Theories that use expected utility maximization to evaluate acts have difficulty handling cases with infinitely many utility contributions. In this paper I present and motivate a way of modifying such theories to deal with these cases, employing what I call “Direct Difference Taking”. This proposal has a number of desirable features: it’s natural and well-motivated, it satisfies natural dominance intuitions, and it yields plausible prescriptions in a wide range of cases. I then compare my account to the most plausible alternative, (...) a proposal offered by Arntzenius :31–58, 2014). I argue that while Arntzenius’s proposal has many attractive features, it runs into a number of problems which Direct Difference Taking avoids. (shrink)

Some environmental ethicists and economists argue that attributing infinite value to the environment is a good way to represent an absolute obligation to protect it. Others argue against modelling the value of the environment in this way: the assignment of infinite value leads to immense technical and philosophical difficulties that undermine the environmentalist project. First, there is a problem of discrimination: saving a large region of habitat is better than saving a small region; yet if both outcomes have (...) infinite value, then decision theory prescribes indifference. Second, there is a problem of swamping probabilities: an act with a small but positive probability of saving an endangered species appears to be on par with an act that has a high probability of achieving this outcome, since both have infinite expected value. Our paper shows that a relative concept of infinite value can be meaningfully defined, and provides a good model for securing the priority of the natural environment while avoiding the failures noted by sceptics about infinite value. Our claim is not that the relative infinity utility model gets every detail correct, but rather that it provides a rigorous philosophical framework for thinking about decisions affecting the environment. (shrink)

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We (...) then bring our theory to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives. (shrink)

There are infinitely many ways the world might be, and there may well be infinitely many people in it. These facts raise moral paradoxes. We explore a conflict between two highly attractive principles: a Pareto principle that says that what is better for everyone is better overall, and a statewise dominance principle that says that what is sure to turn out better is better on balance. We refine and generalize this paradox, showing that the problem is faced by many theories (...) of interpersonal aggregation besides utilitarianism, and by many decision theories besides expected value theory. Considering the range of consistent responses, we find all of them to be quite radical. (shrink)

Among recent objections to Pascal's Wager, two are especially compelling. The first is that decision theory, and specifically the requirement of maximizing expected utility, is incompatible with infinite utility values. The second is that even if infinite utility values are admitted, the argument of the Wager is invalid provided that we allow mixed strategies. Furthermore, Hájek has shown that reformulations of Pascal's Wager that address these criticisms inevitably lead to arguments that are philosophically unsatisfying and historically unfaithful. (...) Both the objections and Hájek's philosophical worries disappear, however, if we represent our preferences using relative utilities rather than a one-place utility function. Relative utilities provide a conservative way to make sense of infinite value that preserves the familiar equation of rationality with the maximization of expected utility. They also provide a means of investigating a broader class of problems related to the Wager. (shrink)

Many think that Pascal’s Wager is a hopeless failure. A primary reason for this is because a number of challenging objections have been raised to the wager, including the “many gods” objection and the “mixed strategy” objection. We argue that both objections are formal, but not substantive, problems for the wager, and that they both fail for the same reason. We then respond to additional objections to the wager. We show how a version of Pascalian reasoning succeeds, giving us (...) a reason to pay special attention to the infinite consequences of our actions. (shrink)

The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined even if it is not sufficiently formal and precise to belong to mathematics proper (in a narrow sense)—and even if (as many have asserted) for that reason the Church–Turing thesis is unprovable. It is proved logically that the class of effective procedures is not decidable, i.e., that no effective procedure is possible for ascertaining whether a given procedure is effective. This (...) undecidability result is proved directly from the notion itself of an effective procedure, without reliance on any (partly) mathematical lemma, conjecture, or thesis invoking recursiveness or Turing-computability. In fact, there is no reliance on anything very mathematical. The proof does not even appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of an effective procedure. Though the result that effectiveness is undecidable is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure invariably terminates with the correct verdict. (shrink)

It is now the majority view amongst philosophers and theologians that any world could have been better. This places the choice of which world to create into an especially challenging class of decision problems: those that are discontinuous in the limit. I argue that combining some weak, plausible norms governing this type of problem with a creator who has the attributes of the god of classical theism results in a paradox: no world is possible. After exploring some ways (...) out of the paradox, I conclude that the classical theist should accept Marilyn Adams’s view that no norms apply to gods. (shrink)

I argue that medieval solutions to the limit decision problem imply four-dimensionalism, i.e. the view according to which substances that persist through time are extended through time as well as through space, and have different temporal parts at different times.

Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in Göttingen in 1921 with a thesis on the decision problem. In his thesis, he solved - independently of Löwenheim and Skolem's earlier work - the decision problem for monadic second-order logic in a framework that combined elements of the algebra of logic and the newer axiomatic approach to logic then being developed in Göttingen. In a talk given in 1921, he outlined this solution, but also presented important programmatic (...) remarks on the significance of the decision problem and of decision procedures more generally. The text of this talk as well as a partial English translation are included. (shrink)

The menu-dependent nature of regret-minimization creates subtleties when it is applied to dynamic decision problems. It is not clear whether forgone opportunities should be included in the menu. We explain commonly observed behavioral patterns as minimizing regret when forgone opportunities are present. If forgone opportunities are included, we can characterize when a form of dynamic consistency is guaranteed.

