Barry Smith recently discussed the diagraphs of book eight of Jacob Lorhard’s Ogdoas scholastica under the heading “birth of ontology” (Smith, 2022; this issue). Here, I highlight the commonalities between the original usage of diagraphs in the tradition of Ramus for didactic purposes and the the usage of their present-day successors–modern ontologies–for computational purposes. The modern ideas of ontology and of the universal computer were born just two generations apart in the breakthrough century of instrumental reason.

This paper will be concerned with hard choices—that is, choice situations where an agent cannot make a rationally justified choice. Specifically, this paper asks: if an agent cannot optimize in a given situation, are they facing a hard choice? A pair of claims are defended in light of this question. First, situations where an agent cannot optimize because of incompleteness of the binary preference or value relation constitute a hard choice. Second, situations where agents cannot optimize because the binary preference (...) or value relation violates acyclicity do not constitute a hard choice. (shrink)

Minimal Type Theory (MTT) is based on type theory in that it is agnostic about Predicate Logic level and expressly disallows the evaluation of incompatible types. It is called Minimal because it has the fewest possible number of fundamental types, and has all of its syntax expressed entirely as the connections in a directed acyclic graph.

Should you be willing to forego any sure good for a tiny probability of a vastly greater good? Fanatics say you should, anti-fanatics say you should not. Anti-fanaticism has great intuitive appeal. But, I argue, these intuitions are untenable, because satisfying them in their full generality is incompatible with three very plausible principles: acyclicity, a minimal dominance principle, and the principle that any outcome can be made better or worse. This argument against anti-fanaticism can be turned into a positive (...) argument for a weak version of fanaticism, but only from significantly more contentious premises. In combination, these facts suggest that those who find fanaticism counterintuitive should favor not anti-fanaticism, but an intermediate position that permits agents to have incomplete preferences that are neither fanatical nor anti-fanatical. (shrink)

This paper provides a general introduction to the use of causal models in the metaphysics of causation, specifically structural equation models and directed acyclic graphs. It reviews the formal framework, lays out a method of interpretation capable of representing different underlying metaphysical relations, and describes the use of these models in analyzing causation.

In solving judgment aggregation problems, groups often face constraints. Many decision problems can be modelled in terms the acceptance or rejection of certain propositions in a language, and constraints as propositions that the decisions should be consistent with. For example, court judgments in breach-of-contract cases should be consistent with the constraint that action and obligation are necessary and sufficient for liability; judgments on how to rank several options in an order of preference with the constraint of transitivity; and judgments on (...) budget items with budgetary constraints. Often more or less demanding constraints on decisions are imaginable. For instance, in preference ranking problems, the transitivity constraint is often contrasted with the weaker acyclicity constraint. In this paper, we make constraints explicit in judgment aggregation by relativizing the rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. We review several general results on judgment aggregation in light of such constraints. (shrink)

This paper will be concerned with hard choices—that is, choice situations where an agent cannot make a rationally justified choice. Specifically, this paper asks: if an agent cannot optimize in a given situation, are they facing a hard choice? A pair of claims are defended in light of this question. First, situations where an agent cannot optimize because of incompleteness of the binary preference or value relation constitute a hard choice. Second, situations where agents cannot optimize because the binary preference (...) or value relation violates acyclicity do not constitute a hard choice. (shrink)

The difference principle, introduced by Rawls (1971, 1993), is generally interpreted as leximin, but this is not how he intended it. Rawls explicitly states that the difference principle requires that aggregate benefits (e.g., average or total) to those in the least advantaged group be given lexical priority over benefits to others, where the least advantaged group includes more than the strictly worst off individuals. We study the implications of adopting different approaches to the definition of the least advantaged group and (...) show that, if acyclicity is required, several seemingly plausible approaches lead to something close to leximin. We then show that significant aggregation is possible, if the least advantaged group is defined as those with those with less benefits than some strictly positive transform of the lowest level of benefits. Finally, we discuss the implications of requiring that, in comparing two alternatives, the cutoff for the least advantaged group of one alternative be the same as that for the other alternative. (shrink)

The exponential growth of social data both in volume and complexity has increasingly exposed many of the shortcomings of the conventional frequentist approach to statistics. The scientific community has called for careful usage of the approach and its inference. Meanwhile, the alternative method, Bayesian statistics, still faces considerable barriers toward a more widespread application. The bayesvl R package is an open program, designed for implementing Bayesian modeling and analysis using the Stan language’s no-U-turn (NUTS) sampler. The package combines the ability (...) to construct Bayesian network models using directed acyclic graphs (DAGs), the Markov chain Monte Carlo (MCMC) simulation technique, and the graphic capability of the ggplot2 package. As a result, it can improve the user experience and intuitive understanding when constructing and analyzing Bayesian network models. A case example is offered to illustrate the usefulness of the package for Big Data analytics and cognitive computing. (shrink)

Suppose that you prefer A to B, B to C, and C to A. Your preferences violate Expected Utility Theory by being cyclic. Money-pump arguments offer a way to show that such violations are irrational. Suppose that you start with A. Then you should be willing to trade A for C and then C for B. But then, once you have B, you are offered a trade back to A for a small cost. Since you prefer A to B, you (...) pay the small sum to trade from B to A. But now you have been turned into a money pump. You are back to the alternative you started with but with less money. This Element shows how each of the axioms of Expected Utility Theory can be defended by money-pump arguments of this kind. The Element also defends money-pump arguments from the standard objections to this kind of approach. This title is also available as Open Access on Cambridge Core. (shrink)

