of the verifiability principle and I will explain the core ideas of Carnap’s confirmability criterion, which attempts to resolve these problems (section 6 and 7). (shrink)

An introductory textbook on metalogic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. The audience is undergraduate students with some background in formal logic.

This paper studies a formalisation of intuitionistic logic by Negri and von Plato which has general introduction and elimination rules. The philosophical importance of the system is expounded. Definitions of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system are formulated and corresponding reduction procedures for maximal formulas and permutative reduction procedures for maximal segments given. Alternatives to the main method used are also considered. It is shown that deductions in the system convert into normal form and that (...) deductions in normal form have the subformula property. (shrink)

forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), symbolizing English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as modal logic, soundness, and functional completeness. Exercises with solutions are available. (...) It is provided in PDF (for screen reading, printing, and a special version for dyslexics), HTML, and in LaTeX source code. (shrink)

This textbook is not a textbook in the traditional sense. Here, what we have attempted is compile a set of assignments and exercise that may be used in critical thinking courses. To that end, we have tried to make these assignments as diverse as possible while leaving flexibility in their application within the classroom. Of course these assignments and exercises could certainly be used in other classes as well. Our view is that critical thinking courses work best when they are (...) presented as skills based learning opportunities. We hope that these assignments speak to that desire and can foster the kinds of critical thinking skills that are both engaging and fun Please feel free to contact us with comments and suggestions. We will strive to correct errors when pointed out, add necessary material, and make other additional and needed changes as they arise. Please check back for the most up to date version. Rebeka Ferreira and Anthony Ferrucci. (shrink)

Mathematics textbooks teach logical reasoning by example, a practice started by Euclid; while logic textbooks treat logic as a subject in its own right without practical application to mathematics. Stuck in the middle are students seeking mathematical proficiency and educators seeking to provide it. To assist them, the article explains in practical detail how to teach logic-based skills such as: making mathematical reasoning fully explicit; moving from step to step in a mathematical proof in logically correct ways; and checking (...) to make sure inferences are logically correct. The methodology can easily be extended beyond the four examples analyzed. (shrink)

*NEWEST VERSION OF THIS RESOURCE ONLINE @ Philosop-her dotcom This textbook has developed over the last few years of teaching introductory symbolic logic and critical thinking courses. It has been truly a pleasure to have benefited from such great students and colleagues over the years. As we have become increasingly frustrated with the costs of traditional logic textbooks (though many of them deserve high praise for their accuracy and depth), the move to open source has become more and more attractive. (...) We're happy to provide it free of charge for educational use. With that being said, there are always improvements to be made here and we would be most grateful for constructive feedback and criticism. We have chosen to write this text in LaTex and have adopted certain conventions with symbols. Certainly many important aspects of critical thinking and logic have been omitted here, including historical developments and key logicians, and for that we apologize. Our goal was to create a textbook that could be provided to students free of charge and still contain some of the more important elements of critical thinking and introductory logic. To that end, an additional benefit of providing this textbook as a Open Education Resource (OER) is that we will be able to provide newer updated versions of this text more frequently, and without any concern about increased charges each time. We are particularly looking forward to expanding our examples, and adding student exercises. We will additionally aim to continually improve the quality and accessibility of our text for students and faculty alike. We have included a bibliography that includes many admirable textbooks, all of which we have benefited from. The interested reader is encouraged to consult these texts for further study and clarification. These texts have been a great inspiration for us and provide features to students that this concise textbook does not. We would both like to thank the philosophy students at numerous schools in the Puget Sound region for their patience and helpful suggestions. In particular, we would like to thank our colleagues at Green River College, who have helped us immensely in numerous different ways. Please feel free to contact us with comments and suggestions. We will strive to correct errors when pointed out, add necessary material, and make other additional and needed changes as they arise. Please check back for the most up to date version. (shrink)

A textbook for modal and other intensional logics based on the Open Logic Project. It covers normal modal logics, relational semantics, axiomatic and tableaux proof systems, intuitionistic logic, and counterfactual conditionals.

Gillian Russell has recently proposed counterexamples to such elementary argument forms as Conjunction Introduction and Identity. These purported counterexamples involve expressions that are sensitive to linguistic context—for example, a sentence which is true when it appears alone but false when embedded in a larger sentence. If they are genuine counterexamples, it looks as though logical nihilism—the view that there are no valid argument forms—might be true. In this paper, I argue that the purported counterexamples are not genuine, on the (...) grounds that they equivocate. Having defused the threat of logical nihilism, I argue that the kind of linguistic context sensitivity at work in Russell’s purported counterexamples, if taken seriously, far from leading to logical nihilism, reveals new, previously undreamt-of valid forms. By way of proof of concept I present a simple logic, Solo-Only Propositional Logic, designed to capture some of them. Along the way, some interesting subtleties about the fallacy of equivocation are revealed. (shrink)

Revised version of chapter in J. N. Mohanty and W. McKenna (eds.), Husserl’s Phenomenology: A Textbook, Lanham: University Press of America, 1989, 29–67. -/- Logic for Husserl is a science of science, a science of what all sciences have in common in their modes of validation. Thus logic deals with universal laws relating to truth, to deduction, to verification and falsification, and with laws relating to theory as such, and to what makes for theoretical unity, both on the side of (...) the propositions of a theory and on the side of the domain of objects to which these propositions refer. This essay presents a systematic overview of Husserl’s views on these matters as put forward in his Logical Investigations. It shows how Husserl’s theory of linguistic meanings as species of mental acts, his formal ontology of part, whole and dependence, his theory of meaning categories, and his theory of categorial intuition combine with his theory of science to form a single whole. Finally, it explores the ways in which Husserl’s ideas on these matters can be put to use in solving problems in the philosophy of language, logic and mathematics in a way which does justice to the role of mental activity in each of these domains while at the same time avoiding the pitfalls of psychologism. (shrink)

The search for the extensions of sentences can be guided by Frege’s “principle of compositionality of extension”, according to which the extension of a composed expression depends only on its logical form and the extensions of its parts capable of having extensions. By means of this principle, a strict criterion for the admissibility of objects as extensions of sentences can be derived: every object is admissible as the extension of a sentence that is preserved under the substitution of (...) co-extensional expressions. The question is: what are the extensions of elementary sentences containing empty singular terms, like ‘Vulcan rotates’. It can be demonstrated that in such sentences, states of affairs as structured objects (but not truth-values) are preserved under the substitution of co-extensional expressions. Hence, such states of affairs are admissible (while truth-values are not) as extensions of elementary sentences containing empty singular terms. (shrink)

In a world filled with information overload and complex problems, the ability to think logically is a superpower. "A Little More Logical" is your guide to mastering this essential skill. This engaging and accessible open educational resource is perfect for students, teachers, and lifelong learners who want to improve their critical thinking abilities and make better decisions in all aspects of life. -/- Through a series of fun and interactive chapters, "A Little More Logical" covers a wide range (...) of topics, from the basics of constructing sound arguments to the application of logic in fields like ethics, science, and computing. You'll learn how to spot and avoid common fallacies, analyze real-world arguments, and use logical reasoning to solve problems and make informed choices. -/- But this book isn't just about abstract concepts – it's about the human story behind logic. You'll discover the fascinating lives and ideas of diverse thinkers, from ancient philosophers to modern-day pioneers, who have shaped the development of logical reasoning throughout history. With thought-provoking examples, engaging exercises, and plenty of humor along the way, "A Little More Logical" makes the study of logic both rigorous and entertaining. -/- Whether you're a student looking to ace your philosophy class, a teacher searching for high-quality educational resources, or a curious reader who wants to sharpen your mind, "A Little More Logical" is the perfect companion on your journey to becoming a more effective thinker. Unlock the power of logical thinking today with this one-of-a-kind open educational resource! (shrink)

Working within the broad lines of general consensus that mark out the core features of John Stuart Mill’s (1806–1873) logic, as set forth in his A System of Logic (1843–1872), this chapter provides an introduction to Mill’s logical theory by reviewing his position on the relationship between induction and deduction, and the role of general premises and principles in reasoning. Locating induction, understood as a kind of analogical reasoning from particulars to particulars, as the basic form of inference (...) that is both free-standing and the sole load-bearing structure in Mill’s logic, the foundations of Mill’s logical system are briefly inspected. Several naturalistic features are identified, including its subject matter, human reasoning, its empiricism, which requires that only particular, experiential claims can function as basic reasons, and its ultimate foundations in ‘spontaneous’ inference. The chapter concludes by comparing Mill’s naturalized logic to Russell’s (1907) regressive method for identifying the premises of mathematics. (shrink)

In the article we consider the relationship of traditional provisions of basic logical concepts and confront them with new and modern approaches to the same concepts. Logic is characterized in different ways when it is associated with syllogistics (referential – semantical model of logic) or with symbolic logic (inferential – syntactical model of logic). This is not only a difference in the logical calculation of (1) concepts, (2) statements, and (3) predicates, but this difference also appears in the (...) treatment of the calculative abilities of logical forms, the ontological-referential status of conceptual content and the inferential-categorical status of logical forms. The basic markers or basic ideas that separate ontologically oriented logic from categorically oriented logic are the (1) concept of truth, the (2) concept of meaning, the (3) concept of identity, and the (4) concept of predication. Here, this differences are explicitly demonstrated by the introduction of differential terminology. From this differential methodology follows a new set of characterizations of logic. (shrink)

