Formal Philosophy

Every foundational framework that attempts to describe the totality of what exists must confront the question of what lies outside its own descriptive reach. The available historical responses have tended to deny that anything lies outside, to name a beyond without specifying its relationship to the inside, or to treat the incompleteness of formal systems as a defect to be worked around rather than a structural feature to be integrated. This paper develops a fourth response within an explicit framework.

Character ethics assesses actions via the trait profile from which they arise. This paper proposes an epistemically conservative character ethics through a formal framework. Such a framework demands two components: an account of how an agent may alter its trait profile, and a criterion for ranking possible trait profiles. We present these components through two formulas. The first is an Aristotelian account of the agent, formalised through a probabilistic dynamic Hotelling-Downs model where the update is driven by a simplified delta rule and a decay power law. The second, analogously to Hilbert's solution within mathematical formalism, defines "lower ethics" as the set of factually reliable epistemic practices and ranks trait profiles-and hence ethical systems themselves-by their capacity to engender behaviours conducive to the formation of justified true beliefs. This answers the background problem-which renders appeals to ethical facts theoretically unattractive-by ranking ethical systems in a non-realist fashion. We adduce arguments in support of this ranking criterion and rebut salient objections.

I propose a “Thomasian” interpretation (epistemological and metaphysical) of two schemes of contemporary abstract formal theory
called Category Theory. They help us to show a epistemological
foundation of the problem of language-world reference and, similarly,
a clearer representation of how Aquinas’ metaphysics of being
is structured; and the connection between transcendental and
predicamental participation. These abstract schemes show the same
logic, ternary and asymmetrical, which reflects, in my opinion, the
fundamental logic of the metaphysics of esse ut actus and, therefore,
the most authentic and productive Tommasian forma mentis.
I argue that today, especially Thomism, cannot avoid confrontation
with the logical-symbolic sciences.

Propongo qui un’interpretazione “tommasiana” (epistemologica e metafisica) di due schemi della teoria formale astratta contemporanea chiamata Teoria delle Categorie. Essi ci aiutano a mostrare una fondazione epistemologica del problema della relazione linguaggio-mondo e, allo stesso modo, una rappresentazione più chiara di come è strutturata la metafisica dell’essere dell’Aquinate e la connessione tra partecipazione trascendentale e predicamentale.
Questi schemi astratti mostrano la stessa logica, ternaria e asimmetrica, che riflette, a mio avviso, la logica fondamentale della metafisica dell’esse ut actus e, quindi, la forma mentis tommasiana più autentica
e produttiva. Sostengo che oggi, soprattutto il tomismo, non possa evitare il confronto con le scienze logico-simboliche.

In this paper we analyse the conditions for attributing to AI autonomous systems the ontological status of "artificial moral agents", in the context of the "distributed responsibility" between humans and machines in Machine Ethics (ME). In order to address the fundamental issue in ME of the unavoidable "opacity" of their decisions with ethical/legal relevance, we start from the neuroethical evidence in cognitive science. In humans, the "transparency" and then the "ethical accountability" of their actions as responsible moral agents is not in contradiction with the unavoidable "opacity" (unawareness) of the brain process by which they perform their moral judgements on the right action to execute. In fact, the moral accountability of our actions depends on what is immediately before and after our "moral judgements" on the right action to execute (formally, deontic first order logic (FOL) decisions). I.e., our moral accountability depends on the "ethical constraints" we imposed to our judgement before performing it in an opaque way. Anyway, our moral accountability depends overall on the "ethical assessment" or explicit "moral reasoning" after and over the moral judgement before executing our actions (deontic higher order logic (HOL) assessment). In this way, in the light of the AI "imitation game", the consistent attribution of the status of ethically accountable artificial moral agents to autonomous AI systems depends on two similar conditions. Firstly, it depends on the presence of "ethical constraints" to be satisfied in their Machine Learning (ML) supervised optimization algorithm during its training phase, to give the system ethical skills ("competences") in its decisions. Secondly-and definitely-, it depends on the presence in an AI autonomous system of a deontic HOL "ethical reasoner" to perform an automatic, and fully transparent assessment (metalogical deontic valuation) about the decisions taken by the ethically skilled ML algorithm about the right action to execute, before executing it. Finally, we show that the proper deontic FOL and HOL for this class of artificial moral agents is Kripke's modal relational