Responsibility is impossible because there is no responsibility-maker and there needs to be one if people are morally responsible. The two most plausible candidates, psychology and decision, fail. A person is not responsible for an unchosen psychology or a psychology that was chosen when the person is not responsible for the choice. This can be seen in intuitions about instantly-created and manipulated people. This result is further supported by the notion that, in general, the right, the good, and virtue (...) rest on the exercise of a capacity rather than the capacity itself. It is also supported by the notion that negligence is not a responsibility-maker. ​ A person is not responsible for a choice that does not reflect his psychology or that does reflect it when he is not responsible for the psychology. This can be seen by considering intuitions regarding acts that are unconnected or arbitrarily connected to a person’s psychology. It can also be seen intuitions about acts that result from a manipulated psychology. The problem with choice as a foundation can be further seen in that an infinite or self-created person would not be responsible despite these superhuman choice-related features. (shrink)

2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and (...) they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics. (shrink)

How should you decide what to do when you’re uncertain about basic normative principles? A natural suggestion is to follow some "second-order:" norm: e.g., obey the most probable norm or maximize expected choiceworthiness. But what if you’re uncertain about second-order norms too—must you then invoke some third-order norm? If so, any norm-guided response to normative uncertainty appears doomed to a vicious regress. This paper aims to rescue second-order norms from the threat of regress. I first elaborate and defend the claim (...) some philosophers have made that the regress problem forces us to accept normative externalism, the view that at least one norm is incumbent on all agents regardless of their normative beliefs. But, I then argue, we need not accept externalism about first-order norms, thus closing off any question of how agents should respond to normative uncertainty. Rather, we can head off the threat of regress by ascribing external force to a single second-order norm: the enkratic principle. (shrink)

This thesis is about making decisions when we are uncertain about what will happen, how valuable it will be, and even how to make decisions. Even the most sure-footed amongst us are sometimes uncertain about all three, but surprisingly little attention has been given to the latter two. The three essays that constitute my thesis hope to do a small part in rectifying this problem. The first essay is about the value of finding out how to make decisions. Society spends (...) considerable resources funding people (like me) to research decision-making, so it is natural to wonder whether society is getting a good deal. This question is so shockingly underresearched that bedrock facts are readily discoverable, such as when this kind of information is valuable. My second essay concerns whether we can compare value when we are uncertain about value. Many people are in fact uncertain about value, and how we deal with this uncertainty hinges on these comparisons. I argue that value comparisons are only sometimes possible; I call this weak comparability. This essay is largely a synthesis of the literature, but I also present an argument which begins with a peculiar view of the self: it is as if each of us is a crowd of different people separated by time (but connected by continuity of experience). I’m not the first to endorse this peculiar view of the self, but I am the first to show how it supports the benign view that value is sometimes comparable. We may be uncertain of any decision rules, even those that would tell us how to act when we face uncertainty in decision rules. We may be uncertain of how to decide how to decide how to... And so on. If so, we might have to accept infinitely many decision rules just to make any mundane decision, such as whether to pick up a five-cent piece from the gutter. My third essay addresses this problem of regress. I think all of our decisions are forced: we must decide now or continue to deliberate. Surprisingly, this allows us to avoid the original problem. I call this solution “when forced, do your best”. (shrink)

The problem of infinite regress presents a profound challenge in epistemology and philosophy, questioning the possibility of achieving foundational knowledge amidst an endless chain of justifications. This paper introduces a set of four axioms designed to directly address and resolve the problem of infinite regress, ensuring theoretical rigor and applicability across diverse scenarios, including simulated or illusory realities. By focusing on Direct Address, Intellectual Rigor in All Realities, Avoiding Pragmatic Dismissals, and Theoretical Consistency, these axioms provide a structured (...) framework for evaluating philosophical theories aimed at overcoming this complex issue. The paper explores current theories that align with these axioms, evaluates popular theories that do not, and argues for the critical role of these axioms in guiding future philosophical inquiry and resolution of infinite regress. (shrink)