This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system, and gives reduction procedures for them. It is then shown that deductions in the system convert into normal form, i.e. deductions that contain neither maximal formulas nor maximal segments, and that deductions in normal form satisfy the subformula property. Tarski’s Rule is treated as a general introduction rule (...) for implication. The general introduction rule for negation has a similar form. Maximal formulas with implication or negation as main operator require reduction procedures of a more intricate kind not present in normalisation for intuitionist logic. (shrink)

We can attend to the logic of Anselm's ontological argument, and amuse ourselves for a few hours unraveling its convoluted word-play, or we can seek to look beyond the flawed logic, to the search for God it expresses. From the perspective of this second approach the Ontological Argument might be seen as more than a mere argument - indeed, as something of a contemplative exercise. One can see in the argument a tantalizing attempt to capture in logical form (...) the devotee’s experience of the presence of God in the contemplation of God. It is a peculiarity of the argument that it can seem hopelessly silly or richly evocative depending upon which of these approaches one takes. In this essay I examine the flawed logic of the Ontological Argument, but then attempt to reflect upon the contemplative experience that may underlie it. (shrink)

Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic `of nonsense' introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic K3W by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where no variable-inclusion conditions are attached; and (...) (iii) that it is hybrid, insofar as it includes both left and right operational introduction as well as elimination rules. (shrink)

This short work presents a popular fringe theory as a source of case studies for use in teaching informal logic in an introductory course. It puts forward ancient astronaut theory as the candidate source, together with a characterization of why it fits the bill. The televised material associated with that theory is well suited to being used as case studies given that they are easy to follow, contain a surprising number of arguments and fallacies, and keep students reliably engaged. The (...) paper includes an overview of the forms of argumentation and fallacies that these cases may be used to teach, along with a sketch of how to best implement them in the classroom. (shrink)

This paper raises some questions about the formalization of sentences containing ‘if’ or similar expressions. In particular, it focuses on three kinds of sentences that resemble conditionals in some respects but exhibit distinctive logical features that deserve separate consideration: whether-or-not sentences, biscuit conditionals, and concessive conditionals. As will be suggested, the examples discussed show in different ways that an adequate formalization of a sentence must take into account the content expressed by the sentence. This upshot is arguably what one (...) should expect on the view that logical form is determined by truth conditions. (shrink)

This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.

My aim in this paper is to explore how we might understand the relation of Deleuze’s early works to ethics, and to develop the connections between this way of understanding Deleuze and the work of Søren Kierkegaard. I will claim that we can view both figures as arguing that the sense or meaning we take from the world, and the metaphysical structure we ascribe to it, is secondary to an ethical stance we take in the face of a world of (...) becoming. As such, the central preoccupation of both Kierkegaard and Deleuze is how we make sense of an existence which is necessarily temporal. As we shall see, recognizing the importance of temporality involves a move away from the traditional resolution of the problem of sense that operates by making temporality an accidental aspect of a world. In the first half of this paper, I want to explore this claim in relation to Deleuze’s reading of Plato, tying his claim that Plato is essentially developing an ethical rather than metaphysical doctrine with the claim that “the task of modern philosophy has been defined: to overturn [renversement] Platonism” (DR 59). My emphasis in this section is how Deleuze, rather than “overturning” Platonism by simply rejecting the priority it gives to Forms or essences over appearances, the renversement of Deleuze’s reading inverts the relation to show how the search for essence is in fact grounded in an ethical decision, or “selection,” in the world of appearances/simulacra itself. As such, both Plato and Deleuze can be seen as presenting different trajectories for making sense of a world of becoming, either by grounding it in a transcendent, atemporal realm, or by seeing it as an intensive field of processes. In the second half, I will argue that Kierkegaard’s philosophy rests on a claim, similar to the one we find in Deleuze’s work, that we need to develop a logic of sense in response to a world of becoming. I will conclude that Deleuze’s reading of Kierkegaard is limited by a focus on the theological aspects of his thought, and that Kierkegaard provides a sophisticated and complementary taxonomy of the ways in which we try to make sense of our existence in a world of becoming by developing diverse ethical postures. (shrink)

The passionate and staunch defence of logic of the controversial thinker Ibn Ḥazm, Abū Muḥammad ʿAlī b. Aḥmad b. Saʿīd of Córdoba (384-456/994-1064), had lasting consequences in the Islamic world. Indeed, his book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples (Kitāb al-Taqrīb li-ḥadd al-manṭiq wa-l-mudkhal ilayhi bi-l-alfāẓ al-ʿāmmiyya wa-l-amthila al-fiqhiyya), composed in 1025-1029, was well known and discussed during and after his time; and it paved the way for the studies (...) of his compatriots Ibn Bājjah (d. 1138), Ibn Ṭufayl (1185), and Ibn Rushd (1198), who each gave demonstrative reasoning a privileged place within the methods of attaining knowledge. Unfortunately, as too often in the history of science, Ibn Ḥazm’s innovative perspectives and contributions in logic have been overlooked or considered with an attitude of contempt. On the one hand, his work has been seen, at best, as promulgating the benefits of studying Aristotle’s logic, so that his contribution is assessed as more didactical than conceptual. And on the other hand, those who do examine his innovations often consider them to be mistaken. As indicated by Chejne (1984, p. 2) contempt towards the logical work of Ibn Ḥazm was also present in its reception by the Eastern philosophers who accused him of deviating from Aristotelian logic and of dabbling in things beyond his capability. However, a reassessment of his work on logic has since begun, by delving into the ways the thinker of Córdoba studied the links between deontic and modal qualification of propositions. In this context Lameer’s (2013) paper on the logical sources of Ibn Ḥazm is worth mentioning; the author (p. 417, footnote 1) observes that, although, strictly speaking, it was al-Fārābī who first drew the parallelism between deontic and modal concepts, it was Ibn Ḥazm who developed it and worked it out in a more precise manner. A primary aim of this paper is to help fill some of these gaps by stressing the role of the work of Ibn Ḥazm in developing a notion of deontic necessity deeply rooted in legal normativity, and in explicitly discussing the transference between deontic and modal concepts. According to our view; the basic units of Islamic deontic logic are what we might call, indulging in terminological anachronism, heteronomous imperatives. As it turns out, the heteronomy of imperatives within Islamic legal systems contrasts with those of the purely moral realm, which seem to be closer to an autonomous conception of moral law. There it concurs again with Leibniz’s proposal to define obligatory as “what is necessary for a good person to do”. In the present paper, we will focus on the heteronomous imperatives of legal systems rather than on the imperatives of the purely moral realm. In this context, the work of Ibn Ḥazm extends the parallelism between the necessity of events and that of human actions stressed by his predecessors. According to our understanding, Ibn Ḥazm’s parallelism can be rendered explicit formally by means of a conditional (or hypothetical) structure shared by both deontic and modal propositions. Moreover, this structure makes apparent that this parallelism displays an underlying system of “degrees”. Indeed, while in the domain of events, given some conditions, it makes sense to distinguish between an event that is more likely to happen than another. Ibn Ḥazm speaks of near and distant possibility (such as the higher degree of likelihood of rain, given the condensation of clouds in December, and its lower degree, when the condensation occurs in summer); and, in the domain of actions, the Islamic notion of weighting actions determines degrees of virtue (or of legal and moral value). So whereas the degree of virtue of performing a forbidden act as determined by the distribution of sanction and reward is 0, we obtain the same value by pondering the likelihood of an impossible event to take place. Furthermore, as discussed in section II.3.2, the system of values at work in the parallelism can be seen as opening the way to a more direct correspondence. Thus, while in the realm of nature, likelihood of occurrence of an event is dependent upon the conditions specific to the occurrence of that event; while, in the realm of jurisprudence, likelihood of performing an action is dependent upon the distribution of reward and sanction specific to that action (being that, given the choice to perform or not perform a given action, those that will be rewarded are more likely to be performed than those that are not). According to this perspective, the point of the parallelism is that both deontic and modal qualifications measure the degree of an action or event to become actual; that is – indulging once more in anachronism (but this time from the Leibnizian background) – the degree measures how feasible (facile) an action or event may be. This suggests that Ibn Ḥazm’s perspectives already herald the links to probability and possibility explored by Leibniz six centuries later – see for example Leibniz’s (1671, A VI, I, p. 424-26) use of probability in the context of conditional right. Nevertheless, it also shows a crucial difference to the approach developed in the Elementa Jura Naturalis: whereas Leibniz’s studies seek to define what is to be just or virtuous, the logical system of deontic imperatives within Islamic jurisprudence presupposes that what is to be virtuous has already been settled. Determining what is to be virtuous is not achieved by logical reasoning within the system of legal jurisprudence, but by delving into the higher objectives of the Sharīʿa. While developing our point, we will delve into the logical structure of the heteronomous imperatives. This distinguishes our contribution from the existing literature, such as the papers of Chejne (1984), Lameer (2014), and Guerrero (1997, 2010, 2014), which do not provide a logical analysis of the deontic concepts put into work by Ibn Ḥazm. The true antecedent to the present paper is the work of Farid Zidani (2007, 2015), who, so far as we know, was the first to undertake such a task. Some of our own developments and general epistemological thoughts go beyond Ibn Ḥazm’s framework and motivations; mainly those contained in sections II.3.2 and IV. However, according to our view, these reflections suggest that Ibn Ḥazm’s approach has the substance for a broader and deeper exploration of the logic of norms. The paper is structured as follows:I.Ibn Ḥazm’s Logic of Heteronomous Imperatives. After presenting some extracts of the relevant text, we proceed by providing a formal reconstruction of the five forms of deontic modalities. II. A Landmark in the History of the Logical Analysis of Norms. Duties and Modalities. In this section, we study the transferences from deontic to modal necessity and possibility. We briefly compare the deontic system of Islamic Jurisprudence with that of Leibniz.III. Leibniz and Hypothetical Imperatives in Law.IV. Beyond Ibn Ḥazm: Conclusions and the Work Ahead. We will conclude the paper by discussing briefly some conceptual points that distinguish the logic of heteronomous imperatives from contemporary deontic logic. Our final words will discuss deontic-modal parallelism in the context of Ibn Ḥazm’s rejection of reasoning by conjecture and what we call “the internalization of nature.”. (shrink)