In “The Irrelevance of the Diachronic Money-Pump Argument for Acyclicity,” The Journal of Philosophy CX, 8 (August 2013), 460-464, Johan E. Gustafsson contends that if Davidson, McKinsey and Suppes’ diachronic money-pump argument in their "Outlines of a Formal Theory of Value, I," Philosophy of Science 22 (1955), 140-160 is valid, so is the synchronic argument Gustafsson himself offers. He concludes that the latter renders irrelevant diachronic choice considerations in general, and the two best-known diachronic solutions to the money pump (...) problem in particular. I argue here that this reasoning is incorrect, and that Gustafsson’s synchronic argument is faulty on independent grounds. Specifically, it is based on a false analogy between the derivation of a synchronic ordinal ranking from a transitive series of pairwise comparisons, and the putative derivation of such a ranking from an intransitive series. The latter is not possible under the assumption of revealed preference theory, and is highly improbable even if that assumption is rejected. Moreover, Gustafsson’s argument raises issues of fidelity to the historical texts that must be addressed. I conclude that the money pump, and cyclical choice more generally, are necessarily diachronic; and therefore that the two best-known diachronic solutions to the money pump problem remain relevant. (shrink)

Molinists hold that there are contingently true counterfactuals about what agents would do if put in specific circumstances, that God knows these prior to creation, and that God uses this knowledge in choosing how to create. In this essay we critique Molinism, arguing that if these theses were true, agents would not be free. Consider Eve’s sinning upon being tempted by a serpent. We argue that if Molinism is true, then there is some set of facts that fully explains both (...) Eve’s action and everything else Eve does that influences that action; and that if this is the case, Eve does not act freely. The first premise of this argument follows from the explanatory relations the Molinist is committed to, and the second premise follows from libertarian intuitions about free will. (shrink)

There are simple mechanical systems that elude causal representation. We describe one that cannot be represented in a single directed acyclic graph. Our case suggests limitations on the use of causal graphs for causal inference and makes salient the point that causal relations among variables depend upon details of causal setups, including values of variables.

In the paper we provide an overview of issues related to the models used in the research on the logic of norms and actions. We present two models of the variability of the world: temporal (acyclic) and atemporal (cyclic). In the first one the past is always clearly defined, and the future is potentially “branched”. The second type of model allows for a return to the situation that took place. Next we describe different approaches towards agency modeling. We present the (...) most important paradigms, including the logic of actions, where actions are interpreted as transitions between the situations and STIT logic, which states only the responsibility of the agent for particular states of affairs. We discuss questions of determinism and indeterminism of actions, identification of basic actions and operations and the issue of identity. The final part of the paper is devoted to deontic categories. In particular, the applicability of the concepts of strong and weak permission and prohibition in different situational contexts, and their relationship to the two concepts of obligation: abstract and derived. (shrink)

This paper develops transfinite extensions of transitivity and acyclicity in the context of population ethics. They are used to argue that it is better to add good lives, worse to add bad lives, and equally good to add neutral lives, where a life's value is understood as personal value. These conclusions rule out a number of theories of population ethics, feed into an argument for the repugnant conclusion, and allow us to reduce different-number comparisons to same-number ones. Challenges to (...) these arguments are addressed, including the issue of comparing existence and non-existence in terms of personal value, the possibility of minimal quanta of time and life, and the meaningfulness of measuring closeness between outcomes with different population sizes. An asymmetry is uncovered between transfinite cycles of worseness and betterness, supporting a version of the weak procreative asymmetry. Transfinite transitivity principles are also favourably compared to the better-known principles of continuity. (shrink)

I provide a characterization of weakly pseudo-rationalizable choice functions---that is, choice functions rationalizable by a set of acyclic relations---in terms of hyper-relations satisfying certain properties. For those hyper-relations Nehring calls extended preference relations, the central characterizing condition is weaker than (hyper-relation) transitivity but stronger than (hyper-relation) acyclicity. Furthermore, the relevant type of hyper-relation can be represented as the intersection of a certain class of its extensions. These results generalize known, analogous results for path independent choice functions.

By separating the general concept of truth into syntactic truth and semantic truth, this article proposes a new theory of truth to explain several paradoxes like the Liar paradox, Card paradox, Curry’s paradox, etc. By revealing the relationship between syntactic /semantic truth and being-nothing-becoming which are the core concepts of dialectical logic, it is able to formalize dialectical logic. It also provides a logical basis for complexity theory by transferring all reasoning into a directed (cyclic/acyclic) graph which explains both paradoxical (...) and paradox-free reasoning. The different structure between cyclic graphs and acyclic graphs is the key to understanding paradoxes. By explaining the immanent between logic, paradox, and cellular automata, it also illustrates dialectical logic as ontology. (shrink)

This paper generalizes rationalizability of a choice function by a single acyclic binary relation to rationalizability by a set of such relations. Rather than selecting those options in a menu that are maximal with respect to a single binary relation, a weakly pseudo-rationalizable choice function selects those options that are maximal with respect to at least one binary relation in a given set. I characterize the class of weakly pseudo-rationalizable choice functions in terms of simple functional properties. This result also (...) generalizes Aizerman and Malishevski's characterization of pseudo-rationalizable choice functions, that is, choice functions rationalizable by a set of total orders. (shrink)

Minimal Type Theory (MTT) shows exactly how all of the constituent parts of an expression relate to each other (in 2D space) when this expression is formalized using a directed acyclic graph (DAG). This provides substantially greater expressiveness than the 1D space of FOPL syntax. -/- The increase in expressiveness over other formal systems of logic shows the Pathological Self-Reference Error of expressions previously considered to be sentences of formal systems. MTT shows that these expressions were never truth bearers, thus (...) never sentences of any formal logic system. (shrink)