al-juzʼ 1. al-Manṭiq al-istiqrārī -- al-juzʼ 2. al-Mushkilāt al-maʻrifīyah -- al-juzʼ 3. al-Manṭiq al-riyāḍī.

This thesis aims to clarify a number of conceptual aspects of the debate surrounding algorithmic fairness. The particular focus here is the role of causal modeling in defining criteria of algorithmic fairness. In Chapter 1, I argue that in the discussion of algorithmic fairness, two fundamentally distinct notions of fairness have been conflated. Subsequently, I propose that what is usually taken to be the problem of algorithmic fairness should be divided into two subproblems, the problem of predictive fairness, and the (...) problem of allocative fairness. At the core of Chapter 2 is the proof of a theorem that establishes that three of the most popular (predictive) fairness criteria are pairwise incompatible. In particular, I show that under certain conditions, a predictive algorithm that satisfies a criterion called counterfactual fairness will with logical necessity violate two other popular predictive fairness criteria called equalized odds and predictive parity. In Chapter 3, a new predictive fairness criterion is developed using a mathematical framework for causal modeling. This fairness criterion, which I call causal relevance fairness, is a relaxation of another popular fairness criterion, counterfactual fairness, but turns out to be more closely in line with philosophical theories of discrimination. In Chapter 4, another infamous impossibility result in algorithmic fairness is analyzed through the lens of causality. I argue that by using a causal inference method called matching, we can modify the two fairness criteria equalized odds and predictive parity in a way that resolves the impossibility. Lastly, Chapter 5 contains an empirical case study. In it, the fairness of a popular recidivism risk prediction tool is analyzed using the criteria of (predictive) fairness developed earlier. (shrink)

The central question of this paper is: are deterministic and indeterministic descriptions observationally equivalent in the sense that they give the same predictions? I tackle this question for measure-theoretic deterministic systems and stochastic processes, both of which are ubiquitous in science. I first show that for many measure-theoretic deterministic systems there is a stochastic process which is observationally equivalent to the deterministic system. Conversely, I show that for all stochastic processes there is a measure-theoretic deterministic system which is observationally equivalent (...) to the stochastic process. Still, one might guess that the measure-theoretic deterministic systems which are observationally equivalent to stochastic processes used in science do not include any deterministic systems used in science. I argue that this is not so because deterministic systems used in science even give rise to Bernoulli processes. Despite this, one might guess that measure-theoretic deterministic systems used in science cannot give the same predictions at every observation level as stochastic processes used in science. By proving results in ergodic theory, I show that also this guess is misguided: there are several deterministic systems used in science which give the same predictions at every observation level as Markov processes. All these results show that measure-theoretic deterministic systems and stochastic processes are observationally equivalent more often than one might perhaps expect. Furthermore, I criticise the claims of the previous philosophy papers Suppes (1993, 1999), Suppes and de Barros (1996) and Winnie (1998) on observational equivalence. (shrink)

Determinism and chance seem to be irreconcilable opposites: either something is chancy or it is deterministic but not both. Yet there are processes which appear to square the circle by being chancy and deterministic at once, and the appearance is backed by well-confirmed scientific theories such as statistical mechanics which also seem to provide us with chances for deterministic processes. Is this possible, and if so how? In this essay I discuss this question for probabilities as they occur in the (...) empirical sciences, setting aside metaphysical questions in connection with free will, divine intervention and determinism in history. (shrink)

We argue that concerns about double-counting -- using the same evidence both to calibrate or tune climate models and also to confirm or verify that the models are adequate --deserve more careful scrutiny in climate modelling circles. It is widely held that double-counting is bad and that separate data must be used for calibration and confirmation. We show that this is far from obviously true, and that climate scientists may be confusing their targets. Our analysis turns on a Bayesian/relative-likelihood approach (...) to incremental confirmation. According to this approach, double-counting is entirely proper. We go on to discuss plausible difficulties with calibrating climate models, and we distinguish more and less ambitious notions of confirmation. Strong claims of confirmation may not, in many cases, be warranted, but it would be a mistake to regard double-counting as the culprit. (shrink)