Major Research Paper Abstract -/- A Part of This World: Deleuze & The Logic Of Creation. -/- Is there a particular danger in following Deleuze’s philosophy to its end result? According to Peter Hallward and Alain Badiou, Deleuze’s philosophy has some rather severe conclusions. Deleuze has been known as a vitalist thinker of life and affirmation. Hallward & Badiou seek to challenge the accepted view of Deleuze; showing that these accepted norms in Deleuzian scholarship should be challenged; and that initially (...) Deleuze calls for the evacuation of political action in order to remain firm in the realm of pure contemplation. I intend to investigate and defend Deleuze’s philosophy and against critics like Badiou and Hallward; and that not only is Deleuze’s philosophy creative and vital but also highly revolutionary and ‘a part of this world.’ I will look at several works in Deleuze’s corpus, as well as look at Deleuzian scholars whom defend Deleuze’s position -/- Hallward sees Deleuze as a theophantic thinker of the one and like Spinoza an individual mode must align oneself with the intellectual love of god, so that creativity and expressivity may mediate through them. Thus, according to Hallward the major theme of Deleuze’s philosophy is creativity; and a subject or a creature must tap into this vital spark of creation, which, is also a form of creatural confinement. Hallward states this creative act can only occur in the realm of the virtual, by lines of flight leading 'out of this world'. The subject is then re-introduced to an extra-worldly existence of contemplation and remains further away from decisions and lived experience. Deleuze, according to Hallward, falls prey to a cosmological pantheism. -/- Badiou has similar concerns. Deleuze’s philosophy is too systematic and abstract. The entirety of Deleuzes’ work is surrounded by metaphysics of the one; and essentially its repercussions lead to an overt asceticism. Badiou notes that Deleuze wants us all to surrender thought to a renewed concept of the one. Through the surrender of the one, the multiple is lost and incorporated into the realm of simulacra. Everything in this Deleuzian world is ‘always-already’ in the infinite and inhuman totality of the one. According to Badiou, this entire process is articulated in the power of inorganic life that operates through all of us. Like Hallward, Badiou sees Deleuze demolishing the subject, who is stuck between machinery and exteriority. Subjects are forced to transcend and go beyond their limits, slowly collapsing into an infinite virtuality. Badiou believes this is a powerful metaphor for a philosophy of death. Thus the conditions of Deleuzian thought are contingent upon asceticism, making a Deleuzian world a sort of ‘crowned anarchy’. Badiou sees Deleuze’s ascetic mission intimately linked with a philosophy of death, and like Hallward we should pay careful attention to the outcome of such an aristocratic philosophy. Death according to Badiou, symbolizes Deleuzian thought, not only making it dangerous, but also actualizing it as an ineffective position. Badiou also points out that Deleuze’s conceptual sources are not only limited but also repeated time and time again through a monotonous selection of concepts. Is this a fair critique and representation of Deleuzian thought? -/- Eugene Holland states, that both Hallward and Badiou have misrepresented Deleuze. Deleuze does invoke the creation of a new earth but one which we all fully believe in. The only world Deleuze wants to get out of is the world of habits, conformity, power; and forces that block creative being. According to Holland, Hallward presents us a Deleuze that inhibits an engagement with the world. However Deleuze’s creative enterprise is insistent on forming concepts that can change and transform our world. -/- So the question arises where does the problem of misrepresentation begin? It begins with both Badiou and Hallward having an erroneous account of the actual/virtual distinction in Deleuze’s Philosophy. According to Protevi, Hallward posits a dualism between the actual and the virtual, denying the role of the intensive. Hallward initially sees the relationship between the intensive and the virtual, ignoring the fact that the intensive has its own ontological register that mediates both the virtual and the actual. However, Protevi notes if one could not accept the intensive for an ontological register and had to place it with one or the other; you would have to accept an interrelationship between the actual and the intensive. Hallward places it in the realm of the virtual, thus, leading us to his major claim that Deleuze’s philosophy leads us out of the world. Protevi states, intensive processes happen in our world they are a part of this world. Hallward completely empties all creativity from the actual, thus depending on the virtual and its slippery slope. Both Hallward and Badiou have missed the point altogether. We live in an intensive/actual world and the main point about Deleuze’s politics has to do with experimentation and social interaction and the transformation and intervention of the concept. As Daniel W. Smith states, unlike Badiou, Deleuze is not searching for an axiomatic approach to the world, one that is prone to reductionism but rather with problematic, inventive and creative methods to transform a society. (shrink)

Ecological economics is an interdisciplinary science that is primarily concerned with developing interventions to achieve sustainable ecological and economic systems. While ecological economists have, over the last few decades, made various empirical, theoretical, and conceptual advancements, there is one concept in particular that remains subject to confusion: critical natural capital. While critical natural capital denotes parts of the environment that are essential for the continued existence of our species, the meaning of terms commonly associated with this concept, such as ‘non-substitutable’ (...) and ‘impossible to substitute,’ require a clearer formulation then they tend to receive. With the help of equations and graphs, this article develops new definite account of critical natural capital that makes explicit what it means for objective environmental conditions to be essential for continued existence. The second main part of this article turns to the question of formally modeling the priority of conserving critical natural capital. While some ecological economists have maintained that, beyond a certain threshold, critical natural capital possesses absolute infinite value, absolute infinite utility models encounter significant problems. This article shows that a relative infinite utility model provides a better way to model the priority of conserving critical natural capital. (shrink)