This study shows that the Turkish expression hani exhibits interesting properties for the study of the semantics and pragmatics interface, because on the one hand, its function is merely pragmatic, but on the other hand, it is subject to the truth conditional effect of other constituents at LF. This notwithstanding, studies on this expression are remarkably scarce. The only attempts to describe its properties are Akar and Öztürk (2020); Akar, Öztürk, Göksel, and Kelepir (2020); Erguvanlı-Taylan (2000). In the present study, we introduce the first formal semantic and pragmatic treatment of clauses containing hani. Unlike previous accounts, we claim that hani can have one of the following two major pragmatic functions: making salient a proposition in the Common Ground or challenging one in a past Common Ground, therefore requiring a Common Ground revision. Despite its variety of occurrences, we argue that hani has a uniform interpretation, and provide a compositional analysis of the different construals that it is associated with. Furthermore, we show that a formally explicit and accurate characterization of hani clauses requires operating on indexical parameters, in particular the context time. Therefore, if our proposal is on the right track, hani clauses may provide indirect empirical evidence in favour of the existence of "monstrous" phenomena adding to the accumulating cross-linguistic evidence in this domain (see Schlenker (2003) and much work since then).

The Zeroth Axiom: Recursion Is God is a treatise that proposes a foundational metaphysical system in which the process of recursion—the self-referential loop inherent to all systems—is identified as the ultimate ground of reality. Drawing on insights from formal logic, phenomenology, and metaphysical inquiry, the work introduces “Axiom 0–0,” which asserts that all systems—including logic, mathematics, physics, time, perception, and consciousness—are recursively constructed, self-validating, and contextually bound. By reinterpreting classical philosophical problems such as the first cause, the hard problem of consciousness, and the ontology of time, this treatise argues that what we consider “truth,” “morality,” and even “divinity” are emergent properties of stable recursive loops. Moreover, the text introduces the concept of “miracle loops,” wherein intentional or symbolic recursive overrides yield phenomena that reconfigure established patterns without violating the underlying system. Ultimately, The Zeroth Axiom: Recursion Is God invites scholars to reconsider the nature of existence and divinity by positing that the recursive act of self-reference—not an external agent—is the Absolute Truth that underlies all being.

Meaning Representation (AMR) is a simple, expressive semantic framework whose emphasis on predicate-argument structure is effective for many tasks. Nevertheless, AMR lacks a systematic treatment of projection phenomena, making its translation into logical form problematic. We present a translation function from AMR to first order logic using continuation semantics, which allows us to capture the semantic context of an expression in the form of an argument. This is a natural extension of AMR's original design principles, allowing us to easily model basic projection phenomena such as quantification and negation as well as complex phenomena such as bound variables and donkey anaphora.

Welcome to FG-2006, the 11th conference on Formal Grammar. This year's conference includes 12 contributed papers covering, as usual, a wide range of areas of formal grammar. In addition to the papers included in this volume, the conference features also two invited talks by .

This work presents an overview of four different approaches to the problem of future contingency and determinism in temporal logics. All of them are bivalent, viz. they share the assumption that propositions concerning future contingent facts have a determinate truth-value (true or false). We introduce Ockhamism, Peirceanism, Actualism and T × W semantics, the four most relevant bivalent alternatives in this area, and compare them from the point of view of their expressiveness and their underlying metaphysics of time.

If Jack is taller than Jill, there is a scale in which entities are ordered by height and which has a segment running from Jack down to Jill. Call that a directed scale-segment. A comparative characterizes a directed scale segment by describing the two ends, the type of scale and optionally the length of the segment. This paper explores the possibility of isolating these descriptions in distinct expressions in the clause tied together by quantification over directed scale segments. Data from Hindi and Navajo are used to motivate this arrangement and then to probe its limits. The resulting discussion is an argument for cross linguistic diversity in the semantics of comparatives.

Welcome to FG-2006, the 11th conference on Formal Grammar. This year's conference includes 12 contributed papers covering, as usual, a wide range of areas of formal grammar. In addition to the papers included in this volume, the conference features also two invited talks by .

