Ioannis G. Ntagkas

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.

This essay proposes a reductive account of robust macro-regularities. On the view proposed, regularities can earn their elite scientific status by featuring in good summaries of restricted regions in the space of physical possibilities: our “modal neighborhoods.‘ I argue that this view vindicates “nomic foundationalism‘, while doing justice to the practice of invoking physically contingent generalizations in higher-level explanations. Moreover, the view suggests an explanation for the particular significance of robust macro-regularities: we rely on summaries of our modal neighborhoods when reasoning hypothetically about “agentially accessible‘ possibilities.

It strikes many as obvious that negative facts—such as that Justin Trudeau is not the prime minister of Australia—are not fundamental: negative facts must ultimately be explained in terms of positive facts (for instance, that Justin Trudeau is the prime minister of Canada). I focus on a particular class of negative facts: contingent negative existentials (such as that there are no 10ft tall humans). If contingent negative existentials are not fundamental, then they must be explained. But the claim that contingent negative existentials are explained is in tension with the widely held view that any universal generalization can be explained by its instances together with a totality fact (i.e. a fact to the effect that the instances exhaust the relevant domain). This is because a totality fact is itself a negative existential, and equivalent to a universal generalization. If the explanation for any contingent negative existential must appeal to another contingent negative existential, then—unless there are no fundamental facts—not all contingent negative existentials can be non-fundamental. I argue that we should give up the age-old mantra that only positive facts can be fundamental. I show that at least some contingent negative existentials are fundamental. I first make the case for including a totality fact in the explanans for a contingent negative existential and show that alternative accounts for explaining such facts are inadequate. I then undermine the standard arguments for subscribing to the view that there are no negative facts—including negative existentials—at the fundamental level.

Humeans and anti-Humeans agree that laws of nature should explain scientifically particular matters of fact. One objection to Humean accounts of laws contends that Humean laws cannot explain particular matters of fact because their explanations are harmfully circular. This article distinguishes between metaphysical and semantic characterizations of the circularity and argues for a new semantic version of the circularity objection. The new formulation suggests that Humean explanations are harmfully circular because the content of the sentences being explained is part of the content of the sentences doing the explaining. I describe the nature of partial content and demonstrate how this account of partial content renders Humean explanations ineffective while sparing anti-Humean explanations from the same fate. 1Introduction2Standard Formulations of the Circularity Charge3Humean Responses4Semantic Characterizations of the Circularity Worry 4.1Hempel and Oppenheim’s semantic circularity concern4.2A new version of the semantic circularity charge4.3Partial content as a guide to circularity5Humean Responses to the Semantic Circularity Charge 5.1Smuggling in metaphysics through the back door?5.2Do anti-Humean laws fare any better?5.3The over-generalization concern6ConclusionAppendix

One conception of the Principle of Sufficient Reason maintains that every fact is metaphysically explained. There are different ways to challenge this version of the PSR; one type of challenge involves pinpointing a specific set of facts that resist metaphysical explanation. Certain identity and distinctness facts seem to constitute such a set. For example, we can imagine a scenario in which we have two qualitatively identical spheres, Castor and Pollux. Castor is distinct from Pollux but it is unclear what could metaphysically explain this distinctness fact. In this paper, I argue that we should not treat identity and distinctness facts as metaphysically fundamental. As such, identity and distinctness facts do not challenge the PSR. We can metaphysically explain them.

This paper offers a metaphysical explanation of the identity and distinctness of concrete objects. It is tempting to try to distinguish concrete objects on the basis of their possessing different qualitative features, where qualitative features are ones that do not involve identity. Yet, this criterion for object identity faces counterexamples: distinct objects can share all of their qualitative features. This paper suggests that in order to distinguish concrete objects we need to look not only at which properties and relations objects instantiate but also how they instantiate these properties and relations. I propose that objects are identical when they stand in certain qualitative relations in virtue of their existence. And concrete objects are distinct when they do not stand in the same kinds of relations to one another in virtue of their existence.

In the _Meditations_ and related texts from the early 1640s, Descartes argues that the self can be correctly considered as either a mind or a human being, and that the self’s properties vary accordingly. For example, the self is simple considered as a mind, whereas the self is composite considered as a human being. Someone might object that it is unclear how merely considering the self in different ways blocks the conclusion that a single subject of predication—the self—is both simple and composite, which is contradictory. In response to this objection, this paper develops a reading of Descartes’s various ways of considering the self. I argue that the best reading of Descartes’s qualified claims about the self, i.e., about the self _qua_ mind or the self qua human being, presupposes an account of the unqualified self, that is, of the self _simpliciter_. I argue that the self _simpliciter_ is not a mind, and that it is not a human being either. This result might suggest the pessimistic conclusion that Descartes’s view of the self is incoherent. To avoid this result, I introduce a new metaphysical account of the Cartesian self. On my view, the self is individuated by a unified mental life. The self is constituted by the beings that jointly produce this mental life, and derives its unity from it.