We develop a simple framework called ‘natural topology’, which can serve as a theoretical and applicable basis for dealing with real-world phenomena.Natural topology is tailored to make pointwise and pointfree notions go together naturally. As a constructive theory in BISH, it gives a classical mathematician a faithful idea of important concepts and results in intuitionism. -/- Natural topology is well-suited for practical and computational purposes. We give several examples relevant for applied mathematics, such as the decision-support system Hawk-Eye, and (...) various real-number representations. -/- We compare classical mathematics (CLASS), intuitionistic mathematics (INT), recursive mathematics (RUSS), Bishop-style mathematics (BISH) and formal topology, aiming to reduce the mutual differences to their essence. To do so, our mathematical foundation must be precise and simple. There are links with physics, regarding the topological character of our physical universe. -/- Any natural space is isomorphic to a quotient space of Baire space, which therefore is universal. We develop an elegant and concise ‘genetic induction’ scheme, and prove its equivalence on natural spaces to a formal-topological induction style. The inductive Heine-Borel property holds for ‘compact’ or ‘fanlike’ natural subspaces, including the real interval [g, h]. Inductive morphisms respect this Heine-Borel property, inversely. This partly solves the continuous-function problem for BISH, yet pointwise problems persist in the absence of Brouwer’s Thesis. -/- By inductivizing the definitions, a direct correspondence with INT is obtained which allows for a translation of many intuitionistic results into BISH. We thus prove a constructive star-finitary metrization theorem which parallels the classical metrization theorem for strongly paracompact spaces. We also obtain non-metrizable Silva spaces, in infinite-dimensional topology. Natural topology gives a solid basis, we think, for further constructive study of topological lattice theory, algebraic topology and infinite-dimensional topology. The final section reconsiders the question of which mathematics to choose for physics. Compactness issues also play a role here, since the question ‘can Nature produce a non-recursive sequence?’ finds a negative answer in CTphys . CTphys , if true, would seem at first glance to point to RUSS as the mathematics of choice for physics. To discuss this issue, we wax more philosophical. We also present a simple model of INT in RUSS, in the two-players game LIfE. (shrink)

We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T.A. Knight and C. Darwin, and sketch a decomposition (...) result involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels’ question, “Can biology lead to new theorems?”. (shrink)

Relative to any reasonable frame, satisfiability of modal quantificational formulae in which “= ” is the sole predicate is undecidable; but if we restrict attention to satisfiability in structures with the expanding domain property, satisfiability relative to the familiar frames (K, K4, T, S4, B, S5) is decidable. Furthermore, relative to any reasonable frame, satisfiability for modal quantificational formulae with a single monadic predicate is undecidable ; this improves the result of Kripke concerning formulae with two monadic predicates.

I explain the shutdown problem: the problem of designing artificial agents that (1) shut down when a shutdown button is pressed, (2) don’t try to prevent or cause the pressing of the shutdown button, and (3) otherwise pursue goals competently. I prove three theorems that make the difficulty precise. These theorems show that agents satisfying some innocuous-seeming conditions will often try to prevent or cause the pressing of the shutdown button, even in cases where it’s costly to do so. And (...) patience trades off against shutdownability: the more patient an agent, the greater the costs that agent is willing to incur to manipulate the shutdown button. I end by noting that these theorems can guide our search for solutions. (shrink)

People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call (...) *Countable Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have. (shrink)

One of the most frequently asked question is whether Hegel’s idea of God is immanent or transcendent. In Transcending Subjects: Augustine, Hegel, and Theology, Geoffrey Holsclaw attempts to solve this puzzle by contrasting the political theologies of Hegel and Augustine. He argues that Hegel produces a political theology of ‘self-transcending immanence’ while Augustine produces a political theology of ‘self-immanentizing transcendence’. The primary problem with Holsclaw’s dialectical procedure results from its uncritical appeal to a transcendent source for the supersession of opposites. (...) Rather than critically annulling each opposed position, he often resorts to simply describing the inadequacy of positions in light of the privileged ideal of Augustinian transcendence. Holsclaw’s dialectic has not been directly derived from Augustine but from the more recent writings of William Desmond. He translates Desmond’s opposition between the second and third types of transcendence into his own opposition between Hegelian self-transcending immanence and Augustinian self-immanentizing transcendence. Hegel’s apparent ambiguity on transcendence seems to expose him to Holsclaw’s critique. Yet Hegel may, arguably, have never needed to answer this objection because the opposition between immanence and transcendence has already been resolved by Hegel’s dialectic of infinity: for if the opposition between the categories of immanence and transcendence that appears at the level of Spirit merely replicates the vanishing opposition between the finite and the infinite at the level of Logic, then the supersession of this negative opposition between the infinite and the finite into the true and speculative infinity can be virtually replicated for religious consciousness in the supersession of transcendence and immanence into an equally speculative transcendence. Where Holsclaw seeks to supersede immanence into transcendence, Hegel seeks to preserve both transcendence and immanence in the true ‘speculative transcendence’ that corresponds to the true ‘speculative infinity’. The decisive disagreement between Hegel and Holsclaw thus concerns, not merely any relation between transcendence and immanence, but – more fundamentally – the very possibility of superseding the spurious transcendence into a genuinely speculative notion of infinity and transcendence. (shrink)

