We give a new and elementary construction of primitive positive decomposition of higher arity relations into binary relations on finite domains. Such decompositions come up in applications to constraint satisfaction problems, clone theory and relational databases. The construction exploits functional completeness of 2-input functions in many-valued logic by interpreting relations as graphs of partially defined multivalued ‘functions’. The ‘functions’ are then composed from ordinary functions in the usual sense. The construction is computationally effective and relies on well-developed methods (...) of functional decomposition, but reduces relations only to ternary relations. An additional construction then decomposes ternary into binary relations, also effectively, by converting certain disjunctions into existential quantifications. The result gives a uniform proof of Peirce’s reduction thesis on finite domains, and shows that the graph of any Sheffer function composes all relations there. (shrink)

We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of predicate calculus. Our algebraic framework unifies natural joins and data dependencies of database theory and relational algebra of clone theory with the bond algebra of C.S. Peirce. We also offer new constructions of reductions, systematically study irreducible relations and reductions to them and introduce a new (...) characteristic of relations, ternarity, that measures their ‘complexity of relating’ and allows to refine reduction results. In particular, we refine Peirce’s controversial reduction thesis, and show that reducibility behaviour is dramatically different on finite and infinite domains. (shrink)

According to the objection from positive duties, Kant's Formula of Universal Law is flawed because it cannot be used to derive any affirmative moral requirements. This paper offers a response to that objection and proposes a novel way to derive positive duties from Kant's formula. The Formula of Universal Law yields positive duties to adopt our own perfection and others’ happiness as ends because we could not rationally fail to will those ends as universal (...) ends. (shrink)

It is well known that the following features hold of AR + T under the strong Kleene scheme, regardless of the way the language is Gödel numbered: 1. There exist sentences that are neither paradoxical nor grounded. 2. There are 2ℵ0 fixed points. 3. In the minimal fixed point the weakly definable sets (i.e., sets definable as {n∣ A(n) is true in the minimal fixed point where A(x) is a formula of AR + T) are precisely the Π1 1 (...) sets. 4. In the minimal fixed point the totally defined sets (sets weakly defined by formulae all of whose instances are true or false) are precisely the ▵1 1 sets. 5. The closure ordinal for Kripke's construction of the minimal fixed point is ωCK 1. In contrast, we show that under the weak Kleene scheme, depending on the way the Gödel numbering is chosen: 1. There may or may not exist nonparadoxical, ungrounded sentences. 2. The number of fixed points may be any positive finite number, ℵ0, or 2ℵ0 . 3. In the minimal fixed point, the sets that are weakly definable may range from a subclass of the sets 1-1 reducible to the truth set of AR to the Π1 1 sets, including intermediate cases. 4. Similarly, the totally definable sets in the minimal fixed point range from precisely the arithmetical sets up to precisely the ▵1 1 sets. 5. The closure ordinal for the construction of the minimal fixed point may be ω, ωCK 1, or any successor limit ordinal in between. In addition we suggest how one may supplement AR + T with a function symbol interpreted by a certain primitive recursive function so that, irrespective of the choice of the Godel numbering, the resulting language based on the weak Kleene scheme has the five features noted above for the strong Kleene language. (shrink)

Ever since Hegel famously objected to Kant’s universalization formulations of the Categorical Imperative on the grounds that they are nothing but an empty formalism, there has been continual debate about whether he was right. In this paper I argue that Hegel got things at least half-right: I argue that even if negative duties (duties to omit actions or not to adopt maxims) can be derived from the universalization formulations, positive duties (duties to commit actions or to adopt maxims) cannot. (...) The paper is divided into three main sections. In the first, I set out the procedures generally accepted among Kantians for deriving positive duties from the universalization formulations. In the second, I set out the arguments from section 1 in more detail and explain why they do not work. In the third, I examine a strategy that might be used to supplement the arguments from section 2 and I argue that it also does not work. (shrink)

According to the standard reading of Kant's formula of universal law (FUL), positive duties can be derived from FUL. In this article, I argue that the standard reading does not work. In the first section, I articulate FUL and what I mean by a positive duty. In the second section, I set out an intuitive version of the standard reading of FUL and argue that it does not work. In the third section, I set out a more (...) rigorous version of the standard reading of FUL and argue that even this more rigorous version does not work. (shrink)

Primitives are both important and unavoidable, and which set of primitives we endorse will greatly shape our theories and how those theories provide solutions to the problems that we take to be important. After introducing the notion of a primitive posit, I discuss the different kinds of primitives that we might posit. Following Cowling (2013), I distinguish between ontological and ideological primitives, and, following Benovsky (2013) between functional and content views of primitives. I then propose that these two distinctions (...) cut across each other leading to four types of primitive posits. I then argue that theoretical virtues should be taken to be meta-theoretical ideological primitives. I close with some reflections on the global nature of comparing sets of primitives. (shrink)

Eternalists believe that there is no ontological difference between the past, present and future. Thus, a challenge arises: in virtue of what does time have a direction? Some eternalists, Oaklander and Tegtmeier ) argue that the direction of time is primitive. A natural response to positing primitive directionality is the suspicion that said posit is too mysterious to do any explanatory work. The aim of this paper is to relieve primitive directionality of some of its mystery by (...) offering a novel way to understand the phenomenon in terms of the recently popularised notion of grounding. (shrink)

Under so-called primitive ontology approaches, in fully describing the history of a quantum system, one thereby attributes interesting properties to regions of spacetime. Primitive ontology approaches, which include some varieties of Bohmian mechanics and spontaneous collapse theories, are interesting in part because they hold out the hope that it should not be too difficult to make a connection between models of quantum mechanics and descriptions of histories of ordinary macroscopic bodies. But such approaches are dualistic, positing a quantum (...) state as well as ordinary material degrees of freedom. This paper lays out and compares some options that primitive ontologists have for making sense of the quantum state. (shrink)

