Ioannis G. Ntagkas

Principia Logico-Metaphysica contains a foundational logical theory for metaphysics, mathematics, and the sciences. It includes a canonical development of Abstract Object Theory [AOT], a metaphysical theory that distinguishes between ordinary and abstract objects.This article reports on recent work in which AOT has been successfully represented and partly automated in the proof assistant system Isabelle/HOL. Initial experiments within this framework reveal a crucial but overlooked fact: a deeply-rooted and known paradox is reintroduced in AOT when the logic of complex terms is simply adjoined to AOT’s specially formulated comprehension principle for relations. This result constitutes a new and important paradox, given how much expressive and analytic power is contributed by having the two kinds of complex terms in the system. Its discovery is the highlight of our joint project and provides strong evidence for a new kind of scientific practice in philosophy, namely, computational metaphysics.Our results were made technically possible by a suitable adaptation of Benzmüller’s metalogical approach to universal reasoning by semantically embedding theories in classical higher-order logic. This approach enables one to reuse state-of-the-art higher-order proof assistants, such as Isabelle/HOL, for mechanizing and experimentally exploring challenging logics and theories such as AOT. Our results also provide a fresh perspective on the question of whether relational type theory or functional type theory better serves as a foundation for logic and metaphysics.

Aristotle said that induction (epagōgē) is a proceeding from particulars to a universal, and the definition has been conventional ever since. But there is an ambiguity here. Induction in the Scholastic and the (so-called) Humean tradition has presumed that Aristotle meant going from particular statements to universal statements. But the alternate view, namely that Aristotle meant going from particular things to universal ideas, prevailed all through antiquity and then again from the time of Francis Bacon until the mid-nineteenth century. Recent scholarship is so steeped in the first-mentioned tradition that we have virtually forgotten the other. In this essay McCaskey seeks to recover that alternate tradition, a tradition whose leading theoreticians were William Whewell, Francis Bacon, Socrates, and in fact Aristotle himself. The examination is both historical and philosophical. The first part of the essay fills out the history. The latter part examines the most mature of the philosophies in the Socratic tradition, specifically Bacon’s and Whewell’s. After tracing out this tradition, McCaskey shows how this alternate view of induction is indeed employed in science, as exemplified by several instances taken from actual scientific practice. In this manner, McCaskey proposes to us that the Humean problem of induction is merely an artifact of a bad conception of induction and that a return to the Socratic conception might be warranted.

Francis Bacon’s method of induction is often understood as a form of eliminative induction. The idea, on this interpretation, is to list the possible formal causes of a phenomenon and, by reference to a copious and reliable natural history, to falsify all of them but one. Whatever remains must be the formal cause. Bacon’s crucial instances are often seen as the crowning example of this method. In this article, I argue that this interpretation of crucial instances is mistaken, and it has caused us to lose sight of why Bacon assigns crucial instances a special role in his quest for epistemic certainty about formal causes. If crucial instances are interpreted eliminatively, then they are subject to the two problems related to underdetermination raised by Duhem: (1) that it is impossible to be certain one has specified all of the possible alternatives and (2) that an experiment falsifies a whole theory, not just a single hypothesis in isolation. I show that Bacon anticipates and aims to dodge both of these problems by conceiving of crucial instances as working, in the ideal case, through direct affirmations that are supported by links to more foundational knowledge.

Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence, business, epidemiology, social science and economics.

With the help of in-depth essays from some of the world's leading philosophers, _The Blackwell Companion to Natural Theology_ explores the nature and existence of God through human reason and evidence from the natural world. Provides in-depth and cutting-edge treatment of natural theology's main arguments Includes contributions from first-rate philosophers well known for their work on the relevant topics Updates relevant arguments in light of the most current, state-of-the-art philosophical and scientific discussions Stands in useful contrast and opposition to the arguments of the 'new atheists'

Given the available evidence, I argue that we face considerable uncertainty about free will. In particular, I argue that the available philosophical evidence does not support being highly confident in our theories about the nature of free will, though this does not necessarily mean that we should suspend judgment about either incompatibilism or compatibilism. For those who accept incompatibilism, however, I argue that there is enough uncertainty about libertarian free will that they should suspend judgment about whether we are ever free, if not reject free will entirely. While I do not claim that compatibilists should be similarly agnostic about the existence of free will, I argue that most compatibilist theories are subject to considerable uncertainty as well, so that most compatibilists should be agnostic about how often we act freely. I conclude with a brief discussion of how we might address these issues going forward.