Monists say that the nature of truth is invariant, whichever sentence you consider; pluralists say that the nature of truth varies between different sets of sentences. The orthodoxy is that logic and logical form favour monism: there must be a single property that is preserved in any valid inference; and any truth-functional complex must be true in the same way as its components. The orthodoxy, I argue, is mistaken. Logic and logical form impose only structural constraints (...) on a metaphysics of truth. Monistic theories are not guaranteed to satisfy these constraints, and there is a pluralistic theory that does so. (shrink)

This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order logics used in metaphysics, and indicate a (...) number of questions which can be raised in such systems using logical vocabulary alone. Using a further example, we return to applications of higher-order logics in metaphysics. We also mention key developments in the history of higher-order logic as it pertains to metaphysics. Finally, we mention certain arguments which have been raised against the use of higher-order logic, and some ways of responding to them. (shrink)

Logicism is the view that mathematical truths are logical truths. But a logical truth is commonly thought to be one with a universally valid form. The form of “7 > 5” would appear to be the same as “4 > 6”. Yet one is a mathematical truth, and the other not a truth at all. To preserve logicism, we must maintain that the two either are different subforms of the same generic form, or that their (...) forms are not at all what they appear. The historical record shows that Russell pursued both these options, but that the struggle with the logical paradoxes pushed him away from the first kind of response and toward the second. An object cannot itself have a kind of inner logical complexity that makes a proposition have a different logical form merely in virtue of being about it, nor can their representatives in logical forms be single things different for different forms, at least not without postulating too many such objects and thereby creating Cantorian diagonal paradoxes. There are only apparent objects which are actually fragments of logical forms, different in different cases. (shrink)

PLEASE NOTE: This is the corrected 2nd eBook edition, 2021. ●●●●● _Critique of Impure Reason_ has now also been published in a printed edition. To reduce the otherwise high price of this scholarly, technical book of nearly 900 pages and make it more widely available beyond university libraries to individual readers, the non-profit publisher and the author have agreed to issue the printed edition at cost. ●●●●● The printed edition was released on September 1, 2021 and is now available through (...) all booksellers, including Barnes & Noble, Amazon, and brick-and-mortar bookstores under ISBN 978-0-578-88646-6. ●●●●● In light of the length of this book, readers who would like to have a more detailed description of the book's objectives and method may find it helpful to read the detailed and clearly written Wikipedia entry about this work: From the Wikipedia search page, use the search phrase "Critique of Impure Reason". At least at the time of this writing (11/29/2021), the Wikipedia entry is well-researched and accurate. ●●●●● In addition, a "Primer on Bartlett's CRITIQUE OF IMPURE REASON" has been made available by the author. It is available under its title through PhilPapers and other philosophy online archives. ●●●●● COMMENDATIONS OF THIS WORK, from the back cover of the published edition: ●●●●● “I admire its range of philosophical vision.” – Nicholas Rescher, Distinguished University Professor of Philosophy, University of Pittsburgh, author of more than 100 books. ●●●●● “Bartlett’s _Critique of Impure Reason_ is an impressive, bold, and ambitious work. Careful scholarship is balanced by original analyses that lead the reader to recognize the limits of meaning, knowledge, and conceptual possibility. The work addresses a host of traditional philosophical problems, among them the nature of space, time, causality, consciousness, the self, other minds, ontology, free will and determinism, and others. The book culminates in a fascinating and profound new understanding of relativity physics and quantum theory.” – Gerhard Preyer, Professor of Philosophy, Goethe-University, Frankfurt am Main, Germany, author of many books including _Concepts of Meaning_, _Beyond Semantics and Pragmatics_, _Intention and Practical Thought_, and _Contextualism in Philosophy_. ●●●●● “[This work’s] goal is of a unique and difficult species: Dr. Bartlett seeks to develop a formal logical calculus on the basis of transcendental philosophical arguments; in fact, he hopes that this calculus will be the formal expression of the transcendental foundation of knowledge.... I consider Dr. Bartlett’s work soundly conceived and executed with great skill.” – C. F. von Weizsäcker, philosopher and physicist, former Director, Max-Planck-Institute, Starnberg, Germany. ●●●●● “Bartlett has written an American “Prolegomena to All Future Metaphysics.” He aims rigorously to eliminate meaningless assertions, reach bedrock, and place philosophy on a firm foundation that will enable it, like science and mathematics, to produce lasting results that generations to come can build on. This is a great book, the fruit of a lifetime of research and reflection, and it deserves serious attention.” — Martin X. Moleski, former Professor, Canisius College, Buffalo, NY, studies of scientific method, the presuppositions of thought, and the self-referential nature of epistemology. ●●●●● “Bartlett has written a book on what might be called the underpinnings of philosophy. It has fascinating depth and breadth, and is all the more striking due to its unifying perspective based on the concepts of reference and self-reference.” – Don Perlis, Professor of Computer Science, University of Maryland, author of numerous publications on self-adjusting autonomous systems and philosophical issues concerning self-reference, mind, and consciousness. ●●●●● ●●●●● The _Critique of Impure Reason: Horizons of Possibility and Meaning_ comprises a major and important contribution to philosophy. Thanks to the generosity of its publisher, this massive 885-page volume has been published as a free open access eBook (3.75MB) as well as an open access printed edition. It inaugurates a revolutionary paradigm shift in philosophical thought by providing compelling and long-sought-for solutions to a wide range of philosophical problems. In the process, the work fundamentally transforms the way in which the concepts of reference, meaning, and possibility are understood. The book includes a Foreword by the celebrated German philosopher and physicist Carl Friedrich von Weizsäcker. ●●●●● In Kant’s _Critique of Pure Reason_ we find an analysis of the preconditions of experience and of knowledge. In contrast, but yet in parallel, the new _Critique_ focuses upon the ways—unfortunately very widespread and often unselfconsciously habitual—in which many of the concepts that we employ _conflict_ with the very preconditions of meaning and of knowledge. ●●●●● This is a book about the boundaries of frameworks and about the unrecognized conceptual confusions in which we become entangled when we attempt to transgress beyond the limits of the possible and meaningful. We tend either not to recognize or not to accept that we all-too-often attempt to trespass beyond the boundaries of the frameworks that make knowledge possible and the world meaningful. ●●●●● The _Critique of Impure Reason_ proposes a bold, ground-breaking, and startling thesis: that a great many of the major philosophical problems of the past can be solved through the recognition of a viciously deceptive form of thinking to which philosophers as well as non-philosophers commonly fall victim. For the first time, the book advances and justifies the criticism that a substantial number of the questions that have occupied philosophers fall into the category of “impure reason,” violating the very conditions of their possible meaningfulness. ●●●●● The purpose of the study is twofold: first, to enable us to recognize the boundaries of what is referentially forbidden—the limits beyond which reference becomes meaningless—and second, to avoid falling victims to a certain broad class of conceptual confusions that lie at the heart of many major philosophical problems. As a consequence, the boundaries of _possible meaning_ are determined. ●●●●● Bartlett, the author or editor of more than 20 books, is responsible for identifying this widespread and delusion-inducing variety of error, _metalogical projection_. It is a previously unrecognized and insidious form of erroneous thinking that undermines its own possibility of meaning. It comes about as a result of the pervasive human compulsion to seek to transcend the limits of possible reference and meaning. ●●●●● Based on original research and rigorous analysis combined with extensive scholarship, the _Critique of Impure Reason_ develops a self-validating method that makes it possible to recognize, correct, and eliminate this major and pervasive form of fallacious thinking. In so doing, the book provides at last provable and constructive solutions to a wide range of major philosophical problems. ●●●●● CONTENTS AT A GLANCE ▪▪▪▪▪ Preface ▪▪▪▪▪ Foreword by Carl Friedrich von Weizsäcker ▪▪▪▪▪ Acknowledgments ▪▪▪▪▪ Avant-propos: A philosopher’s rallying call ▪▪▪▪▪ Introduction ▪▪▪▪▪ A note to the reader ▪▪▪▪▪ A note on conventions ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART I ▪▪▪▪▪ ▪▪▪▪▪ WHY PHILOSOPHY HAS MADE NO PROGRESS AND HOW IT CAN ▪▪▪▪▪ 1 Philosophical-psychological prelude ▪▪▪▪▪ 2 Putting belief in its place: Its psychology and a needed polemic ▪▪▪▪▪ 3 Turning away from the linguistic turn: From theory of reference to metalogic of reference ▪▪▪▪▪ 4 The stepladder to maximum theoretical generality ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART II ▪▪▪▪▪ THE METALOGIC OF REFERENCE ▪▪▪▪▪ A New Approach to Deductive, Transcendental Philosophy ▪▪▪▪▪ 5 Reference, identity, and identification ▪▪▪▪▪ 6 Self-referential argument and the metalogic of reference ▪▪▪▪▪ 7 Possibility theory ▪▪▪▪▪ 8 Presupposition logic, reference, and identification ▪▪▪▪▪ 9 Transcendental argumentation and the metalogic of reference ▪▪▪▪▪ 10 Framework relativity ▪▪▪▪▪ 11 The metalogic of meaning ▪▪▪▪▪ 12 The problem of putative meaning and the logic of meaninglessness ▪▪▪▪▪ 13 Projection ▪▪▪▪▪ 14 Horizons ▪▪▪▪▪ 15 De-projection ▪▪▪▪▪ 16 Self-validation ▪▪▪▪▪ 17 Rationality: Rules of admissibility ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART III ▪▪▪▪▪ PHILOSOPHICAL APPLICATIONS OF THE METALOGIC OF REFERENCE ▪▪▪▪▪ Major Problems and Questions of Philosophy and the Philosophy of Science ▪▪▪▪▪ 18 Ontology and the metalogic of reference ▪▪▪▪▪ 19 Discovery or invention in general problem-solving, mathematics, and physics ▪▪▪▪▪ 20 The conceptually unreachable: “The far side” ▪▪▪▪▪ 21 The projections of the external world, things-in-themselves, other minds, realism, and idealism ▪▪▪▪▪ 22 The projections of time, space, and space-time ▪▪▪▪▪ 23 The projections of causality, determinism, and free will ▪▪▪▪▪ 24 Projections of the self and of solipsism ▪▪▪▪▪ 25 Non-relational, agentless reference and referential fields ▪▪▪▪▪ 26 Relativity physics as seen through the lens of the metalogic of reference ▪▪▪▪▪ 27 Quantum theory as seen through the lens of the metalogic of reference ▪▪▪▪▪ 28 Epistemological lessons learned from and applicable to relativity physics and quantum theory ▪▪▪▪▪ ▪▪▪▪▪ PART IV ▪▪▪▪▪ HORIZONS ▪▪▪▪▪ 29 Beyond belief ▪▪▪▪▪ 30 _Critique of Impure Reason_: Its results in retrospect ▪▪▪▪▪ ▪▪▪▪▪ SUPPLEMENT ▪▪▪▪▪ The Formal Structure of the Metalogic of Reference ▪▪▪▪▪ APPENDIX I ▪▪▪▪▪ The Concept of Horizon in the Work of Other Philosophers ▪▪▪▪▪ APPENDIX II ▪▪▪▪▪ Epistemological Intelligence ▪▪▪▪▪ References ▪▪▪▪▪ Index ▪▪▪▪▪ About the author. 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It is argued, on the basis of ideas derived from Wittgenstein's Tractatus and Husserl's Logical Investigations, that the formal comprehends more than the logical. More specifically: that there exist certain formal-ontological constants (part, whole, overlapping, etc.) which do not fall within the province of logic. A two-dimensional directly depicting language is developed for the representation of the constants of formal ontology, and means are provided for the extension of this language to enable the representation of certain materially necessary (...) relations. The paper concludes with a discussion of the relationship between formal logic, formal ontology, and mathematics. (shrink)