Recent work in moral theory has seen the refinement of theories of moral standing, which increasingly recognize a position of intermediate standing between fully self-conscious entities and those which are merely conscious. Among the most sophisticated concepts now used to denote such intermediate standing is that of primitive self-consciousness, which has been used to more precisely elucidate the moral standing of human newborns. New research into the structure of the avian brain offers a revised view of the cognitive abilities (...) of birds. When this research is approached with a species-specific focus, it appears likely that one familiar species, the chicken (Gallus gallus domesticus), also exhibits primitive self-consciousness. Given the likelihood that they are primitively self-consciousness, chickens warrant a degree of moral standing that falls short of that enjoyed by persons, but which exceeds the minimal standing of merely conscious entities. (shrink)

I argue that McDowell-style disjunctivism, as the position is often cashed out, goes wrong because it takes the good epistemic standing of veridical perception to be grounded in “manifest” facts which do not necessarily satisfy any epistemic constraints. A better form of disjunctivism explains the difference between good and bad cases in terms of epistemic constraints that the states satisfy. This view allows us to preserve McDowell’s thesis that good cases make facts manifest, as long as manifest facts must satisfy (...) epistemic constraints. (shrink)

Drawing upon a distinction between epistemically and metaphysically motivated notions of a concept, I consider the insurmountable problems of theories that appeal to our epistemic capacities to address the problem of the nature of concepts satisfactorily. Prominent theories of concepts hold that primitive concepts must have internal structure if they are to account for the explanatory functions that cognitive scientists have attributed to such constructs as prototypes, exemplars, and theories. Vindicating the role of non-experimental philosophy in the critical examination (...) of empirical theories, I argue that the explanatory effectiveness of those constructs is orthogonal to an argument concerning the structure of primitive concepts. Conceptual atomism provides an alternative approach to individuating primitive concepts the precise formulation of which has yet to be worked out. Despite its unpopularity, the atomist alternative is still in a better position to face the question of what concepts are than its competitors. (shrink)

Rational agents seem more confident in any possible event than in an impossible event. But if rational credences are real-valued, then there are some possible events that are assigned 0 credence nonetheless. How do we differentiate these events from impossible events then when we order events? de Finetti (1975), Hájek (2012) and Easwaran (2014) suggest that when ordering events, conditional credences and subset relations are as relevant as unconditional credences. I present a counterexample to all their proposals in this paper. (...) While their proposals order possible and impossible events correctly, they deliver the wrong verdict for disjoint possible events assigned equal positive credence. (shrink)

Many metaphysicians posit primitives. These vary with respect to the theoretical work that they perform, but are all undefinable in more basic terms. I argue against the existence of metaphysical primitives on the grounds that, if they existed, they would be essentially primitive. However, if primitives were essentially primitive, then they would have an essence. Because they are primitive, they lack an essence, which undermines the original supposition that they are primitive. I close by mentioning some (...) implications this has both for metaphysicians and for metaphysics more generally. (shrink)

My goal in this paper is to show that it is not the case that positive duties can be derived from Kant’s so-called universalizability tests. I begin by explaining in detail what I mean by this and distinguishing it from a few things that I am not doing in this paper. After that, I confront the idea of a maxim contradictory, a concept that is advanced by many com- mentators in the attempt to derive positive duties from the (...) universalizability tests. I ex- plain what a maxim contradictory is and how the concept is used to derive positive duties. Then I argue that the notion of a maxim contradictory presupposes an objectionable form of maxim realism. I move from there to the idea of a maxim contrary and the deliberative field. These two ideas are used in tandem by commentators who do not appeal to maxim contradictories. I explain how these concepts are used to derive positive duties and then I argue that there is a systematic error in the derivations that enables one to see that they cannot work. (shrink)

Preference, according to many theories of human behaviour, is a very important phenomenon. It is therefore some what surprising that philosophers of mind pay so little attention to it. One question about preference concerns its variety. Is preference always preference for one option or state of affairs rather than another? Or is there also, as ordinary language suggests, object-preference – preferences for one person rather than another, for one country rather than another, for one value rather than another? Another question (...) or rather group of questions concerns the nature of preference. Is it a mental state, disposition, act or episode, a theoretical construct, a purely behavioural phenomenon? If it is a mental state or act, is it an intellectual, affective or a conative phenomenon? If it is an affective phenomenon, does it enjoy a positive or negative “valence”? Is preference to be understood as a relation between a person’s attitudes or is it a primitive phenomenon? (shrink)

It is quite well-known from Kurt G¨odel’s (1931) ground-breaking Incompleteness Theorem that rudimentary relations (i.e., those definable by bounded formulae) are primitive recursive, and that primitive recursive functions are representable in sufficiently strong arithmetical theories. It is also known, though perhaps not as well-known as the former one, that some primitive recursive relations are not rudimentary. We present a simple and elementary proof of this fact in the first part of the paper. In the second part, we (...) review some possible notions of representability of functions studied in the literature, and give a new proof of the equivalence of the weak representability with the (strong) representability of functions in sufficiently strong arithmetical theories. (shrink)

My modest aim in this piece is to frame and illuminate some of the issues surrounding normative motivation, rather than take a firm position on any of them. I begin by clarifying the key terms in my title of this essay, and unpacking some of the assumptions that underpin its question. I then distinguish four kinds of answers one might give. In this short essay I will not be able to properly develop and evaluate an argument for the view that (...) normative motivations are psychologically primitive, but I will have some comments about what such an argument might look like, and what it would have to show. (shrink)

In this paper I am going to raise a problem for recent attempts to derive positive duties from Kant’s universalizability tests. In particular, I argue that these recent attempts are subject to reductio and that the most obvious way of patching them renders them impracticable. I begin by explaining the motivation for these attempts. Then I describe how they work and begin my attack. I conclude by considering some patches.