In Ireland, HSE issued guidelines about practicing sex in the time of coronavirus, and the two key recommendations are: “Taking a break from physical and face-to face interactions is worth considering, especially if you usually meet your sex partners online or make a living by having sex. Consider using video dates, sexting or chat rooms. Make sure to disinfect keyboards and touch screens that you share with others. / Masturbation will not spread coronavirus, especially if you wash your hands with soap and water for at least 20 seconds before and after

Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational philosophy with a focus on metaphysics. In this paper, we (a) develop results in modal metaphysics whose discovery was computer assisted, and (b) conclude that these results work not only to the obvious benefit of philosophy but also, less obviously, to the benefit of computer science, since the new computational techniques that led to these results may be more broadly applicable within computer science. The paper includes a description of our background methodology and how it evolved, and a discussion of our new results.

In this presentation, I first outline three different notions of concepts: one derives from Leibniz, while the other two derive from Frege. The Leibnizian notion is the subject of his “calculus of concepts” (which is really an algebra). One notion of concept from Frege is what we would call a “property”, so that when Frege says “x falls under the concept F”, we would say “x instantiates F” or “x exemplifies F”. The other notion of concept from Frege is that of the notion of sense, which played various roles within Frege's theory. This notion of concept can be generalized and, as such, accounts for our intuitive talk of “x's concept of …”, where the ellipsis can be filled in with a name for individual, a property, or a relation, etc. After outlining these three notions, I then discuss how (axiomatic) object theory offers a distinct, precise regimentation of each of the three notions.

This book tackles the issues that arise in connection with intensional logic -- a formal system for representing and explaining the apparent failures of certain important principles of inference such as the substitution of identicals and existential generalization -- and intentional states --mental states such as beliefs, hopes, and desires that are directed towards the world. The theory offers a unified explanation of the various kinds of inferential failures associated with intensional logic but also unifies the study of intensional contexts and intentional states by grounding the explanation of both phenomena in a single theory. When an axiomatized realm of abstract entities is added to the metaphysical structure of the world, we can use them to identify and individuate the contents of directed mental states. The special abstract entities can be viewed as the objectified contents of mental files, and they play a crucial role in the analysis of truth conditions of the sentences involved in inferential failures.

The last six lines of Aristotle's Metaphysics A.7 draw some important conclusions about Aristotle's predecessors' (the Presocratics' and Plato's) grasp of the four types of cause. Aristotle argues that his account of his predecessors supports his conception of the four causes and his claim that in first philosophy, too, we should seek to understand our subject-matter on the basis of these four causes. I offer a detailed textual and philosophical interpretation of these lines, connect them with Aristotle's argument in Metaphysics A.1-6, and examine their metaphysical, epistemological, and methodological presuppositions.

There are several innocuous or trivial ways in which to explicate Aristotle’s hylomorphism. For example: objects are characterisable in terms of matter and form; or analysable into matter and form; or understood on the basis of matter and form. Serious problems arise when we seek to specify the sorts of relation holding among the different contributors to the hylomorphic picture. Here are some central general questions: a. What types of relation are most suitable for each n-tuple of contributors? b. What direction and modal profile should each relation have? In addressing such questions we find that the types, directions, or modal character of the relations that we or Aristotle may favour are often in tension with each other, or clearly lead to inconsistencies. The paper focuses on the Modal Question, also known as ‘Ackrill’s problem’: is form essentially or contingently related to matter? I outline a hylomorphic model, what I label the ‘causal-explanatory’ model, and show how it can tackle M.