The dominant approach to assessing decision-making capacity in medicine focuses on determining the extent to which individuals possess certain core cognitive abilities. Critics have argued that this model delivers the wrong verdict in certain cases where patient values that are the product of mental disorder or disordered affective states undermine decision-making without undermining cognition. I argue for a re-conceptualization of what it is to possess the capacity to make medical treatment decisions. It is, I argue, the ability to (...) track one’s own personal interests at least as well as most people can. Using this idea, I demonstrate that it is possible to craft a solution for the problem cases—one that neither alters existing criteria in dangerous ways (e.g. does not open the door to various kinds of abuse) nor violates the spirit of widely accepted ethical constraints on decision-making assessment. (shrink)

I argue that the Universal Law formulation of the Categorical Imperative is best interpreted as a test or decision procedure of moral rightness and not as a criterion intended to explain the deontic status of actions. Rather, the Humanity formulation is best interpreted as a moral criterion. I also argue that because the role of a moral criterion is to explain, and thus specify what makes an action right or wrong, Kant's Humanity formulation yields a theory of relevant descriptions.

Aristotle (384-322 B.C), a well know Greek philosopher, physician, scientist and politician. A variety of identifying researches have been written on him. It is therefore a considerable pride for the researcher to write something about him when even mentioning his name and his father's name is a point of prestige in the Greek Language. His name means the preferable sublimity whereas Nicomachus (his father's name) means the definable negotiator. His father's and mother's origin belongs to Asclepiade, the favorite origin in (...) Greek. Points of view regarding this figure are controversial some praise him and consider him the peak of philosophical thinker which makes humanity in general owe this genius thinker a great deal. Others believe that the effect of his thought on humanity is the reason behind the non-progress of science. Whatever ones opinion is, his thoughts have a wonderful force in stimulating and positively affecting the people's thinking. His philosophy is the greatest philosophy which the world has ever witnessed or which may ever witness., if it couldn’t solve some of the problems of philosophy, it at least, makes the world more rational than before. He is the founder of the philosophical language in describing a large number of philosophical terms which are still in use nowadays. Moreover his books and platonic dialogues are considered encyclopedias in providing a basis for philosophy even before Socrates. For theses among other reasons, I am choosing Aristotle as a subject for research and concentrating on natural philosophy. The critical side deals with the criticism of natural philosophers. In order to fully understand Aristotle, we should understand his predecessors. Their virtue is undeniable. Without them, Aristotle's and Plato's genius would never be in this ideal shape. In addition to that, they are philosophers and scientists who mixes between science, philosophy, morality and politics in a complementary form. They are a source of illumination to the human thinking in general. Without them humanity could never have got rid of mythology. This is the code of life, for many generations should pass before the rare genius could attain a prominent idea. When Tales formulates the philosophical question, where does the world come from? This is a decisive moment in human thinking similar to the coming moments, the one Parmenides, and Protagoras statement: man is the norm for all things. Pre-Socrates philosophers are all considered glowing points in drawing Aristotle's philosophy. Thus my book is entitles (Aristotle's criticism of Pre-Socratic Natural Philosophy) which means the concentration on the critical operation through which the natural side of the previous philosophers appears. The nature of the title forces me to deal with Aristotle's ideas from every point of view. Thus the book proceeds according to structure and criticism and the construction of Aristotle's philosophy. Because the title is comprehensive and limited simultaneously, I have chosen the critical subjects in the lights of the natural philosophy. I have divided the book into four chapters with fourteen sections in addition to the implemented parts included in every section purporting to cover every part of criticism looking for comprehensiveness. I have found it obligatory to mention something about Aristotle's view in criticism, in addition to a precise delimitation of nature and its subjects. This is the subject of the first chapter. The second chapter deals with the principles of natural body, i.e., the principles dealt with pre-Aristotle philosophy and then these three principles (Hyle, form ,and Non-being). After delaminating these sides, it is possible to deal with the details (Movement, Place, Time, Vacuum and Infinite) which are natural concepts for the third chapter. As a complementation to the natural sides, the chapter four deals with two topics , Universal and corruption, and theory of elements. This book, in my own opinion, is comprehensive to the majority of natural philosophers and it focuses on the argument of Aristotle's criticism to the views of natural philosophers before Socrates together with the discussion of the Aristotelian alternative from these points of view. Aristotle sometimes tends to praise the previous philosophers. This does not mean the non-conformity between what he wants to say and what they described. When he, for example, says that the previous philosophers realized the material defect in Thales idea that water is the origin of all things but Thales’ water is not like Aristotle's Hyle, it is completely different thing. Finally I have viewed the index of Arab Library, and was unable to trace a book which is especially oriented in this subject i.e. writings on Aristotle's criticism to natural philosophy before Socrates. Therefore I have been stimulated to write about a very new subject. This subject fills a gap in Arab studies. (shrink)

The halting theorem counter-examples present infinitely nested simulation (non-halting) behavior to every simulating halt decider. Whenever the pure simulation of the input to simulating halt decider H(x,y) never stops running unless H aborts its simulation H correctly aborts this simulation and returns 0 for not halting.