In this paper I argue that, in Leibniz’s mature metaphysics, primary matter is not a positive constituent which must be added to the form in order to have a substance. Primary matter is merely a way to express the negation of some further perfection. It does not have a positive ontological status and merely indicates the limitation or imperfection of a substance. To be sure, Leibniz is less than explicit on this point, and in many texts he writes (...) as if primary matter were a positive constituent of a substance. It seems to me, however, that the view most in keeping with the thrust of his mature philosophical system is that captured by a striking remark of 1695: “Materia rerum est nihilum: id est limitatio [The matter of things is nothing: that is, limitation].” This becomes especially apparent in texts showing that Leibniz’s conception of primary matter corresponds to his conception of creaturely limitation. I start by discussing the notion of primary matter in the scholastic tradition. I then show that although Leibniz places the scholastic terminology of primary matter at a crucial juncture of his metaphysics, he thinks of primary matter in a way which significantly deviates from earlier scholastic views. I conclude that despite his adoption of distinctive terminology of Aristotelian scholasticism, instead of holding a broadly Aristotelian concept of primary matter as the ultimate subject of inherence, Leibniz thinks of primary matter according to a Neoplatonic blue-print in which matter is non-being, privation, mere absence of perfection. (shrink)

This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F, G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of definite (...) descriptions recommended here and the more usual approach that uses a term-forming operator ι, where ιxF means ‘the F’. (shrink)

We describe (essential features and an axiomatization of) a new metamathematical (cognitive) ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions, and playing a fundamental role in Artificial Mathematical Intelligence (or Cognitive-computational metamathematics). Furthermore, we present an initial (first-order) formalization of this mechanism together with its characterizing relation with classic notions like primitive positive definability and Diophantiveness. Additionally, we analyze the semantic variability of functional conceptual substratum when small syntactic modifications are (...) done. Finally, we describe cognitively natural inference rules for (mathematical) definitions inspired by functional conceptual substratum and we show that they are sound and complete w.r.t.\ standard calculi. (shrink)

Kant posits the schema as a hybrid bridging the generality of pure concepts and the particularity of sensible intuitions. However, I argue that countenancing such schemata leads to a third-man regress. Siding with those who think that the mid-way posit of the Critique of Pure Reason's schematism section is untenable, my diagnosis is that Kant's transcendental inquiry goes awry because it attempts to analyse a form/matter union that is primitive. I therefore sketch a nonrepresentational stance aimed at respecting this (...) primitivity. (shrink)

In this paper I argue that there would be no obligatory maxims if the only standards for assessing maxims were Kant’s universalizability tests. The paper is divided into five sections. In the first, I clarify my thesis: I define my terms and disambiguate my thesis from other related theses for which one might argue. In the second, I confront the view that says that if a maxim passes the universalizability tests, then there is a positive duty to adopt that (...) maxim; I also confront a close relative of this view. In the third, I confront the view that says that if a maxim does not pass the universalizability tests, then there is a positive duty to adopt the contradictory of that maxim. In the fourth, I confront two variations of the view that says that if a maxim does not pass the universalizability tests and an agent is deliberating about the action in the maxim, then the agent has a positive duty to adopt the contrary of that maxim. In the fifth, I confront the view that says that if an agent has adopted a maxim of ends, then the agent has a positive duty to universalize that end. I then wrap up the paper with some concluding remarks. (shrink)

In this paper, I confront Parfit’s Mixed Maxims Objection. I argue that recent attempts to respond to this objection fail, and I argue that their failure is compounded by the failure of recent attempts to show how the Formula of Universal Law can be used to demarcate the category of obligatory maxims. I then set out my own response to the objection, drawing on remarks from Kant’s Metaphysics of Morals for inspiration and developing a novel account of how the (...) Formula of Universal Law can be employed to determine the deontic status of action tokens, action types, and maxims. (shrink)

Primitive, unanalysable grounding relations are considered by many to be indispensable constituents of the metaphysician’s toolkit. Yet, as a primitive ontological posit, grounding must earn its keep by explaining features of the world not explained by other tools already at our disposal. Those who defend grounding contend that grounding is required to play two interconnected roles: accounting for widespread intuitions regarding what is ontologically prior to what, and forming the backbone of a theory of metaphysical explanation, in much (...) the same way that causal relations have been thought to underpin theories of scientific explanation. This thesis undermines the need to posit grounding relations to perform either of these jobs. With regard to the first, it is argued that a pair of human psychological mechanisms—for which there is substantial empirical support—can provide a more theoretically virtuous explanation of why we have the intuitions that we do. With regard to the second, I begin by considering what we want from a theory of explanation, and go on to develop three attractive (yet grounding-free) theories of metaphysical explanation. I offer: i) a psychologistic theory that calls upon the aforementioned psychological mechanisms, as well as the modal relations of necessitation and supervenience, ii) a metaphysical variant of the deductive-nomological theory of scientific explanation, and iii) a metaphysical variant of the unificationist theory of scientific explanation. Furthermore, these theories draw upon mechanisms and relations (both logical and ontological) to which we are already committed. Thus, to posit grounding relations in order to explain our priority intuitions, or in order to develop a theory of metaphysical explanation, is ontologically profligate. I conclude that we should not posit relations of ground. (shrink)