The text is a drought outlining the development of logic in Bosnia and Herzegovina through several periods of history: period of Ottoman occupation and administration of the Empire, period of Austro-Hungarian occupation and administration of the Monarchy, period of Communist regime and administration of the Socialist Republic and period from the aftermath of the aggression against the Republic of Bosnia and Herzegovina to this day (the Dayton Bosnia and Herzegovina) and administration of the International Community. For each of the aforementioned (...) periods, the text treats the organization of education, the educational paradigm of the model, status of logic as a subject in the educational system of a period, as well as the central figures dealing with the issue of logic (as researchers, lecturers, authors) and the key works written in each of the periods, outlining their main ideas. Thework of aNeoplatonic philosopher Porphyry, “Introduction” (Greek: Eisagogee), Latin: Isagoge; Arabic: Īsāġūğī), can be seen, in all periods of education in Bosnia and Herzegovina, as the main text, the principal textbook, as a motivation for logical thinking. That gave me the right to introduce the syntagm Bosnia Porphyriana. (shrink)

Tschumi believes that the quality of architecture depends on the theoretical factor it contains. Such a view led to the creation of architecture that would achieve visibility and comprehensibility only after its interpretation. On his way to creating such an architecture he took on a purely philosophical reflection on the basic building block of architecture, which is space. In 1975, he wrote an essay entitled Questions of Space, in which he included several dozen questions about the nature of space. The (...) questions he formulated could be regarded as analogous to the situation in the philosophy of the time, in which the interest in questioning the most obvious forms of understanding the world and intellectual categories increased. The research on space is an area common to many fields of natural sciences, humanities and artistic creation, but it also deals with other problems, such as issues of experience. The concept of space-time continuum proposed by Hermann Minkowski drew attention to the identity of time and space with the events taking place. Probably regardless of the postulates of physicists commenting on Einstein’s discoveries, also in philosophy it increased the importance of the concept of the event which became dominant in Heidegger’s latest work Contributions of Philosophy. Of the event. Furthermore, Tschumi’s reflections on space entered into relation with the problem of experience, which aroused the interest of a group of French philosophers trying to assimilate Georges Bataille’s concept of “inner experience”. Both Tschumi and Derrida referred to Bataille because his views could be used not only to modify the concept of the subject, but also to change the understanding of what constitutes the area of architecture. The discussion on experience has led to the recognition that the subject is not sovereign, but actually a form of what is on their outside. Such insights make it possible to treat the area of the Parc de La Villette as existing mainly when it is organised by its users. The decisive features of the Park are its assumptions, according to which it is a variety of active void that leads to agreeing new social relations with it. The park does not force to participate in already existing moral or political communities, but tries to move into an unknown future in which the scope of free functioning of individuals will be increased. Doubts about the principles of functioning of the individual self and its discovery as a whole composed of non-coherent parts, as well as its dependence on its own depth full of disordered forces, influenced the understanding of architecture as a set of contradictions whose source is a fundamental void anticipating the empty phenomenal space. The use of this phenomenal void in architecture, as well as the rejection of the whole and unity, had a specific political purpose and drew its inspiration from political analyses. In the Parc de La Villette, metaphysics and politics were brought closer together because the philosophy of void was used to create new conditions for community action. It can be argued that the source of this philosophy was the perception of errors in existing societies dependent on the shortcomings of traditional metaphysics. Spacing (espacement) was one of the key terms in Derrida’s philosophy, which was also combined with the concepts of différance and chôra. The study of the nature of space, especially its transition from the level of pure possibility to the level of sensual phenomenon, also contributes to understanding how well designed space can have an impact on its audience. This explanation is based on Tschumi’s assumption that the space of the Parc de La Villette contradicts the integrating approaches and instead exposes contradictions, but it does so in a way that combines incompatible properties into a single piece of architecture. The specificity of such integration is similar to the invention of a musical phrase, which is an ideological message: moral and political. Such a thesis may raise doubts, however, if both the clearly adopted assumptions and those deduced from the work allow for their ↪Quart Nr 2(52)/2019 logically ordered presentation then to a limited extent it may be assumed that the work has achieved a connection between a specific philosophy of space and its practical application. Derrida combined the problem of spatiality with the problem of transcendental imagination in Kant’s philosophy, who in the first version of Critique of Pure Reason assumed that pure imagination precedes the appearance of time and space, even in their transcendental forms. The imagination in such a situation can be described as a factor activating time and space, which indicates what function is played by movement in this activity. This leads us to recognize that the ultra originary source of pure forms of sensual intuition is movement, which in early Greek philosophy was identified with void and its lack of resistance to phenomena occurring in it. Derrida’s philosophy in search of a certain super-transcendental source of time and space pointed to différance which, like void or the chôra, does not have material features or even any other form of being. Différance is the primary cause of the disruption of motionlessness and the introduction of activity into motionless time and space, thus its activity can be described as spacing (espacement). Derrida’s discoveries in this respect are not entirely original, because Hegel already pointed out when examining the present that it is primarily a differential relation (differente Beziehung), which, being seemingly neutral, influences the present with supernatural force and makes it unidentifiable with itself. Differente Beziehung must similarly influence the originary space, negating its initial character by multiplying its divisions and expanding its boundaries. Différance acts by revealing contradictions wherever there is apparent undifferentiation. Tschumi, composing the Parc de La Villette as a variety of void and a set of incompatible layers, followed the rules of différance or the chôra: he made void visible together with its saturation with contradictions. If space can be considered to be the result of the activity of difference, such activity has a certain regularity, which influences the behaviour of its observers. Differences or contradictions fall into a certain rhythm, which can be considered a manifestation of transcendent order. The problem is that what can be considered the source of such order, namely the logos or God, is partly disorder and error. According to descriptions contained in Timaeus, the world is a combination of forces that drive to order with forces of erroneous necessity that resounds in every order and forces it to return to disorder. Derrida denied the possibility of understanding différance as a theological value, even if it were a negative or apophatic theology, but no categorical denial could be perfect. The assumption that différance or the chôra are not endowed with any substance properties cannot deny their activity, and thus a certain force. Already since Democritus, philosophy has multiplied the names of such a force and the contradictory variety of its manifestations, never forgetting also the necessity for reason to withdraw from the possibility of giving its correct characteristics. Such a withdrawal may be interpreted as an expression of respect and, in certain situations, as a cult of the force that precedes reasonableness. The Parc de La Villette, which is an artistic divagation about the contradictions and forces behind them, can be considered as a place of their sublimation, and therefore as a variation of the temple of what differs from order and disorder. (shrink)

This chapter reviews some of the history of discussions of logical form and offers a truth-theoretic account that traces back to Donald Davidson.