Evidential Decision Theory is flawed, but its flaws are not fully understood. David Lewis (1981) famously charged that EDT recommends an irrational policy of managing the news and “commends the ostrich as rational”. Lewis was right, but the case he appealed to—Newcomb’s Problem—does not demonstrate his conclusion. Indeed, decision theories other than EDT, such as Committal Decision Theory and Functional Decision Theory, agree with EDT's verdicts in Newcomb’s Problem, but their flaws, whatever they may be, do (...) not stem from any ostrich-like recommendations. We offer a new case which shows that EDT mismanages the news, thus vindicating Lewis’s original charge. We argue that this case reveals a flaw in the “Why ain’cha rich?” defense of EDT. We argue further that this case is an advance on extant putative counterexamples to EDT. (shrink)

Because of its non-representational nature, music has always had familiarity with computational and algorithmic methodologies for automatic composition and performance. Today, AI and computer technology are transforming systems of automatic music production from passive means within musical creative processes into ever more autonomous active collaborators of human musicians. This raises a large number of interrelated questions both about the theoretical problems of artificial musical creativity and about its ethical consequences. Considering two of the most urgent ethical problems of (...) Musical AI (music job replacement and machine musical authorship), we show in this essay the strict dependence of every form of acknowledgment of a moral and legal status to systems of automatic music production from the theoretical account of musical creativity by turns implicitly or explicitly adopted, arguing, on the basis of pragmatic reasons, for the necessity and the desirability of this acknowledgment. (shrink)

Jackson (1991) proposes an interpretation of consequentialism, namely, the Decision Theoretic Consequentialism (DTC), which provides a middle ground between internal and external criteria of rightness inspired by decision theory. According to DTC, a right decision either leads to the best outcomes (external element) or springs from right motivations (internal element). He raises an objection to fully external interpretations, like objective consequentialism (OC), which he claims that DTC can resolve. He argues that those interpretations are either too objective, (...) which prevents them from giving guidance for action, or their guidance leads to wrong and blameworthy actions or decisions. I discuss how the emphasis on blameworthiness in DTC constraints its domain to merely the justification of decisions that relies on rationality to provide a justification criterion for moral decisions. I provide examples that support the possibility of rational but immoral decisions that are at odds with DTC’s prescription for right decisions. Moreover, I argue what I call the desire-luck problem for the external element of justification criterion leads to the same objection for DTC that Jackson raised for OC. Therefore, DTC, although successful in response to some objections, fails to provide a prescription for the right decision. (shrink)

Andy Egan recently drew attention to a class of decision situations that provide a certain kind of informational feedback, which he claims constitute a counterexample to causal decision theory. Arntzenius and Wallace have sought to vindicate a form of CDT by describing a dynamic process of deliberation that culminates in a “mixed” decision. I show that, for many of the cases in question, this proposal depends on an incorrect way of calculating expected utilities, and argue that it (...) is therefore unsuccessful. I then tentatively defend an alternative proposal by Joyce, which produces a similar process of dynamic deliberation but for a different reason. (shrink)

A common argument for atheism runs as follows: God would not create a world worse than other worlds he could have created instead. However, if God exists, he could have created a better world than this one. Therefore, God does not exist. In this paper I challenge the second premise of this argument. I argue that if God exists, our world will continue without end, with God continuing to create value-bearers, and sustaining and perfecting the value-bearers he has already created. (...) Given this, if God exists, our world—considered on the whole—is infinitely valuable. I further contend that this theistic picture makes our world's value unsurpassable. In support of this contention, I consider proposals for how infinitely valuable worlds might be improved upon, focusing on two main ways—adding value-bearers and increasing the value in present value-bearers. I argue that neither of these can improve our world. Depending on how each method is understood, either it would not improve our world, or our world is unsurpassable with respect to it. I conclude by considering the implications of my argument for the problem of evil more generally conceived. (shrink)

For aggregative theories of moral value, it is a challenge to rank worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds—without a cardinal value for each world, we cannot apply expected value theory. How then can we compare such lotteries? To date, we have just one method for doing so (proposed (...) separately by Arntzenius, Bostrom, and Meacham), which is to compare the prospects for value at each individual location, and to then represent and compare lotteries by their expected values at each of those locations. But, as I show here, this approach violates several key principles of decision theory and generates some implausible verdicts. I propose an alternative—one which delivers plausible rankings of lotteries, which is implied by a plausible collection of axioms, and which can be applied alongside almost any ranking of infinite worlds. (shrink)