Immanuel Kant (1724-1804), the German philosopher, is considered as the father of modern ethics and one of the great philosophers in the history of philosophy. He wanted to establish a firm foundation for moral philosophy. He contributed something new to modern ethics which was not attempted by earlier ethicists. He wanted to show by using reason that morality is based on a single supreme universal principle, which is binding to all rational beings. Precisely, Kant wanted to establish the first principle (...) of morality which neglects all consideration of self-interest and even particular human problems. In the Groundwork of the Metaphysics of Morals, Kant claimed that his intention is to seek out and establish the supreme principle of morality, and that supreme principle is the categorical imperative. He puts the supreme principle of morality or the categorical imperative in at least five ways. These are formula of universal law (FUL), formula of universal law (FLN), formula of humanity (FH), formula of humanity (FA), and formula of realm of ends (FRE). However, Kant affirms that there is one canonical and general formulation of the categorical imperative and it is the FUL. For him, the other formulas are not distinct ethical principles; rather they are the reformulations or variant formulations of the single categorical imperative. Kant put this position in his works, The Groundwork of the Metaphysics of Morals. So, in this paper, I will mainly concentrate on the fundamental doctrine of the Groundwork of the Metaphysics of Morals. As I have tried to make clear before, Kant’s aim in the Groundwork of the Metaphysics of Morals is to search for and establish the supreme principle of morality (i.e., categorical imperative). He attempted to do this at the end of the Groundwork of the Metaphysics of Morals. But, to me, the way he attempted to justify the categorical imperative is problematic. Thus, in this paper, I argue that Kant did not put the categorical imperative or morality on a solid ground. (shrink)

My goal in this piece is to show that there is a problem lurking in the shadows of recent attempts to derive positive duties from Kant’s so-called universalizability tests and, further, to show that the most obvious way of fixing these attempts renders them unable to fulfill their function. I shall begin by motivating and explaining such an attempt.

This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means ‘The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown (...) to be sound and complete for the semantics. The system has a number of novel features and is briefly compared to the usual approach of formalising ‘the F ’ by a term forming operator. It does not coincide with Hintikka’s and Lambert’s preferred theories, but the divergence is well-motivated and attractive. (shrink)

For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. (...) It is further shown that each member of one class is synonymous with each member of the other class; thus that all of the theories are definitionally equivalent with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories. (shrink)

I argue for an idealist ontology consistent with empirical observations, which seeks to explain the facts of nature more parsimoniously than physicalism and bottom-up panpsychism. This ontology also attempts to offer more explanatory power than both physicalism and bottom-up panpsychism, in that it does not fall prey to either the ‘hard problem of consciousness’ or the ‘subject combination problem’, respectively. It can be summarized as follows: spatially unbound consciousness is posited to be nature’s sole ontological primitive. We, as well (...) as all other living organisms, are dissociated alters of this unbound consciousness. The universe we see around us is the extrinsic appearance of phenomenality surrounding—but dissociated from—our alter. The living organisms we share the world with are the extrinsic appearances of other dissociated alters. As such, the challenge to artificially create individualized consciousness becomes synonymous with the challenge to artificially induce abiogenesis. (shrink)