Donald Davidson contributed to the discussion of logical form in two ways. On the one hand, he made several influential suggestions on how to give the logical forms of certain constructions of natural language. His account of adverbial modification and so called action-sentences is nowadays, in some form or other, widely employed in linguistics (Harman (forthcoming) calls it "the standard view"). Davidson's approaches to indirect discourse and quotation, while not as influential, also still attract attention today. (...) On the other hand, Davidson provided a general account of what logical form is. This paper is concerned with this general account. Its foremost aim is to give a faithful and detailed picture of what, according to Davidson, it means to give the logical form of a sentence. The structure of the paper is as follows. (1) I will first informally introduce a notion of logical form as the form that matters in certain kinds of entailments, and indicate why philosophers have taken an interest in such a notion. (2) The second section develops constraints that we should arguably abide by in giving an account of logical form. (3) I then turn to Davidson’s view of what is involved in giving such an account. To this end, I will try to reconstruct Davidson’s view of the connection between an assignment of logical forms, a truth theory and a meaning theory. (4) Finally, I will briefly discuss possible problems of Davidson’s account as developed in this paper. (shrink)

I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain how the syllogistic (...) is a fragment of my system of Core Logic. Then I introduce my main innovation: the use of binary quantifiers, governed by introduction and elimination rules. The syllogisms in all four figures are re-proved in the binary system, and are thereby revealed as all on a par with each other. I conclude with some comments and results about grammatical generativity, ecthesis, perfect validity, skeletal validity and Aristotle's chain principle. (shrink)

This paper articulates and defends a conception of logical form as semantic form revealed by a compositional meaning theory. On this conception, the logical form of a sentence is determined by the semantic types of its primitive terms and their mode of combination as it relates to determining under what conditions it is true. We develop this idea in the framework of truth-theoretic semantics. We argue that the semantic form of a declarative sentence in (...) a language L is revealed by a (canonical) proof of its T- sentence in an interpretive truth theory for L. We give a precise characterization of sameness of logical form between any two declarative sentences in any two languages in terms of the notion of corresponding proofs in interpretive truth theories for the languages. We illustrate the utility of this approach with a number of examples. We then extend the characterization to non-declaratives in a generalization of truth-theoretic semantics that appeals to fulfillment conditions, of which truth conditions are one variety. On this approach, logical forms are not reified, and the notion of sameness of logical form is treated as conceptually basic. We discuss the relation of this conception of logical form to the project of identifying logical constants, reviewing two approaches, one of which takes topic neutrality as central, the other recursion. We argue that the project of identifying logical constants for the purposes of classifying together valid arguments is largely independent of that identifying logical form of sentences, and urge an ecumenical approach to extending talk of logical constants beyond where it is currently well-grounded. (shrink)

This article discusses the logical form of action sentences with particular attention to the role of adverbial modification, reviewing and extending the event analysis of action sentences.

This paper claims that there is no such thing as the correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfil two major theoretical roles that pertain respectively to logic and semantics. The first part of the paper outlines the thesis that a unique notion of logical form fulfils both roles, and argues that the alleged best candidate for making it true is unsuited (...) for one of the two roles. The second part spells out a considerably different notion which is free from that problem, although it does not fit the other role. As it will be suggested, each of the two notions suits at most one role, so the uniqueness thesis is ungrounded. (shrink)

From my ongoing "Metalogical Plato" project. The aim of the diagram is to make reasonably intuitive how the Socratic elenchos (the logic of refutation applied to candidate formulations of virtues or ruling knowledges) looks and works as a whole structure. This is my starting point in the project, in part because of its great familiarity and arguable claim to being the inauguration of western philosophy; getting this point less wrong would have broad and deep consequences, including for philosophy’s self-understanding. -/- (...) (i.) is the first pass at elenchos in which the Socratic interlocutor does not reflect on knowledge being the crux of the problem. (ii.) is the second, rarer, reflective pass in which they are, making the investigation explicitly about knowledge. Its centrality in the Charmides makes that neglected dialogue of superlative importance. This structure is also the gateway through which the discussion/dialectic crosses into the Agathology (discussion of the form of the good) at Republic 505. -/- The problem of elenchos, then, grasped as a whole structure, is that it seems that knowledge can neither satisfactorily be included in nor excluded from its own scope. The development of the ti esti (“what is ---?”) question leads to the introduction of knowledge into its own scope (i. implicitly, as goodness contrasted with blind rule-following ii. explicitly qua knowledge) while the development of the dual peri tinos (“----about what?) question leads to K’s elimination from its own scope. The introductions are motivated to avoid contradiction, but produce regress; the eliminations are motivated to avoid regress, but produce contradiction. In scholarship, and in the history of philosophy, the ti esti question is universally recognized, to the point of being identified with philosophy’s origin and essence; the peri tinos question is neglected textually and never recognized as the equal dual to the ti esti. This, I claim, has blocked the development of a nontrivial logical appreciation of what Plato's Socrates is up to. (One rather disastrous effect of this neglect is taking Aristotle as the beginning of the development of logic, rather than, correctly, for the beginning of logic’s fatal separation from mathematics and dialectic.) -/- Further, because of this monopticism of the ti esti, the function of consistency in the elenchos has not been understood, even with respect to the ti esti. The ti esti is actually in search of completeness, given a norm of consistency; the peri tinos is in search of consistency, given a norm of completeness. Only appreciating the two questions as dual allows space in the structure to clarify these different orientations relative to consistency. (And, dually, to completeness, whose function in the elenchos is generally entirely missed by scholars and relegated to discussions of eros; it's not out of place there, of course, but its significance is secured here.) Recognizing the duality of the ti esti and peri tinos questions is thus the royal road, in the Socratic-Platonic context, to catching sight of what we post-Cantorians can recognize as the metalogical duality of consistency and completeness. (The salutary disruptive effects of this Plato-Cantor proximity have, of course, been traced in complementary ways by Badiou.) -/- Note that the diagram is supposed to provide a relatively accessible orientation, not to stand on its own, and certainly not to be the last word on any subject. An important qualification (telegraphed in the previous paragraph) is that what elenchos shows is not finally circular or paradoxical, though the problem first presents as such (stubbornly, obdurately, as "difficult" Plato's Socrates always says with characteristic understatement). What is depicted here is meant, at a first pass, to be the shape of that first presentation, the form of the problem of elenchos, rather than of its solution. It's not an accident that this problem strongly resembles "Russell's paradox" (not Russell's not a paradox.) Problem is to solution as RP is to the diagonal theorems. (shrink)

This paper deals with the logical form of quantified sentences. Its purpose is to elucidate one plausible sense in which quantified sentences can adequately be represented in the language of first-order logic. Section 1 introduces some basic notions drawn from general quantification theory. Section 2 outlines a crucial assumption, namely, that logical form is a matter of truth-conditions. Section 3 shows how the truth-conditions of quantified sentences can be represented in the language of first-order logic consistently (...) with some established undefinability results. Section 4 sketches an account of vague quantifier expressions along the lines suggested. Finally, section 5 addresses the vexed issue of logicality. (shrink)

In my book Logical Form I outline some reasons for thinking that, in the sense of «logical form» that matters to logic, logical form is determined by truth conditions. This paper compares three theories of propositions that might be employed to substantiate the underlying notion of truth conditions: the naturalized propositions theory, the truthmaker theory, and the classificatory theory. Its aim is to show that, while the naturalized propositions theory and the truthmaker theory accord (...) equally well with the idea that logical form is determined by truth conditions, the classificatory theory is more problematic in some respects. (shrink)

Physicalistic theories of psychology are a classic case of scientific imperialism: the explanatory capacity of physics, both with respect to its methods and to its domain, is taken to extend beyond the traditional realm of physics, and into that of psychology. I argue in this paper that this particular imperialistic venture has failed. Contemporary psychology uses methods not modelled on those of physics, embracing first-personal methodology where physics is strictly impersonal. I make the case that whether or not scientific imperialism (...) is in general harmful, in this instance naturalists who reject first philosophy should give up physicalist imperialism. Using only general principles from the philosophy of logic plus accepted physicalist criteria of identity, I show that first-personal psychology embodies a minor but fruitful increase in expressive strength compared to impersonal psychology: the ability to distinguish descriptively indiscriminable posits. (shrink)