The paper argues that on three out of eight possible hypotheses about the EPR experiment we can construct novel and realistic decision problems on which (a) Causal Decision Theory and Evidential Decision Theory conflict (b) Causal Decision Theory and the EPR statistics conflict. We infer that anyone who fully accepts any of these three hypotheses has strong reasons to reject Causal Decision Theory. Finally, we extend the original construction to show that anyone who gives (...) any of the three hypotheses any non-zero credence has strong reasons to reject Causal Decision Theory. However, we concede that no version of the Many Worlds Interpretation (Vaidman, in Zalta, E.N. (ed.), Stanford Encyclopaedia of Philosophy 2014) gives rise to the conflicts that we point out. (shrink)

According to Leibniz’s infinite-analysis account of contingency, any derivative truth is contingent if and only if it does not admit of a finite proof. Following a tradition that goes back at least as far as Bertrand Russell, several interpreters have been tempted to explain this biconditional in terms of two other principles: first, that a derivative truth is contingent if and only if it contains infinitely complex concepts and, second, that a derivative truth contains infinitely complex concepts if and (...) only if it does not admit of a finite proof. A consequence of this interpretation is that Leibniz’s infinite-analysis account of contingency falls prey to Robert Adams’s Problem of Lucky Proof. I will argue that this interpretation is mistaken and that, once it is properly understood how the idea of an infinite proof fits into Leibniz’s circle of modal notions, the problem of lucky proof simply disappears. (shrink)

The question of the rationality of conspiratorial belief ¬divides philosophers into mainly two camps. The particularists believe that each conspiracy theory ought to be examined on its own merits. The generalist, by contrast, argues that there is something inherently suspect about conspiracy theories that makes belief in them irrational. Recent empirical findings indicate that conspiratorial thinking is commonplace among ordinary people, which has naturally shifted attention to the particularists. Yet, even the particularist must agree that not all conspiracy belief is (...) rational, in which case she must explain what separates rational from non-rational conspiratorial thinking. In this paper, I contrast three strategies to this end: 1) the probabilistic objectivist, who assesses the objective probability of conspiracies; 2) the subjectivist, who rather focuses on the perspective of the believer, and typically views the decision to believe in a conspiracy as a problem of decision making under risk. Approaches 1) and 2) rely on assessments of the probability of conspiracy which, I argue, limits their applicability. Instead, I explore 3) viewing the problem facing the potential believer as a decision problem under uncertainty about probabilities. I argue, furthermore, that focusing solely on epistemic utilities fails to do justice to the particular character of conspiracy beliefs, which are not exclusively epistemically motivated, and I investigate the rationality of such beliefs under a number of standard decision rules. (shrink)

The dispute in philosophical decision theory between causalists and evidentialists remains unsettled. Many are attracted to the causal view’s endorsement of a species of dominance reasoning, and to the intuitive verdicts it gets on a range of cases with the structure of the infamous Newcomb’s Problem. But it also faces a rising wave of purported counterexamples and theoretical challenges. In this paper I will describe a novel decision theory which saves what is appealing about the causal view while (...) avoiding its most worrying objections, and which promises to generalize to solve a set of related problems in other normative domains. (shrink)

Decision-making capacity (DMC) plays an important role in clinical practice—determining, on the basis of a patient’s decisional abilities, whether they are entitled to make their own medical decisions or whether a surrogate must be secured to participate in decisions on their behalf. As a result, it’s critical that we get things right—that our conceptual framework be well-suited to the task of helping practitioners systematically sort through the relevant ethical considerations in a way that reliably and transparently delivers correct verdicts (...) about who should and should not have the authority to make their own medical decisions. Unfortunately, however, the standard approach to DMC does not get things right. It is of virtually no help in identifying and clarifying the relevant ethical considerations. And, embedded in the prevailing anti-paternalist paradigm, DMC assessments obfuscate and distort the underlying ethical justification for granting or withholding decisional authority. Here, we describe the core commitments of the standard approach to DMC and then highlight three problems with it. We then argue that these problems are significant enough that they call for more than merely tinkering and fine tuning—variations of the standard approach cannot adequately address them. Instead, we should ditch DMC. (shrink)

Draft for presentation at the 14th International Kant-Congress, September 2024. -/- Abstract: Kant claims we intuit infinite space. There’s a problem: Kant thinks full awareness of infinite space requires synthesis—the act of putting representations together and comprehending them as one. But our ability to synthesize is finite. Tobias Rosefeldt has argued in a recent paper that Kant’s notion of decomposing synthesis offers a solution. This talk criticizes Rosefeldt’s approach. First, Rosefeldt is committed to nonconceptual yet determinate awareness of (...) (potentially) infinite space, but I argue that such awareness is (1) prima facie implausible, as well as contravened by textual evidence from Kant’s (2a) definitions of ‘infinity’ and (2b) account of geometrical construction. Second, scrutiny of how Kant thinks awareness of potential infinity is afforded by geometrical construction (e.g., extending a line segment ad indefinitum) indicates no essential role for decomposing synthesis. Familiar synthesis from parts to wholes is sufficient. (shrink)