There is a robust debate on different linguistic levels of quantifier ambiguity resolution. Many accounts of the quantifier ambiguity are extensively examined in Turkish by semantic-prosodic and syntactic-semantic levels in previous studies. In this study, we aimed to investigate the prosodic and syntactic processes of the universal quantifier (her (‘every’) and existential quantifier bir (‘a/an’)) by using an on-line picture matching experiment with 75 young adults and native speakers of Turkish. Our stimuli consisted of 120 sentences (30×4) for each of the conditions with order (her–bir (‘every–a/an’) vs. bir–her ‘a/an–every’) × focus (subject position vs. object position), respectively. In each trial, participants were asked to listen to the auditory stimuli and to judge sentences they heard. Our findings showed that the focused existential quantifier bir (‘a/an’) assigned wider scope than the universal quantifier her (‘every’) for the judgment task rates. This finding suggested ...

May’s Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to May’s axioms, we can uniquely determine how to vote on three alternatives (setting aside tiebreaking). In particular, we add two axioms stating that the voting method should mitigate spoiler effects and avoid the so-called strong no show paradox. We prove a theorem stating that any preferential voting method satisfying our enlarged set of axioms, which includes some weak homogeneity and preservation axioms, must choose from among the Minimax winners in all three- alternative elections. When applied to more than three alternatives, our axioms also distinguish Minimax from other known voting methods that coincide with or refine Minimax for three alternatives.

Hunter (2016) proposed that a speech report with a parenthetical interpretation but non-parenthetical syntax will contribute a modal discourse relation of the form ⌃R to discourse logical form. This paper provides a compositional account of the mechanism by which these modal relations are triggered. It then extends Hunter’s proposal to reports involving factive embedding verbs and provides an explanation of why explicit discourse connectives sometimes block parenthetical readings of reports in their scope.

In this paper, I present the suggestion that a suitable theory of “justice as fairness” could offer a consistent path for solving many issues related to the actual crisis of the classical liberal model of economy and democracy, by substituting the abstract “equality” principle, with the concrete “equity” one in the notion of justice. After a short discussion of some main characters of the present worldwide crisis of the classical liberal model, I present two main theories of justice as fairness. John Rawls’ theory in political philosophy that emphasizes how really equitable judgements must overcome the equalitarianism of the Classical Liberalism, by considering the real possibilities of individuals and groups of accessing and enjoying commodities and utilities, as well as, the “basic liberties” defining the citizen equal dignity in the Modern State. Rawls propose, therefore, a notion of fairness compliant with the Kantian normativism, and a notion of fair distributive justice based ...

Mahavira, 24 th Tirthankara of Jainism is highly celebrated figure in the world for his ideas that revolutionized the world. He was a realist thinker who tried hard to spread humanitarian values, his human-centric teachings centred on making one's life viable for himself and for others. This paper is an attempt to present in brief one aspect of Mahavira's model of individual well-being and comparing it with 'Capability-approach' by Nobel Laureate Amartya Sen which was a path-breaking reform in the field of economics. This paper briefly elaborates both approaches, then draw parallel between them by holding up particular dimensions like views on poverty, freedom, development etc. It also presents how Mahavira went a step ahead by reaching the way to attain desired end as Sen visualised and solved the major loophole of Sen's approach.

Mahavira, 24 th Tirthankara of Jainism is highly celebrated figure in the world for his ideas that revolutionized the world. He was a realist thinker who tried hard to spread humanitarian values, his human-centric teachings centred on making one's life viable for himself and for others. This paper is an attempt to present in brief one aspect of Mahavira's model of individual well-being and comparing it with 'Capability-approach' by Nobel Laureate Amartya Sen which was a path-breaking reform in the field of economics. This paper briefly elaborates both approaches, then draw parallel between them by holding up particular dimensions like views on poverty, freedom, development etc. It also presents how Mahavira went a step ahead by reaching the way to attain desired end as Sen visualised and solved the major loophole of Sen's approach.