Preface/Introduction: The question under discussion is metaphysical and truly elemental. It emerges in two aspects — how did we come to be conscious of our own existence, and, as a deeper corollary, do existence and awareness necessitate each other? I am bold enough to explore these questions and I invite you to come along; I make no claim to have discovered absolute answers. However, I do believe I have created here a compelling interpretation. You’ll have to judge for yourself. -/- (...) What follows is the presentation of three essays I have worked on over the past several years seeing publication for the first time. “Hollows of Experience” was written first as an invited chapter for a collection on the ontology of consciousness. However, when cuts became necessary, my chapter got the knife. Its length has prohibited it from publication in any print journal. “Myth and Mind” was written next as a journal article, but as my involvement with it grew so did its length, so it has also idled on my websty awaiting its call. “From Panexperientialism to Conscious Experience” was written most recently, but it is the only one to have been available to the public elsewhere than my own website. Under the name, “The Continuum of Experience”, it was Target Article #95 on the recently closed Karl Jaspers Forum (for discussion purposes only). -/- I have put them in a different sequence here, for reasons of logical sense. Up first, “Panexperientialism” deals with an idea difficult for many to accept, namely that conscious experience is a particular mode of symbolically reflected experience that is largely unique to our species. However, I aver that experienced sensation in itself (as found, for example, in autonomic sensory response systems) goes “all the way down” into nature, and thus the title, panexperientialism. -/- Understanding this idea is helpful to dealing with the focus on language in Part I of “Hollows”, next, since here speech and general symbolic interaction in general are found to be the catalysts for the creation of our consciously experienced world (our “lived reality”). In Part II, however, I explore how experienced sensations must be coeval with existence, and, with even greater temerity, how all this sensational existence might have arisen within some literally inconceivable background of awareness-in-itself that yet has a dynamism that occasionally breaks into existence as experiential events and entities. (The latter may sound wacky, but physicists and cosmologists are themselves attempting to come to terms with that which seethes with vast potential energy in what they refer to as the quantum vacuum.) -/- “Myth and Mind” was put third since it deals with a major lacuna in “Hollows” — that presumed prehistoric period when members of our species made the painful crossing of the symbolic threshold into the beginnings of cultural consciousness. Speech plays a central role here, too, but I look more at narrative structures from the dawn of self-awareness when ritual and myth became vital to human survival. Why would fantastic stories and bizarre rituals be necessary? I speculate that growing foresight led to the unavoidable realization of certain mortality, from which, in turn, emerged the secondary realization that we were now alive. In contrast to our yet-to-come death, we have life here and now, and by ritually identifying with a symbolically expanded mythic, i.e., sacred, reality, we may continue to live on after bodily death, just as our ancestors and loved ones must also do. Language and mythmaking are necessary to avoid mortal despair and they remain at the core of human consciousness. -/- As Ernst Cassirer (1944) has noted, language and myth are “twin creatures”, both metaphoric webs over a reality we can never wholly comprehend. We live in the symbolic and construct our works of imagination and wars of conquest to make life meaningful, to feel immortal, and to sense that we ourselves participate in a reality greater than ourselves. No doubt we do, but this does not mean our culturally constructed self-identities survive the death of our bodies, and it does not imply that our symbolic concepts can ever indicate the ultimate truth. We simply must symbolize an extended reality that was sacred to our ancestors: “Is it not our way, as illusory as it may be, to force continuance on our world and our life in the face of their inevitable ending? Are we not compelled to extend those imaginary horizons as far as we can despite the terror and the sometime joy their extension incites? Is their closure not a form of death?” (Crapanzano, p. 210) -/- Of course, this leaves me in the uncomfortable position of being forced to admit that this venture of mine must inevitably be another attempt at meaningful mythmaking. But what else could it be? This is certainly not a scientific proof though it is indeed an academically rigorous exploration. (Just try to count the citations!) I hope the reader will judge my thesis on the basis of its coherence, the sense of meaning it evokes, my intellectual responsibility, and, finally, the engagement it inspires. If you have read my expositions and found yourself immersed in the timeless questions I here call forth, I would call these writings successful (even if you violently disagree with my answers). -/- I am very grateful to Huping Hu for granting me this special issue of JCER in which to present my ideas in some detail. He has patiently dealt with my exuberant approach and allowed the many changes I kept coming up with right until the final publication date. I also wish to thank the many potential commentators who politely replied to my invitation, and, even more, I thank those who made time to write actual commentaries. -/- References -/- Cassirer, E. (1944). An Essay on Man: An Introduction to a Philosophy of Human Culture. New Haven/London: Yale UP. -/- Crapanzano, V. (2004). Imaginative Horizons: An Essay in Literary-Philosophical Anthropology. Chicago: U of Chicago Press. -/- Gregory M. Nixon University of Northern British Columbia Prince George, British Columbia, Canada Email: [email protected] Websty: http://members.shaw.ca/doknyx. (shrink)

Bertrand Russell, in the second of his 1914 Lowell lectures, Our Knowledge of the External World, asserted famously that ‘every philosophical problem, when it is subjected to the necessary analysis and purification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical’ (Russell 1993, p. 42). He went on to characterize that portion of logic that concerned the study of forms of propositions, or, as (...) he called them, ‘logical forms’. This portion of logic he called ‘philosophical logic’. Russell asserted that ... some kind of knowledge of logical forms, though with most people it is not explicit, is involved in all understanding of discourse. It is the business of philosophical logic to extract this knowledge from its concrete integuments, and to render it explicit and pure. (p. 53) Perhaps no one still endorses quite this grand a view of the role of logic and the investigation of logical form in philosophy. But talk of logical form retains a central role in analytic philosophy. Given its widespread use in philosophy and linguistics, it is rather surprising that the concept of logical form has not received more attention by philosophers than it has. The concern of this paper is to say something about what talk of logical form comes to, in a tradition that stretches back to (and arguably beyond) Russell’s use of that expression. This will not be exactly Russell’s conception. For we do not endorse Russell’s view that propositions are the bearers of logical form, or that appeal to propositions adds anything to our understanding of what talk of logical form comes to. But we will be concerned to provide an account responsive to the interests expressed by Russell in the above quotations, though one clarified of extraneous elements, and expressed precisely. For this purpose, it is important to note that the concern expressed by Russell in the above passages, as the surrounding text makes clear, is a concern not just with logic conceived narrowly as the study of logical terms, but with propositional form more generally, which includes, e.g., such features as those that correspond to the number of argument places in a propositional function, and the categories of objects which propositional.... (shrink)