The paper seeks to specify how, according to Plato’s Sophist, true statements achieve their being about objects and their saying that ‘what is about such objects is’. Drawing on the 6th definition of the sophist, I argue for a normative-teleological conception of truth in which the best condition of our soul –in its making statements or having mental states– consists in its seeking to attain the telos of truth. Further, on the basis of Plato’s discussion of original and image, his distinction between correct and incorrect image, and the 7th definition, I argue that achieving the telos of truth involves preserving the original’s proportions and appropriate features. The view that Plato’s conception of truth takes statements or mental states to be certain types of image is not ground-breaking. The important contribution of my argument is that it offers a plausible way to understand two recalcitrant claims made by Plato: first, that falsity obtains not only in the region of incorrect images (appearances) but also within correct images (likenesses); second, that some incorrect images are based on knowledge and so could be true.

In Wittgenstein on Rules and Private Language, Saul Kripke presents a controversial skeptical argument, which he attributes to Wittgenstein’s interlocutor in the Philosophical Investigations [PI]. The argument purports to show that there are no facts that correspond to what we mean by our words. Kripke maintains, moreover, that the conclusion of Wittgenstein’s so-called private language argument is a corollary of results Wittgenstein establishes in §§137-202 of PI concerning the topic of following-a-rule, and not the conclusion of an independently developed argument in §§243ff of PI, as most commentators take it to be. In this work, I assess Kripke’s skeptical argument both in its own right, and as an interpretation of the rule-following sections of PI. In its own right, I try to show that it is critically flawed. However, as an interpretation of the rule-following sections of PI, I try to show that it is essentially correct. I do this by showing that Kripke’s interpretation squares with and supports the meta-philosophical framework developed by Wittgenstein in §§107-136 of PI, which immediately precedes his remarks on following-a-rule. (Oct 16, 2008. Committee: Paul Horwich, Galen Strawson, Stephen Neale, Michael Levin)

Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that are simple enough. This contradiction points to the fruitlessness of trying to solve the Logical Omniscience Problem qualitatively if the rationality of agents is to be maintained. We provide a quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness. More precisely, we provide a test for the logical omniscience problem in a given formal theory of knowledge. The quantitative measures we use are inspired by the complexity theory. We illustrate our framework with a number of examples ranging from the traditional implicit representation of knowledge in modal logic to the language of justification logic, which is capable of spelling out the internal inference process. We use these examples to divide representations of knowledge into logically omniscient and not logically omniscient, thus trying to determine how much information about the reasoning process needs to be present in a theory to avoid logical omniscience.

In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle /all truths are knowable/, when expressed as a bi-modal principle F --> K♢F, yields an unacceptable omniscience property /all truths are known/. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it relies, but rather to the knowability principle itself. Further, we show that, from a verifiability perspective, the knowability principle fails in the classical logic setting because it is missing the explicit incorporation of a hidden assumption of /stability/: ‘the proposition in question does not change from true to false in the process of discovery.’ Once stability is taken into account, the resulting /stable knowability principle/ and its nuanced versions more accurately represent verification-based knowability and do not yield omniscience.

Justification Logic provides an axiomatic description of justifications and delegates the question of their nature to semantics. In this note, we address the conceptual issue of the logical type of justifications: we argue that justifications in the logical setting are naturally interpreted as sets of formulas which leads to a class of epistemic models that we call modular models. We show that Fitting models for Justification Logic naturally encode modular models and can be regarded as convenient pre-models of the former.

We outline an intuitionistic view of knowledge which maintains the original Brouwer–Heyting–Kolmogorov semantics for intuitionism and is consistent with the well-known approach that intuitionistic knowledge be regarded as the result of verification. We argue that on this view coreflectionA→KAis valid and the factivity of knowledge holds in the formKA→ ¬¬A‘known propositions cannot be false’.We show that the traditional form of factivityKA→Ais a distinctly classical principle which, liketertium non datur A∨ ¬A, does not hold intuitionistically, but, along with the whole of classical epistemic logic, is intuitionistically valid in its double negation form ¬¬(KA¬A).Within the intuitionistic epistemic framework the knowability paradox is resolved in a constructive manner. We argue that this paradox is the result of an unwarranted classical reading of constructive principles and as such does not have the consequences for constructive foundations traditionally attributed it.