Interval bipolar neutrosophic set is a significant extension of interval neutrosophic set where every element of the set comprises of three independent positive membership functions and three independent negative membership functions. In this study, we first define correlation coefficient, and weighted correlation coefficient measures of interval bipolar neutrosophic sets and prove their basic properties. Then, we develop a new multi-attribute decision making strategy based on the proposed weighted correlation coefficient measure. Finally, we solve an investment problem with interval bipolar (...) neutrosophic information and comparison is given to demonstrate the applicability and effectiveness of the proposed strategy. (shrink)

Context: The infinite has long been an area of philosophical and mathematical investigation. There are many puzzles and paradoxes that involve the infinite. Problem: The goal of this paper is to answer the question: Which objects are the infinite numbers (when order is taken into account)? Though not currently considered a problem, I believe that it is of primary importance to identify properly the infinite numbers. Method: The main method that I employ is conceptual analysis. In (...) particular, I argue that the infinite numbers should be as much like the finite numbers as possible. Results: Using finite numbers as our guide to the infinite numbers, it follows that infinite numbers are of the structure w + (w* + w) a + w*. This same structure also arises when a large finite number is under investigation. Implications: A first implication of the paper is that infinite numbers may be large finite numbers that have not been investigated fully. A second implication is that there is no number of finite numbers. Third, a number of paradoxes of the infinite are resolved. One change that should occur as a result of these findings is that “infinitely many” should refer to structures of the form w + (w* + w) a + w*; in contrast, there are “indefinitely many” natural numbers. Constructivist content: The constructivist perspective of the paper is a form of strict finitism. (shrink)

The problem of the man who met death in Damascus appeared in the infancy of the theory of rational choice known as causal decision theory. A straightforward, unadorned version of causal decision theory is presented here and applied, along with Brian Skyrms’ deliberation dynamics, to Death in Damascus and similar problems. Decision instability is a fascinating topic, but not a source of difficulty for causal decision theory. Andy Egan’s purported counterexample to causal decision theory, (...) Murder Lesion, is considered; a simple response shows how Murder Lesion and similar examples fail to be counterexamples, and clarifies the use of the unadorned theory in problems of decision instability. I compare unadorned causal decision theory to previous treatments by Frank Arntzenius and by Jim Joyce, and recommend a well-founded heuristic that all three accounts can endorse. Whatever course deliberation takes, causal decision theory is consistently a good guide to rational action. (shrink)

Big decisions in a person’s life often affect the preferences and standards of a good life which that person’s future self will develop after implementing her decision. This paper argues that in such cases the person might lack any reasons to choose one way rather than the other. Neither preference-based views nor happiness-based views of justified choice offer sufficient help here. The available options are not comparable in the relevant sense and there is no rational choice to make. Thus, (...) ironically, in many of a person’s most important decisions the idea of that person’s good seems to have no application. (shrink)

This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.

A comment on Paul Schoemaker's target article in Behavioral and Brain Sciences, 14 (1991), p. 205-215, "The Quest for Optimality: A Positive Heuristic of Science?" (https://doi.org/10.1017/S0140525X00066140). This comment argues that the optimizing model of decision leads to an infinite regress, once internal costs of decision (i.e., information and computation costs) are duly taken into account.

This book examines the philosophy of the nineteenth-century Indian mystic Sri Ramakrishna and brings him into dialogue with Western philosophers of religion, primarily in the recent analytic tradition. Sri Ramakrishna’s expansive conception of God as the impersonal-personal Infinite Reality, Maharaj argues, opens up an entirely new paradigm for addressing central topics in the philosophy of religion, including divine infinitude, religious diversity, the nature and epistemology of mystical experience, and the problem of evil.

This paper uses a schema for infinite regress arguments to provide a solution to the problem of the infinite regress of justification. The solution turns on the falsity of two claims: that a belief is justified only if some belief is a reason for it, and that the reason relation is transitive.

The classic formulation of causal decision theory (CDT) appeals to counterfactuals. It says that you should aim to choose an option that would have a good outcome, were you to choose it. However, this version of CDT faces trouble if the laws of nature are deterministic. After all, the standard theory of counterfactuals says that, if the laws are deterministic, then if anything—including the choice you make—were different in the present, either the laws would be violated or the distant (...) past would be changed. And as several authors have shown, it's easy to transform this upshot of the standard theory of counterfactuals into full-blown counterexamples to CDT. In response to these counterexamples, I argue here that the problem lies, not so much with CDT's guiding idea—that it's the expected causal consequences of your actions that matter for rational decision-making—but with the fact that the classic formulation of CDT doesn't pay sufficient attention to the context-sensitivity of counterfactuals. I develop a contextualist version of CDT which better accounts for this context-sensitivity. And I show that my theory avoids the problems faced by the classic formulation of CDT in determinstic worlds. (shrink)