The Shadow of God in the Philosopher’s Garden. The Parc de La Villette in Paris in the context of the philosophy of chôra I Bernard Tschumi’s project of the Parc de La Villette could have won the competition and was implemented thanks to the political atmosphere that accompanied the victory of the left-wing candidate in the French presidential elections in 1981. François Mitterand’s revision of the political programme and the replacement of radical reforms with the construction of prestigious architectural objects (...) and urban assumptions in the French capital gave Tschumi a unique opportunity to realise ideas that polemicised with traditional forms of social life, questioned the basic principles of architecture and included architectural work in the philosophical disputes over the issues of metaphysics. Tschumi’s theoretical assumptions put forward during the design of the Parc de La Villette highlighted the questions of conflict between the main components of the project and suggested that the intensification of differences was analogous to Jacques Derrida’s creation of the concept of différance. It was this philosopher who in a special commentary to Derrida’s project also introduced the concept of maintenant, which aimed at demonstrating that the architect’s polemical inclinations remain in a hidden balance with his inclinations to affirmation of architectural principles. During the discussion between Derrida and Peter Eisenman, who was to take part in the design of the Parisian park, the concept of the chôra was also put forward, which in the course of the debate led to an additional confusion of architectural and philosophical problems. II In the period from the Antiquity to the Renaissance, the dialogue Timaeus was the most frequently commented work of Plato. At present, the most frequently discussed is the issue of the chôra included in it, which aroused fascination among philosophers, researchers of rhetoric, religion, feminism, but also architecture. The work on the chôra also influenced the development of the interpretation of the Parc de La Villette, among which the topics related to the beginning and the change were highlighted. In early uses of the word chôra in Greek, as in Homer’s 18th Book of Iliad, it meant both dancing and a place to dance. On this occasion, it can be seen that it is not possible to determine which phenomenon took precedence in the creation of the name. It cannot be denied, however, that the word concerned a specific movement, as if circular and returning to an indefinable beginning. Despite gaining more and more general meanings, the word chôra has retained its connection with the dance of people on the threshing floor, the dance of bees (choros meliton) or the dance of stars (choros astron). In Timaeus, the chôra is a space filled with movement with an effect similar to shaking the sieve to husk the grain: it separates similar elements from the dissimilar ones. The juxtaposition of the Parc de La Villette and the chôra already at this stage leads to the suggestion that the park was treated by the architect as a place of dynamic changes leading to the establishment of new social solutions. In his statements, the architect confirmed that the park was to be a space of new politics and ethics. The book by Julia Kristeva La Révolution du langage poétique contributed to the spread of the belief that works of art can play a role as factors of political revolution. In this work, the author put forward the thesis that the chôra is a kind of space, the character of which has a destructive influence on attempts to conclude language games. The chôra gives beginning to words, but at the same time, by leaving a trace of this beginning it forces us to renew their meanings. The chôra understood in this way, turns out to be an irremovable beginning, to which one has to return all the time. Kristeva found manifestations of the chôra’s activity in avant-garde French poetry, to which she attributed the role of a mediator between criticism of metaphysics and aspirations for social change. The chôra, violating the language, introduces some voids into it, as if traces of the abyss, which direct the consciousness towards understanding the necessity of political changes. The Parc de La Villette was to pursue similar objectives in the city space. In his essays, Tschumi considered the problems of creating spaces that would give rise to a radical democracy. The proposed rebellious spaces should have the characteristics of a void, in which contradictory forces would occur as forms of pure activity. The means of achieving this goal was to concentrate contradictions and make them visible. The Parc de La Villette was supposed to collect differences as indelible and at the same time by showing them it was supposed to raise awareness of the social world as a conglomerate of differences. Saturation of the space of the park with subversive values results from the character of this space suppressed in the consciousness, as well as from the social diversity which has not been taken into account so far. The main contradictions contained in space relate to the division that exists between its presentation as a mental problem and a sensual one. The park was the deliberate creation of a place that transcends such a division and creates a separate space for negotiation between architectural theories and its practical applications. The purpose of the park was to become a place of future events, which would not hide their conflicting character coming from diversity of both space and society. The method of composition usually aimed at achieving a harmonious whole has been replaced by Tschumi with a system of juxtaposition of non-coherent elements or those resulting from variations and transformations. Tschumi did not seek direct influence on politics in the Parc de La Villette, but made room for thinking about the possibilities of the future. He introduced problems rather than showed solutions to them. The task of the park was to put the principles of architecture into a kind of vibration that would inspire users to participate in the new community. III Tschumi believes that the quality of architecture depends on the theoretical factor it contains. Such a view led to the creation of architecture that would achieve visibility and comprehensibility only after its interpretation. On his way to creating such an architecture he took on a purely philosophical reflection on the basic building block of architecture, which is space. In 1975, he wrote an essay entitled Questions of Space, in which he included several dozen questions about the nature of space. The questions he formulated could be regarded as analogous to the situation in the philosophy of the time, in which the interest in questioning the most obvious forms of understanding the world and intellectual categories increased. The research on space is an area common to many fields of natural sciences, humanities and artistic creation, but it also deals with other problems, such as issues of experience. The concept of space-time continuum proposed by Hermann Minkowski drew attention to the identity of time and space with the events taking place. Probably regardless of the postulates of physicists commenting on Albert Einstein’s discoveries, also in philosophy it increased the importance of the concept of the event which became dominant in Martin Heidegger’s latest work Contributions of Philosophy: Of the event. Furthermore, Tschumi’s reflections on space entered into relation with the problem of experience, which aroused the interest of a group of French philosophers trying to assimilate Georges Bataille’s concept of “inner experience”. Both Tschumi and Derrida referred to Bataille because his views could be used not only to modify the concept of the subject, but also to change the understanding of what constitutes the area of architecture. The discussion on experience has led to the recognition that the subject is not sovereign, but actually a form of what is on their outside. Such insights make it possible to treat the area of the Parc de La Villette as existing mainly when it is organised by its users. The decisive features of the park are its assumptions, according to which it is a variety of active void that leads to agreeing new social relations with it. The park does not force to participate in already existing moral or political communities, but tries to move into an unknown future in which the scope of free functioning of individuals will be increased. Doubts about the principles of functioning of the individual self and its discovery as a whole composed of non-coherent parts, as well as its dependence on its own depth full of disordered forces, influenced the understanding of architecture as a set of contradictions whose source is a fundamental void anticipating the empty phenomenal space. The use of this phenomenal void in architecture, as well as the rejection of the whole and unity, had a specific political purpose and drew its inspiration from political analyses. In the Parc de La Villette, metaphysics and politics were brought closer together because the philosophy of void was used to create new conditions for community action. It can be argued that the source of this philosophy was the perception of errors in existing societies dependent on the shortcomings of traditional metaphysics. Spacing (espacement) was one of the key terms in Derrida’s philosophy, which was also combined with the concepts of différance and chôra. The study of the nature of space, especially its transition from the level of pure possibility to the level of sensual phenomenon, also contributes to understanding how well designed space can have an impact on its audience. This explanation is based on Tschumi’s assumption that the space of the Parc de La Villette contradicts the integrating approaches and instead exposes contradictions, but it does so in a way that combines incompatible properties into a single piece of architecture. The specificity of such integration is similar to the invention of a musical phrase, which is an ideological message: moral and political. Such a thesis may raise doubts, however, if both the clearly adopted assumptions and those deduced from the work allow for their logically ordered presentation then to a limited extent it may be assumed that the work has achieved a connection between a specific philosophy of space and its practical application. Derrida combined the problem of spatiality with the problem of transcendental imagination in the philosophy of Immanuel Kant, who in the first version of Critique of Pure Reason assumed that pure imagination precedes the appearance of time and space, even in their transcendental forms. The imagination in such a situation can be described as a factor activating time and space, which indicates what function is played by movement in this activity. This leads us to recognize that the ultra originary source of pure forms of sensual intuition is movement, which in early Greek philosophy was identified with void and its lack of resistance to phenomena occurring in it. Derrida’s philosophy in search of a certain super-transcendental source of time and space pointed to différance which, like void or the chôra, does not have material features or even any other form of being. Différance is the primary cause of the disruption of motionlessness and the introduction of activity into motionless time and space, thus its activity can be described as spacing (espacement). Derrida’s discoveries in this respect are not entirely original, because Georg Wilhelm Friedrich Hegel already pointed out when examining the present that it is primarily a differential relation (differente Beziehung), which, being seemingly neutral, influences the present with supernatural force and makes it unidentifiable with itself. Differente Beziehung must similarly influence the originary space, negating its initial character by multiplying its divisions and expanding its boundaries. Différance acts by revealing contradictions wherever there is apparent undifferentiation. Tschumi, composing the Parc de La Villette as a variety of void and a set of incompatible layers, followed the rules of différance or the chôra: he made void visible together with its saturation with contradictions. If space can be considered to be the result of the activity of difference, such activity has a certain regularity, which influences the behaviour of its observers. Differences or contradictions fall into a certain rhythm, which can be considered a manifestation of transcendent order. The problem is that what can be considered the source of such order, namely the logos or God, is partly disorder and error. According to descriptions contained in Timaeus, the world is a combination of forces that drive to order with forces of erroneous necessity that resounds in every order and forces it to return to disorder. Derrida denied the possibility of understanding différance as a theological value, even if it were a negative or apophatic theology, but no categorical denial could be perfect. The assumption that différance or the chôra are not endowed with any substance properties cannot deny their activity, and thus a certain force. Already since Democritus, philosophy has multiplied the names of such a force and the contradictory variety of its manifestations, never forgetting also the necessity for reason to withdraw from the possibility of giving its correct characteristics. Such a withdrawal may be interpreted as an expression of respect and, in certain situations, as a cult of the force that precedes reasonableness. The Parc de La Villette, which is an artistic divagation about the contradictions and forces behind them, can be considered as a place of their sublimation, and therefore as a variation of the temple of what differs from order and disorder. IV In the texts that presented the theoretical assumptions of the Parc de La Villette, Tschumi used a large number of terms that contradicted not only the traditional principles of composing architecture, but also negated the rules of social order and the foundations of Western metaphysics. Tschumi’s statements, which are a continuation of his leftist political fascinations from the May 1968 revolution, as well as his interest in the philosophy of French poststructuralism and his collaboration with Derrida, prove that terms such as “disruption”, “dissociation”, “disfunction”, “disjunction” and “dispersion” not only referred to architectural problems but also applied to political criticism and the deepest foundations of thinking itself. His collaboration with Derrida manifested itself primarily in the publication La Case Vide: La Villette 1985, in which the architect’s design drawings and texts explaining his concepts related to the Parc de La Villette were accompanied by an extensive essay by Derrida, which included theoretical problems taken up by Tschumi in a philosophical context. Architectural and philosophical issues were also combined during seven discussion meetings organised by Eisenman, invited by Tschumi to collaborate on the design of the Parc de La Villette. Eisenman, who, like Tschumi, invited Derrida to participate in the design of the park and also led to the publication of Chora L Works: Jacques Derrida and Peter Eisenman, in which his ideas were confronted with Derrida’s philosophical text. In this case, Derrida’s essay was not a direct commentary on the architect’s concepts, but rather a reflection on the question of the chôra presented by Plato in Timaeus. During the discussion and in his essay, Derrida pointed out that the chôra is a component of the created world, yet it does not belong to it, but precedes it. The originality of the chôra is so radical that she also precedes all the factors of creating the world, including ideas and the Demiurge. Thus athesis appeared in the metaphysics of the West that the chôra is a form of active abyss, in relation to which all beings are secondary, both those perfect (as ideas or God) and those created, such as the world, things, people or language. This leads to the conclusion that the chôra does not exist, because all existence is a derivative of the chôra. Nor could the chôra be described, since it is a form of developing a space that is preceded by a lack of space characteristic of the chôra. Derrida intended the chôra to be an instance with an exceptional degree of transcendentalism, an anti-metaphysical instance, but also an a-theological one. However, this attempt failed, both in the field of secular philosophy and in the field of theology. Derrida’s characteristics of the chôra to strengthen its transcendentalism and negation of metaphysics had to be expressed in a language that immediately produces new concepts and a new metaphysics that reproduces the categories of the beginning, the origin or the foundation known from earlier philosophical traditions. All forms of criticism of metaphysics are also inspired by negative, apophatic and mystical theology. The undermining of many concepts of permanent meaning and the introduction of new concepts of unstable meaning, characteristic of the philosophy of deconstruction, had many features of originality, but it was directed towards problems whose solutions repeat, with the use of new vocabulary, the findings known in culture since Democritus. Thus, if apophatic philosophy can be regarded as deconstruction avant la lettre, then deconstruction itself in its late versions began to take on the features of a new religion. The exchange of inspiration between theology and deconstruction was manifested in a series of scientific conferences and publications in which Derrida’s philosophical concepts were interpreted within the scope of religious thought. Theological threads began to be found in such concepts of deconstruction as différance or the chôra, while at the same time Derrida himself undertook in his philosophy to study problems such as the Other (L’Autre) or the Impossible (Impossible), which belonged to newer theological traditions. As a consequence of the new problems, the deconstruction became closer to the features of a new religion. Philosophy, at least from Kant’s time, has tried to create a system that would take over from religion the tasks of setting moral and political goals. Similarly, Derrida has directed his interest towards the problems of democracy and ethics, which would enable their renewal. Attempts to create a new religion (cleared of old metaphors), a new community or a new democracy bring problems and threats which may be no less troublesome than the previous systems. All promises of freedom carry with them threats, the greater the more they strive for perfection. The renewal of existential orders, sometimes carried out by means of violent changes, is a certain repetitive feature of human cultures. Deep changes, however, do not protect against the return of both old gods and old demons. Tschumi and Derrida were shaped in their youth by the atmosphere of leftist rebellion against the moral and political limitations of ossified communities and the imperfections of democracy. The ethical theme distinguishes many of their works, including the Parc de La Villette. The opposition to the metaphysical traditions of philosophy and architecture contained in this park was prompted by specific political situations and resulted from bringing political issues to the level of philosophical considerations. Achievements made at the level of pure concepts were then subject to elevation, to a kind of sacralization, which made them religious concepts. The deconstruction reached for the status of the new religion especially when it found its followers and began to generate moral obligations. In the new situation, terms such as the chôra, l’Autre or the Impossible were absolutized and in relation to them a cult and attitude of adoration emerged. The Parc de La Villtette then gained new post-secular meanings, which allow it to be assigned the function of a Temple of Otherness (L’Autre) and Impossible. V In the traditional sense, a work of art creates an illustration of the outside world, or of a certain text or doctrine. Sometimes it is considered that such an illustration is not literal, but is an interpretation of what is visible, or an interpretation of a certain literary or ideological message. It can also be assumed that a work of art creates its own visual world, a separate story or a separate philosophical statement. Parc de La Villette represents the last of these possibilities: it is a philosophical statement that develops the premises derived from poststructuralist philosophies and the philosophy of deconstruction. The uniqueness of its being status, however, is that it does so not only at the level of the theoretical assumptions, but also through its functioning as an active philosophical work. This means that a park is a happening philosophy. Its activity, however, does not refer only to the present tense, but is also an attempt to penetrate the future, all otherness and impossibility. This kind of activity assumes that the work, in a sense, does not yet fully exist, but is also still produced in the processes of its interpretation. The theoretical foundations of the park included texts by Tschumi, in which he questioned traditional ways of creating a work of architecture, postulating in return the use of a long series of negations, which were comparable to the crisis of metaphysics characteristic of contemporary philosophy. It is therefore no coincidence that the publication containing Tschumi’s theoretical text on Parc de La Villette was accompanied by an essay by Derrida developing some of the architect’s concepts. The next step in integrating philosophy into the process of park design was a series of discussions between Eisenman and Derrida, who completely moved the creation of the park into the world of thoughts, without accentuating the need for their realization in the material reality. The main topic of these discussions was the problem of the chôra, which was taken up by later commentators and used to interpret the park as a work in which the philosophy of the beginning is manifested relating to issues of politics, morality and religion. The park was therefore interpreted as a space of invention within the scope of creating new rules of functioning of the community and democracy. Thinking about the political future may, however, exceed the horizon of ordinary expectations. Although philosophical thought is always connected with contemporary problems and metaphysics sometimes intertwines with current politics, yet at the same time the customs of philosophy also include crossing horizons and thinking about absolute otherness and impossibility. Initially, the chôra, différance, absolute otherness (tout autre) and the Impossible were concepts of pure philosophy of atheistic character, but with the further development of the discussion, more and more theological motifs began to emerge. One of the reasons for this phenomenon was the fact that radical negations of all being, which were contemplated in contemporary philosophy (by Heidegger and Derrida, among others), had previously been manifested in negative and apophatic theologies (by Master Eckhart, among others).Also the category of the “Other”, taken from Emmanuel Levinas, was clearly connected with the thought about God. A further reason for connecting the chôra with the theological thought was the interest in the philosophy of deconstruction expressed by some theologians. John Caputo in particular managed to persuade Derrida to participate in discussions on the current status of religion. In the late period of Derrida’s writing, further statements on religious topics appeared. All these reasons led to posing a question about the identity of the chôra and God. Although there were no satisfactory conclusions on this issue, the discussion was also important to create an interpretation of the park as a place of worship. The chôra, representing, according to Plato, the preoriginal emptiness is the place of every beginning, but it turns out that it is not neutral to the being created in it. The chôra deposits itself in every being as an irremovable beginning that interferes with its stability. The chôra, therefore, forces us into a palintropical movement, but it also turns out to be a pure compulsion, an erring necessity and a fundamental force from which, in the human perception, motifs useful to the individual and to the community are extracted. All definitions of this force, including its anthropomorphisation, are formulated in such a way that they allow for building private and collective morality upon them. Such definitions are changed depending on variable political situations. It is difficult to determine whether in the processes of changes in the formulation of “God’s names” any essential value is retained, which is not subject to change. The current definitions of the chôra (God?), which can be found, for example, in the philosophy of Caputo, stress that she is a combination of various and contradictory forces. This characteristic inherits much of Plato’s concept, reminds us of Master Eckhart’s views on Gottheit and, at the same time, is not unfamiliar to Tschumi, whose essays were an apologia of contradictions. The current concept of chôra, transferred into the sphere of politics, is the praise of social diversity and the protection of the difference from the forces of order. In the Parc de La Villette, the future community and democracy were elevated as a system of safe existence of individuals in all their singularity. The park is a temple of a future community in which individual beings have nothing in common. (shrink)