The Universal Formula: Solving the Problem of Free Will Through the Law of Balance By Angelito Malicse Introduction The problem of free will has puzzled humanity for centuries, often viewed as a philosophical or metaphysical enigma. This essay presents a universal formula that resolves this dilemma by focusing on the law of karma and the universal law of balance. It explores the interconnectedness of systems, the critical role of accurate knowledge, and the evolution of emotions in maintaining harmony. (...) By examining real-world examples such as overpopulation, environmental degradation, economic instability, and the flaws of capitalism, this essay demonstrates how the universal formula can guide human decision-making to achieve a balanced and sustainable world. The Law of Karma: Systems and Balance The universal formula begins with the law of karma, which extends beyond cause and effect to encompass the integrity of systems, both natural and man-made. Every system—whether ecological, social, or economic—operates according to the universal law of balance. When imbalances arise, the system becomes dysfunctional, leading to adverse consequences. For example, while humans sit at the top of the food chain, the Earth's ecosystem cannot sustain unchecked overpopulation of our species. Overpopulation leads to the destruction of natural resources as humans consume everything, including plants, animals, and even insects. This voracious consumption damages ecosystems, accelerates deforestation, depletes biodiversity, and disrupts the delicate balance of the natural world. To ensure the sustainability of life on Earth, it is crucial to regulate population growth, conserve natural resources, and refrain from exploiting all animals on land and in the sea. By preserving biodiversity and maintaining the integrity of ecosystems, we protect the foundation of life that supports all species, including humans. Free Will and the Dependence on Correct Knowledge Human free will is not an autonomous force but is entirely dependent on correct knowledge and information. Errors in decision-making, often caused by ignorance, false beliefs, and distorted theories, disrupt the balance of systems. For instance, the failure to regulate overpopulation creates cascading problems, including climate change, pollution, and resource depletion. Without accurate knowledge about the consequences of overpopulation, individuals and societies continue to make decisions that exacerbate these imbalances. Education and government policy play vital roles in addressing these issues. Policies that promote population regulation can maintain a sustainable economy, while education fosters awareness of the need to protect ecosystems and biodiversity. Correct information empowers individuals to make decisions that align with the universal law of balance, preventing errors that destabilize systems. The Flaws of Capitalism and the Need for Balance The efficiency of the capitalistic system increases over time, leading to significant flaws if left unchecked. Private companies continually strive to reduce overhead and operating expenses, often by automating processes and replacing human labor with robotics. While this enhances profitability, it also reduces employment opportunities, suppresses wages, and widens income inequality. These principles, central to the management strategies of most private companies, create systemic imbalances in the economy. The solution lies in adopting a mixed economic system that counterbalances the excesses of capitalism with socialist principles. Governments must play a pivotal role in addressing these imbalances by implementing the following measures: Creating High-Salary Government Jobs: These jobs provide stable income and stimulate local economies. Providing Unemployment Benefits or Universal Basic Income (UBI): These measures ensure that individuals who lose jobs due to automation and efficiency gains still have the purchasing power to meet their needs. Offering Free Healthcare and Education: These fundamental services reduce the financial burden on families, enabling them to invest in other areas of life. Promoting Government Spending: By investing in infrastructure, renewable energy, and public services, governments can create new jobs and maintain the flow of money in the economy. Government spending serves as a balancing mechanism by injecting funds into the economy, which in turn supports private companies through increased consumer demand. This feedback loop creates private-sector jobs, stabilizes the economy, and ensures a balanced flow of resources between public and private sectors. The Role of Emotions in Balancing Systems Human emotions, both positive and negative, serve as essential feedback mechanisms for maintaining balance. Positive emotions, such as love and joy, encourage cooperative behavior and strengthen familial and social bonds. Negative emotions, such as fear and anger, signal imbalances that require corrective action. For example, the unconditional love within a family fosters a nurturing environment that supports the emotional and psychological development of children. This foundation contributes to a high-quality next generation of parents, capable of fostering further generational improvement. Conversely, the absence of such love or a dysfunctional family structure often leads to crime, substance abuse, and other societal problems. These negative outcomes are the effects of systemic imbalances, whether caused by poor parenting, economic hardship, or the lack of a government safety net. Addressing Environmental and Social Imbalances The universal formula underscores the importance of a holistic education system in addressing systemic imbalances. Education must instill values such as cleanliness, discipline, ethics, and good manners while fostering a respect for nature. Teaching children the importance of not harming wildlife and preserving ecosystems is critical to protecting biodiversity and ensuring a harmonious coexistence with other species. Government policies also play a crucial role. Regulations that protect natural resources, reduce pollution, and promote renewable energy can prevent environmental degradation. Policies that provide social safety nets can alleviate poverty and reduce crime by addressing the root causes of economic and social imbalance. The Importance of Holistic Systems Thinking The universal formula emphasizes the interconnectedness of systems, demonstrating that imbalances in one area often ripple through others. For instance, a lack of holistic education contributes to ignorance, which leads to poor decision-making. This, in turn, exacerbates issues such as overpopulation, resource depletion, and social unrest. Producing a high-quality young generation requires a combination of good parenting, access to education, and supportive government policies. By fostering an environment that values balance, discipline, and ethics, societies can produce individuals capable of making decisions that align with the universal law of balance. Conclusion The universal formula offers a comprehensive solution to the problem of free will by integrating the law of karma, the universal law of balance, and the evolutionary role of emotions. By understanding and addressing the root causes of imbalance—whether environmental, social, or economic—humanity can achieve harmony within and across systems. Real-world examples, such as overpopulation, economic instability, environmental destruction, and the flaws of capitalism, highlight the urgent need to apply this formula. Through holistic education, informed policies, and an unwavering commitment to balance, individuals and societies can prevent errors, correct existing imbalances, and create a sustainable and harmonious future. The time to act is now. By embracing the universal formula, humanity can unlock the full potential of free will, ensuring a balanced and equitable world for generations to come. ---. (shrink)

Inductively defined structures are ubiquitous in mathematics; their specification is unambiguous and their properties are powerful. All fields of mathematical logic feature these structures prominently: the formula of a language, the set of theorems, the natural numbers, the primitive recursive functions, the constructive number classes and segments of the cumulative hierarchy of sets. -/- This dissertation gives a mathematical characterization of a species of inductively defined structures, called accessible domains, which include all of the above examples except the (...) set of theorems. The concept of an accessible domain comes from Wilfried Sieg's analysis of proof-theoretic practices, starting with his dissertation. In particular, he noticed the special epistemological character of elements of an accessible domain: they can always be uniquely identified with their build-up. Generally, the unique build-up of elements justifies the principles of induction and recursion. -/- I use category theory to give an abstract characterization of accessible domains. I claim that accessible domains are all instances of initial algebras for endofunctors. Grounded in the historical roots of Sieg's discussions, this dissertation shows how the properties of initial algebras for endofunctors and accessible domains coincide in a satisfying and natural way. -/- Filling out this characterization, I show how important examples of accessible domains fit into this broad characterization. I first characterize some accessible domains by relatively simple functors (e.g. finite, polynomial, those that preserve certain colimits) where we can see how iterating the functor can produce the accessible domain. Then I describe accessible domains that result from more involved specifications (e.g. ordinals and segments of the cumulative hierarchies associated with CZF, IZF, and ZF) by relying heavily on algebraic set theory. I end with a discussion of some of the methodological features of category theory in particular that helped characterize accessible domains. (shrink)

Non‐Humean theories of natural necessity invoke modally‐laden primitives to explain why nature exhibits lawlike regularities. However, they vary in the primitives they posit and in their subsequent accounts of laws of nature and related phenomena (including natural properties, natural kinds, causation, counterfactuals, and the like). This article provides a taxonomy of non‐Humean theories, discusses influential arguments for and against them, and describes some ways in which differences in goals and methods can motivate different versions of non‐Humeanism (and, for that matter, (...) Humeanism). In short, this article provides an introduction to non‐Humeanism concerning the metaphysics of laws of nature and natural necessity. (shrink)

The paper points out that the modern formulation of Bohm’s quantum theory known as Bohmian mechanics is committed only to particles’ positions and a law of motion. We explain how this view can avoid the open questions that the traditional view faces according to which Bohm’s theory is committed to a wave-function that is a physical entity over and above the particles, although it is defined on configuration space instead of three-dimensional space. We then enquire into the status of the (...) law of motion, elaborating on how the main philosophical options to ground a law of motion, namely Humeanism and dispositionalism, can be applied to Bohmian mechanics. In conclusion, we sketch out how these options apply to primitive ontology approaches to quantum mechanics in general. (shrink)