We investigate the general properties of general Bayesian learning, where “general Bayesian learning” means inferring a state from another that is regarded as evidence, and where the inference is conditionalizing the evidence using the conditional expectation determined by a reference probability measure representing the background subjective degrees of belief of a Bayesian Agent performing the inference. States are linear functionals that encode probability measures by assigning expectation values to random variables via integrating them with respect to the probability measure. If (...) a state can be learned from another this way, then it is said to be Bayes accessible from the evidence. It is shown that the Bayes accessibility relation is reflexive, antisymmetric and non-transitive. If every state is Bayes accessible from some other defined on the same set of random variables, then the set of states is called weakly Bayes connected. It is shown that the set of states is not weakly Bayes connected if the probability space is standard. The set of states is called weakly Bayes connectable if, given any state, the probability space can be extended in such a way that the given state becomes Bayes accessible from some other state in the extended space. It is shown that probability spaces are weakly Bayes connectable. Since conditioning using the theory of conditional expectations includes both Bayes’ rule and Jeffrey conditionalization as special cases, the results presented generalize substantially some results obtained earlier for Jeffrey conditionalization. (shrink)

This article contributes to the literature on the evaluation of sets of opportunities. The starting point is Lancaster's characteristics approach. However, instead of assuming the existence of a canonical utility function, a reference point or reference level is postulated from which an agent evaluates set expansions in appropriate directions. One of the major tools for this exercise is the notion of directed cones. Desirability of characteristics is restricted to the interior of these cones. Satiation and non-monotonic evaluation is considered as (...) well. An axiomatic characterization for various cases is provided. (shrink)

Suppose that we acquire various items of information from various sources and that our degree of confidence in the content of the information set is sufficiently high to believe the information. Now a new item of information is being presented by a new information source. Are we justified to add this new item of information to what we already believe? Consider the following parable: “I go to a lecture about wildlife in Greenland which was supposed to be delivered by an (...) expert in the field. When I arrive I notice that the expert has excused himself and that the biology department has sent a newcomer to fill in for him. I have no beliefs about wildlife in Greenland, but I do have some beliefs about Greenland’s climate and about the kinds of climate conditions that various types of wildlife favor. Suppose that our newcomer proclaims that large colonies of elk roam in a particular valley on the southern tip of Greenland. Then I would certainly be willing to accept this item of information. But suppose that he proclaims that large colonies of armadillos roam in the same valley. Then I would not be willing to accept this item of information. Why do I accept the former but not the latter item of information? Let us suppose that neither item of information is logically inconsistent with what I already believe. Clearly, the former item of information is not inconsistent. But also the latter item is not: after all, there may be small pockets of Greenland with special climatological conditions and some Texan sailors may have set loose a pair of armadillos as a practical joke. But whereas the former item of information is quite plausible given my previous beliefs, the latter item of information is not. And this is what makes for the difference. Now suppose that our newcomer proclaims that large colonies of wild boars roam this valley in Greenland. I am not that sure anymore. Given everything I believe, I find wild boars in Greenland more plausible than armadillos in Greenland, but certainly less plausible than elk in Greenland. Had our expert presented the lecture and provided precisely the 2 same information, then I would have been willing to adopt the belief that there are wild boars in Greenland, but, with our newcomer delivering the lecture, I am not willing to do so. It is not that I would believe anything out of the expert’s mouth: also he could not have convinced me that there are armadillos in Greenland. But when it comes to wild boars, the difference between the expert’s and the newcomer’s credentials simply makes for the difference.” What we learn from this story is that the question of belief expansion has something to do with the reliability of the information source as well as with the plausibility of the new information, given what I already believe. The more reliable the information source is, the less plausible the new information needs to be given what I already believe, for me to be justified to add the belief to our belief set. The more plausible the new information is given what I already believe, the less reliable the information source needs to be given what I already believe, for me to be justified to add the belief to my belief set. The challenge is: can a precise account of this relationship be provided? (shrink)

Cheap talk has often been thought incapable of supporting the emergence of cooperation because costless signals, easily faked, are unlikely to be reliable (Zahavi and Zahavi, 1997). I show how, in a social network model of cheap talk with reinforcement learning, cheap talk does enable the emergence of cooperation, provided that individuals also temporally discount the past. This establishes one mechanism that suffices for moving a population of initially uncooperative individuals to a state of mutually beneficial cooperation even in the (...) absence of formal institutions. (shrink)