This paper outlines an account of concessive conditionals that rests on two main ideas. One is that the logical form of a sentence as used in a given context is determined by the content expressed by the sentence in that context. The other is that a coherent distinction can be drawn between a reading of ‘if’ according to which a conditional is true when its consequent holds on the supposition that its antecedent holds, and a stronger reading according (...) to which a conditional is true when its antecedent supports its consequent. As we will suggest, the logical form of concessive conditionals can be elucidated by relying on this distinction. (shrink)

What is the relation of logic to thinking? My dissertation offers a new argument for the claim that logic is constitutive of thinking in the following sense: representational activity counts as thinking only if it manifests sensitivity to logical rules. In short, thinking has to be minimally logical. An account of thinking has to allow for our freedom to question or revise our commitments – even seemingly obvious conceptual connections – without loss of understanding. This freedom, I argue, (...) requires that thinkers have general abilities to respond to support and tension among their thoughts. And these abilities are constituted by following logical rules. So thinkers have to follow logical rules. But there isn’t just one correct logic for thinking. I show that my view is consistent with logical pluralism: there are a range of correct logics, any one of which a thinker might follow. A logic for thinking does, however, have to contain certain minimal principles: Modus Ponens and Non-Contradiction, and perhaps others. We follow logical rules by exercising logical capacities, which display a distinctive first-person/third-person asymmetry: a subject can find the instances of a rule compelling without seeing them as instances of a rule. As a result, there are two limits on illogical thinking. First, thinkers have to tend to find instances of logical rules compelling. Second, thinkers can’t think in obviously illogical ways. So thinking has to be logical – but not perfectly so. When we try to think, but fail, we produce nonsense. But our failures to think are often subjectively indistinguishable from thinking. To explain how this occurs, I offer an account of nonsense. To be under the illusion that some nonsense makes sense is to enter a pretence that the nonsense is meaningful. Our use of nonsense within the pretence relies on the role of logical form in understanding. Finally, while the normativity of logic doesn’t fall directly out of logical constitutivism, it’s possible to build an attractive account of logical normativity which has logical constitutivism as an integral part. I argue that thinking is necessary for human flourishing, and that this is the source of logical normativity. (shrink)