Over the past fifteen years there has been a considerable amount of debate concerning what theoretical population dynamic models tell us about the nature of natural selection and drift. On the causal interpretation, these models describe the causes of population change. On the statistical interpretation, the models of population dynamics models specify statistical parameters that explain, predict, and quantify changes in population structure, without identifying the causes of those changes. Selection and drift are part of a statistical description of population (...) change; they are not discrete, apportionable causes. Our objective here is to provide a definitive statement of the statistical position, so as to allay some confusions in the current literature. We outline four commitments that are central to statisticalism. They are: 1. Natural Selection is a higher order effect; 2. Trait fitness is primitive; 3. Modern Synthesis (MS)-models are substrate neutral; 4. MS-selection and drift are model-relative. (shrink)

Donald Davidson was one of the most influential philosophers of the last half of the 20th century, especially in the theory of meaning and in the philosophy of mind and action. In this paper, I concentrate on a field-shaping proposal of Davidson’s in the theory of meaning, arguably his most influential, namely, that insight into meaning may be best pursued by a bit of indirection, by showing how appropriate knowledge of a finitely axiomatized truth theory for a language can put (...) one in a position both to interpret the utterance of any sentence of the language and to see how its semantically primitive constituents together with their mode of combination determines its meaning (Davidson 1965, 1967, 1970, 1973a). This project has come to be known as truth-theoretic semantics. My aim in this paper is to render the best account I can of the goals and methods of truth-theoretic semantics, to defend it against some objections, and to identify its limitations. Although I believe that the project I describe conforms to the main idea that Davidson had, my aim is not primarily Davidson exegesis. I want to get on the table an approach to compositional semantics for natural languages, inspired by Davidson, but extended and developed, which I think does about as much along those lines as any theory could. I believe it is Davidson’s project, and I defend this in detail elsewhere (Ludwig 2015; Lepore and Ludwig 2005, 2007a, 2007b, 2011). But I want to develop and defend the project while also exploring its limitations, without getting entangled in exegetical questions. (shrink)

Adolf Reinach belongs to the Brentanian lineage of Austrian Aristotelianism. His theory of social acts is well known, but his account of ownership has been mostly overlooked. This paper introduces and defends Reinach’s account of ownership. Ownership, for Reinach, is not a bundle of property rights. On the contrary, he argues that ownership is a primitive and indivisible relation between a person and a thing that grounds property rights. Most importantly, Reinach asserts that the nature ownership is not determined (...) by positive law but presupposed by it. Some have objected that such realism raises insuperable difficulties as to the origin of ownership, difficulties that could only be dealt with under a more conventionalist approach. I argue that the independence of the nature ownership from positive law is, in fact, compatible with the claim that its existence is dependent on human conventions. (shrink)

An increasing amount of twenty-first century metaphysics is couched in explicitly hyperintensional terms. A prerequisite of hyperintensional metaphysics is that reality itself be hyperintensional: at the metaphysical level, propositions, properties, operators, and other elements of the type hierarchy, must be more fine-grained than functions from possible worlds to extensions. In this paper I develop, in the setting of type theory, a general framework for reasoning about the granularity of propositions and properties. The theory takes as primitive the notion of (...) a substitution on a proposition (property, etc.) and, among other things, uses this idea to elucidate a number of theoretically important distinctions. A class of structures are identified which can be used to model a wide range of positions about the granularity of reality; certain of these structures are seen to receive a natural treatment in the category of M-sets. (shrink)

This paper considers the question of whether chimpanzees possess at least a primitive sense of normativity: i.e., some ability to internalize and enforce social norms—rules governing appropriate and inappropriate behaviour—within their social groups, and to make evaluations of others’ behaviour in light of such norms. A number of scientists and philosophers have argued that such a sense of normativity does exist in chimpanzees and in several other non-human primate and mammalian species. However, the dominant view in the scientific and (...) philosophical literature is that psychological capacities for social norms evolved uniquely in the human lineage, after our last common ancestor with chimpanzees and bonobos. After reviewing some of the existing evidence for normative capacity in chimpanzees, I defend the thesis of chimpanzee normativity against three key theoretical objections that have been presented in the literature, each of which have played a part in motivating the dominant sceptical position. I argue that, while we still have much to learn about the nature and extent of the normative capacities of other animals, there is strong prima facie evidence for social norms and normative evaluation in chimpanzees and the main theoretical objections to chimpanzee normativity are not at all compelling. (shrink)

Sometimes two expressions in a discourse can be about the same thing in a way that makes that very fact evident to the participants. Consider, for example, 'he' and 'John' in 'John went to the store and he bought some milk'. Let us call this 'de jure' coreference. Other times, coreference is 'de facto' as with 'Mark Twain' and 'Samuel Clemens' in a sincere use of 'Mark Twain is not Samuel Clemens'. Here, agents can understand the speech without knowing that (...) the names refer to the same person. After surveying many available linguistic and pragmatic tools (intentions to corefer, presuppositions, meanings, indexing, discourse referents, binding etc.) I conclude that we must posit a new semantic primitive to account for de jure coreference. (shrink)

The distinction between presentism and eternalism is usually sought in some formula like ‘Only presently existing things exist’ or ‘Past, present, and future events are equally real’. I argue that ambiguities in the copula prevent these slogans from distinguishing significant opposed positions. I suggest in addition that one can find a series of significant distinctions if one takes spacetime structure into account. These presentisms and eternalisms are not contradictory. They are complementary elements of a complete naturalistic philosophy of time.