G is the result of adjoining the schema (qAA)qA to K; the axioms of G* are the theorems of G and the instances of the schema qAA and the sole rule of G* is modus ponens. A sentence is -provable if it is provable in P(eano) A(rithmetic) by one application of the -rule; equivalently, if its negation is -inconsistent in PA. Let -Bew(x) be the natural formalization of the notion of -provability. For any modal sentence A and function mapping sentence (...) letters to sentences of PA, inductively define A by: p = (p) (p a sentence letter); = ; (AB)su}= (A B); and (qA)= -Bew(A )(S) is the numeral for the Gödel number of the sentence S). Then, applying techniques of Solovay (Israel Journal of Mathematics 25, pp. 287–304), we prove that for every modal sentence A, G A iff for all , PA A ; and for every modal sentence A, G* A iff for all , A is true. (shrink)

SC , CA , QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras, and quasipolyadic equality algebras of dimension , respectively. Generalizing a result of Németi on cylindric algebras, we show that for K {SC, CA, QA, QEA} and ordinals , the class Nr K of -dimensional neat reducts of -dimensional K algebras, though closed under taking homomorphic images and products, is not closed under forming subalgebras (i.e. is not a variety) if (...) and only if > 1.From this it easily follows that for 1 , the operation of forming -neat reducts of algebras in K does not commute with forming subalgebras, a notion to be made precise. (shrink)

SC, CA, QA and QEA denote the class of Pinter’s substitution algebras, Tarski’s cylindric algebras, Halmos’ quasi-polyadic and quasi-polyadic equality algebras, respectively. Let . and . We show that the class of n dimensional neat reducts of algebras in K m is not elementary. This solves a problem in [2]. Also our result generalizes results proved in [1] and [2].

SC, CA, QA and QEA denote the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasi-polyadic algebras and quasi-polyadic equality algebras, respectively. Let ω ≤ α < β and let K ∈ {SC,CA,QA,QEA}. We show that the class of α -dimensional neat reducts of algebras in Kβ is not elementary. This solves a problem in [3]. Also our result generalizes results proved in [2] and [3].

SC, CA, QA and QEA denote the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasi-polyadic algebras and quasi-polyadic equality algebras, respectively. Let ω ≤ α < β and let K ∈ {SC,CA,QA,QEA}. We show that the class of α -dimensional neat reducts of algebras in Kβ is not elementary. This solves a problem in [3]. Also our result generalizes results proved in [2] and [3].

Das weit uber die Zeit seiner Abfassung und uber die Grenzen seines Entstehungslandes hinaus unter dem Namen "Qabusname" bekannte, literarisch wie kulturgeschichtlich bedeutsame Werk heisst wortlich "Buch der Ratschlage," persisch "nasihat-name." Sein Verfasser Kej Kawus wurde um 1021/22 n.Chr. geboren und genoss die fur die persischen Furstensohne seit Jahrhunderten vorgeschriebene Erziehung, bei der eine Synthese von ritterlichen und geistigen, vornehmlich religiosen Tugenden angestrebt wurde. Es handelt sich um eines der interessantesten und eigenartigsten Erzeugnisse der mittelalterlichen iranischen Literatur. Mit Recht werden (...) der intime Ton des Werks und die reizvolle Schlichtheit der hubschen Anekdoten sowie die auf Schmuck verzichtende Einfachheit der Erzahlkunst geruhmt. Die vorliegende Ubersetzung des "Qabusname" ist die erste in deutscher Sprache, die nach dem persischen Original vorgenommen wurde. Die einzige fruhere deutsche Ubersetzung des Orientalisten H. F. von Diez erfolgte aus dem Turkischen und wurde 1811 veroffentlicht. Schon Goethe beschaftigte sich bei seiner Begegnung mit dem klassischen Schrifttum der Perser unter der Fuhrung H. F. von Diez eindringlich mit dem Qabusname. Der Beziehung des Dichters zu diesem so bedeutsamen Stuck der persischen Literatur ist daher ein besonderes Kapitel gewidmet. (shrink)

Metaphysics; utopias; Fārābī; political and social views.

Free will and determinism; philosophy; history.

Philosophy, Arab; Arab countries; intellectual life; 20th century.