Aristotle's famous sea-battle argument in De interpretatione 9 launched a still-ongoing debate over the status of future contingents. For present purposes I'll follow Todd (3) in taking these to be propositions stating of some causally contingent event-type (e.g., a sea-battle) either that it will happen or that it will not happen. 1 Aristotle seems to have held that such propositions are neither true nor false so long as both the event's occurrence and non-occurrence remains an open question, that is, so long as the event remains both causally contingent and future. On this view, there being true future contingents is incompatible with the causal contingency of the events they describe. Despite the esteem generally accorded Aristotle, the majority view has long been that he was wrong on this point: There are true future contingents. This became the majority view partly for theological and partly for philosophical reasons. Theologically, belief in true future contingents is driven by the idea that God is omniscient and provident, and therefore knows exactly how the future plays out. Philosophically, it is driven mainly by conceptual worries about bivalence and excluded middle. Until recently, the main source of dissent from the majority view has been determinism, both its theistic and physical varieties: There are no true future contingents because there is no causal contingency. Of late another dissenting view now known as open futurism has emerged as a major player in both philosophical and theological contexts. Open futurism affirms causal contingency (over against determinism) but also denies that there are any true future contingents (over against the majority view). Philosophically, open futurism derives support from recent developments in physics (esp. quantum mechanics), logic (tense and multi-valued), metaphysics (esp. issues of temporal ontology and alethic grounding), and of course Aristotelian-style worries about whether an alethically settled future is compatible with causal contingency (esp. human free will). Theologically, open futurism derives support from perspectives like open theism and process theism, both of which affirm that the future is (to some degree) open-ended from God's own perspective. It is in the context of open futurism that Patrick Todd's book is situated. Unlike Aristotelian-style non-bivalentist open futurism, which says that future contingents are neither true nor false, Todd contends that all future contingents are unequivocally false. I'll call this all-falsist open futurism. Todd is not the first to argue for such a view, 2 but he is the first to give it a book-length defense, and with a major academic publisher to boot. This will likely secure a 1 While I follow Todd's usage here, it's better to think of future contingents as causally contingent event-types rather than as propositions about those things. Focusing on propositions adds an unnecessary conceptual layer that makes it harder to integrate future contingents with probabilities. See (Rhoda Forthcoming). 2 See, for example, (Hartshorne 1965).

This study shows that the Turkish expression hani exhibits interesting properties for the study of the semantics and pragmatics interface, because on the one hand, its function is merely pragmatic, but on the other hand, it is subject to the truth conditional effect of other constituents at LF. This notwithstanding, studies on this expression are remarkably scarce. The only attempts to describe its properties are Akar and Öztürk (2020); Akar, Öztürk, Göksel, and Kelepir (2020); Erguvanlı-Taylan (2000). In the present study, we introduce the first formal semantic and pragmatic treatment of clauses containing hani. Unlike previous accounts, we claim that hani can have one of the following two major pragmatic functions: making salient a proposition in the Common Ground or challenging one in a past Common Ground, therefore requiring a Common Ground revision. Despite its variety of occurrences, we argue that hani has a uniform interpretation, and provide a compositional analysis of the different construals that it is associated with. Furthermore, we show that a formally explicit and accurate characterization of hani clauses requires operating on indexical parameters, in particular the context time. Therefore, if our proposal is on the right track, hani clauses may provide indirect empirical evidence in favour of the existence of "monstrous" phenomena adding to the accumulating cross-linguistic evidence in this domain (see Schlenker (2003) and much work since then).

A significant chapter of the short history of formal philosophy is related with the notion and the theory of the so-called "Social Welfare Functions (SWFs)", as a substantial component of the "social choice theory". One of the main uses of SWFs is aimed, indeed, at representing coherent patterns (effectively, algebraic structures of relations) of individual and collective choices/preferences, with respect to a fixed ranking of alternative social/economical states. Indeed, the SWF theory is originally inspired by Samuelson's pioneering work on the foundations of mathematical economic analysis. It uses explicitly Gibbs' thermodynamics of ensembles "at equilibrium" based on statistical mechanics as the physical paradigm for the mathematical theory of economic systems. In both theories, indeed, the differences and the relationships among individuals are systematically considered as irrelevant. On the contrary, in the mathematical theory of "Social Choice Functions" (SCFs) developed by Amartya Sen, the interpersonal comparison and the real-time information exchanges among different social actors and their environments-differentethical values and constraints, included-play an essential role. This means that the inspiring physical paradigm is no longer "gas" but "fluid thermodynamics" of interacting systems passing through different "phases" of fast "dissolution/aggregation of coherent behaviors", and then staying persistently in far from equilibrium conditions. These processes are systematically studied by the quantum field theory (QFT) of "dissipative systems", at the basis of the physics of condensed matter, modeled by the "algebra doubling" of coalgebras. This coalgebraic modeling is highly

We focus on framework used by T. Jarmużek for the reconstruction of Diodorus Kronus' Master Argument. The Master Argument, crucial to determinism, can be formalized under different assumptions regarding time structure. This is partly due to the logic chosen as the basis for such formalization. Given the versatility of positional logic, even a branching time structure can be used to formalize the Master Argument.