Could there be a single logical system that would allow us to work simultaneously with classical, paraconsistent, and paracomplete negations? These three negations were separately studied in logics whose negations bear their names. Initially we will restrict our analysis to propositional logics by analyzing classical negation, ¬c, as treated by Classical Propositional Logic (LPC); the paraconsistent negation, ¬p, as treated through the hierarchy of Paraconsistent Propositional Calculi Cn (0 ≤ n ≤ ω); and the paracomplete negation, ¬q, as treated by (...) the hierarchy of Paracomplete Propositional Calculi Pn (0 ≤ n ≤ ω). In “Logics that are both paraconsistent and paracomplete” (1989), Newton da Costa proposed a system with approximate characteristics to what we are looking for. In the hierarchy of Non-Alethical Propositional Calculi Nn (0 ≤ n ≤ ω), only one negation is introduced (as primitive), called a “non-alethic” (¬n), whose operation preserves the properties of classical, or paraconsistent or paracomplete negation -- depending on the well or ill behavior of the formula connected to it. However, as we shall see, in the hierarchy Nn we can not reiterate negations with different behaviors in a same formula (e.g., ¬p¬cα or ¬q¬c¬p α), or even analyze a formula like ¬cα → ¬pα. In view of these problems, can we really say that the hierarchy Nn allows us to understand the relationships and interactions of the three types of negations? In order to deal with this, given the initial problem, we will present four axiomatic systems (KG) in which, unlike Nn, the three negations are directly introduced -- offering a semantics and a method of proofs by analytic tableaux. Through the KG Systems we will show how the negations interact, obtaining non-demonstrable theorems in LPC, Cn, Pn, and Nn (0 ≤ n ≤ ω). Finally, we will also offer a first-order extension for the KG Systems. (shrink)

Spinoza ’s letter of June 2, 1674 to his friend Jarig Jelles addresses several distinct and important issues in Spinoza ’s philosophy. It explains briefly the core of Spinoza ’s disagreement with Hobbes’ political theory, develops his innovative understanding of numbers, and elaborates on Spinoza ’s refusal to describe God as one or single. Then, toward the end of the letter, Spinoza writes: With regard to the statement that figure is a negation and not anything positive, it is obvious (...) that matter in its totality, considered without limitation [indefinitè consideratam], can have no figure, and that figure applies only to finite and determinate bodies. For he who says that he apprehends a figure, thereby means to indicate simply this, that he apprehends a determinate thing and the manner of its determination. This determination therefore does not pertain to the thing in regard to its being [esse]; on the contrary, it is its non-being [non-esse]. So since figure is nothing but determination, and determination is negation [Quia ergo figura non aliud, quam determinatio, et determinatio negatio est], figure can be nothing other than negation, as has been said. Arguably, what is most notable about this letter is the fate of a single subordinate clause which appears in the last sentence of this passage: et determinatio negatio est. That clause was to be adopted by Hegel and transformed into the slogan of his own dialectical method: Omnis determinatio est negatio. Of further significance is the fact that, while Hegel does credit Spinoza with the discovery of this most fundamental insight, he believes Spinoza failed to appreciate the importance of his discovery. The issue of negation and the possibility of self-negation stand at the very center of the philosophical dialogue between the systems of Spinoza and Hegel, and in this paper I will attempt to provide a preliminary explication of this foundational debate between the two systems. In the first part of the paper I will argue that the “determination is negation” formula has been understood in at least three distinct senses among the German Idealists, and as a result many of the participants in the discussion of this formula were actually talking past each other. The clarification of the three distinct senses of the formula will lead, in the second part of the paper, to a more precise evaluation of the fundamental debate between Spinoza and Hegel regarding the possibility of self-negation. In this part I will evaluate the validity of each interpretation of the determination formula, and motivate the positions of the various participants in the debate. (shrink)

Forgiveness is clearly an important aspect of our moral lives, yet surprisingly Kant, one of the most important authors in the history of Western ethics, seems to have very little to say about it. Some authors explain this omission by noting that forgiveness sits uncomfortably in Kant’s moral thought: forgiveness seems to have an ineluctably ‘elective’ aspect which makes it to a certain extent arbitrary; thus it stands in tension with Kant’s claim that agents are autonomous beings, capable of determining (...) their own moral status through rational reflection and choice. Other authors recognise that forgiveness plays a role in Kant’s philosophy but fail to appreciate the nature of this duty and misrepresent the Kantian argument in support of it. This paper argues that there is space in Kant’s philosophy for a genuine theory of forgiveness and hopes to lay the grounds for a correct interpretation of this theory. I argue that from a Kantian perspective, forgiveness is not ‘elective’ but, at least in some cases, morally required. I claim that, for Kant, we have an imperfect duty of virtue to forgive repentant wrongdoers that have embarked on a project of self-reflection and self-reform. I develop a novel argument in support of this duty by drawing on Kant’s theory of rational agency, the thesis of radical evil, Kant’s theory of moral development, and the formula of humanity. However, it must be noted that this is a conditional duty and Kant’s position also entails that absence of repentance on the part of the wrongdoer should be taken as evidence of a lack of commitment to a project of self-reflection and self-reform. In such cases, Kant claims, we have a perfect duty to ourselves not to forgive unrepentant wrongdoers. I argue that this duty should be understood as one of the duties of self-esteem, which involves the duty to respect and recognise our own dignity as rational beings. (shrink)

A theory of the first-person plural occupies a unique place in philosophical investigations into intersubjectivity and social cognition. In order for the referent of the first-person plural—“the We”—to come into existence, it seems there must be a shared ground of communicative possibility, but this requires a non-circular explanation of how this ground could be shared in the absence of a pre-existing context of communicative conventions. Margaret Gilbert’s and John Searle’s theories of collective intentionality capture important aspects of the We, but (...) fail to fully account for this shared ground of communicative possibility. This paper argues that Merleau-Ponty’s concept of intercorporeity helps reconcile the positive aspects of these accounts while also explaining how the genesis of the social world is continuous with perceptual life in general. This enables an account of the first-person plural as dependent on reciprocal communicative interaction without the need to posit a primitive or primordial “we-mode” of consciousness. “Intercorporeity” designates a bodily openness to others that is not fundamentally different in kind from the general style of bodily comportment found in Merleau-Ponty’s rich analyses of perceptual life. (shrink)

David Lewis objected to theories that posit necessary connections between distinct entities and to theories that involve a magical grasping of their primitives. In On the Plurality of Worlds, Lewis objected to nondescript ersatzism on these grounds. The literature contains several reconstructions of Lewis’ critique of nondescript ersatzism but none of these interpretations adequately address his main argument because they fail to see that Lewis’ critique is based on broader methodological considerations. I argue that a closer look at his methodology (...) reveals the broader objection he presented against nondescript ersatzism. This objection, I further argue, remains a challenge for the ersatzer who posits structure-less entities as possible worlds. (shrink)

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the (...) Law which appears to be unquestionable, in the sense that the Priestian dialetheist is committed to accept it without also accepting something inconsistent with it, on pain of trivialism—that is to say, on pain of lapsing into the position according to which everything is the case. This will be achieved via (a) a discussion of Priest's dialetheic treatment of the notions of rejection and denial; and (b) the characterization of a negation via the primitive intuition of content exclusion. Such a result will not constitute a cheap victory for the friends of consistency. We may just learn that different things have been historically conflated under the label of 'Law of Non-Contradiction'; that dialetheists rightly attack some formulations of the Law, and orthodox logicians and philosophers have been mistaken in assimilating them to the indisputable one. (shrink)

This chapter examines Bertrand Russell’s various confrontations with Bergson’s work. Russell’s meetings with Bergson during 1911 would be followed in 1912 by the publication of Russell’s earliest polemical pieces. His 1912 review of Bergson’s Laughter ridicules the effort to develop a philosophical account of humour on the basis of some formula. In his 1912 “The Philosophy of Bergson”, Russell develops a series of objections against Bergson’s accounts of number, space, and duration. Bergson’s position is defended against Russell’s onslaught by (...) H. W. Carr (1913) and Karin Costelloe-Stephen (1914), though Russell only replies to the former. By contrast to Bergson’s silence in the face of Russell’s criticisms, Russell would continue responding to Bergson’s views in multiple works during the 1910s and 1920s. As this chapter shows, Russell not only develops further objections against specific theses upheld by Bergson, but also comments upon the political implications of Bergson’s philosophy, as well as its positioning within the history of French philosophy. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Spinoza and the Theory of Organism HANS JONAS I CARTESIANDUALISMlanded speculation on the nature of life in an impasse: intelligible as, on principles of mechanics, the correlation of structure and function became within the res extensa, that of structure-plus-function with feeling or experience (modes of the res cogitans) was lost in the bifurcation, and thereby the fact of life itself became unintelligible at the same time that the explanation (...) of its bodily performance seemed to be assured. The impasse became manifest in Occasionalism : its tour de force of an extraneous, divine "synchronization" of the outer and the inner world (the latter denied to animals) not only suffered from its extreme artificiality, the common failing of such ad hoc constructions, but even at so high a cost failed to accomplish its theoretical purpose by its own terms. For the animal machine, like any machine, raises beyond the question of the "how" that of the "what for" of its functioning---of the purpose for which it had thus been constructed by its maker.1 Its performance, however devoid of immanent teleology, must serve an end, and that end must be someone's end. This end may (directly) be itself, as indeed Descartes had implied when declaring self-preservation to be the effect of the functioning of the organic automaton. In that case the existence as such of the machine would be its end--either terminally, or in turn to benefit something else. In the former case, the machine would have to be more than a machine, for a mere machine cannot enioy its existence. But since, by the rigorous conception of the res extensa, it cannot be more than a machine, its function and/or existence must serve something other than itself. Automata in Descartes ' time were mainly for entertainment (rather than work). But the raison d'etre of the living kingdom could not well be seen in God's indulging his mechanical abilities or in the amusement of celestial spectators--especially since mere complexity of arrangement does not create new quality and thus add something to the unrelieved sameness of the simple substratum that might enrich the spectrum of being. For quality, beyond the primitive determinations of the extended per se, is the subjective creature of sensation, the confused representation of quantity in a mind; and thus organisms cannot harbor it because as mere machines they lack mentality, and pure spirits cannot because they lack sensuality, or the privilege of confusion and thereby of illusion with its possible enjoyment. And as to their intellectual enjoyment, even that, deprived of the thrill of discovery by the same token, would pale in the contemplation of what to sufficiently large The concept of "machine," adopted for its strict confinementto efficientcause, is still a finalisticconcept,even thoughthe final cause is no longer internal to the entity, as a mode of its own operation,but external to it as antecedent design. [43] 44 HISTORY OF PHILOSOPHY intellects is nothing but the ever-repeated exemplification of the same few, elementary (and ultimately trivial) truths. There remained, then, the time-honored--Stoic as well as Christian--idea that plants and animals are for the benefit of Man. Indeed, since the existence of a living world is the necessary condition for the existence of any of its members, the self-justifying nature of at least one such member (= species) would justify the existence of the whole. In Stoicism, Man provided this end by his possession of reason, which makes him the culmination of a terrestrial scale of being that is also self-justifying throughout all its grades (the end as the best of many that are good in degrees) ; in Christianity, by his possession of an immortal soul, which makes him the sole imago Dei in creation (the end as the sole issue at stake) ; and Cartesian dualism radicalized this latter position by making man even the sole possessor of inwardness or "soul" of any kind, thus the only one of whom "end" can meaningfully be predicated as he alone can entertain ends. All other life then, the product of physical necessity, can be considered his means. However, this traditional idea, in its anthropocentric vanity never a... (shrink)