In the Transcendental Ideal Kant discusses the principle of complete determination: for every object and every predicate A, the object is either determinately A or not-A. He claims this principle is synthetic, but it appears to follow from the principle of excluded middle, which is analytic. He also makes a puzzling claim in support of its syntheticity: that it represents individual objects as deriving their possibility from the whole of possibility. This raises a puzzle about why Kant regarded (...) it as synthetic, and what his explanatory claim means. I argue that the principle of complete determination does not follow from the principle of excluded middle because the externally negated or ?negative? judgement ?Not (S is P)? does not entail the internally negated or ?infinite? judgement ?S is not-P.? Kant's puzzling explanatory claim means that empirical objects are determined by the content of the totality of experience. This entails that empirical objects are completely determinate if and only if the totality of experience has a completely determinate content. I argue that it is not a priori whether experience has such a completely determinate content and thus not analytic that objects obey the principle of complete determination. (shrink)

Non-determined game logic is the logic of two player board games where the game may end in a draw: unlike the case with determined games, a loss of one player does not necessarily constitute of a win of the other player. A calculus for non-determined game logic is given in [4] and shown to be complete. The calculus adds a new rule for the treatment of greatest fixpoints, and a new unfolding axiom for iterations of the universal player. The (...) technique of the completeness proof is inspired by the canonical model construction for propositional dynamic logic (PDL). In this paper, this is extended to the logic of determined games. It is proved that the calculus for nondetermined game logic, together with the axiom of determinacy, is complete for determined game logic. Next, it is shown that the axioms and rules of the new calculus can all be derived from the calculus proposed by Parikh in [5], for which the completeness was still open. This proves Parikh’s conjecture that his calculus is complete for determined games. (shrink)

The focus of this work is the analysis of changes in completed family size and possible determinants of that size over time, in an attempt to characterize the evolution of reproductive patterns during the demographic transition. With this purpose in mind, time trends are studied in relation to the mean number of live births per family (as an indirect measure of fertility), using family reconstitution techniques to trace the reproductive history of each married woman. The population surveyed is a Spanish (...) rural community called Lanciego, located at the southern end of the province of Alava (Basque Country). A total of 24,510 parish records of baptisms, marriages and burials made between 1800 and 1969 were examined to obtain the demographic data set. For each reconstituted family, the variables included in the study were the number of live births per family or family size (FAMS), year of marriage (YEAR), age at marriage of both partners (AMAN, AWOM), wife’s age at the end of marriage (WEND), duration of marriage (MARD), age at first maternity (A1CH), length of reproductive span (REPS) and number of children dying before their first anniversary (MINF). Through a principal component analysis, three factors were found that explained more than 75% of the total variance. Association of variables in factors I and III was particularly useful in characterizing the variability of mean family size in pre-transitional, transitional and post-transitional cohorts. During demographic transition, a decreasing trend is observed in the variables FAMS, REPS and MINF, while variables AWOM, AMAN, WEND and A1CH show a tendency to increase over the 20th century. Results obtained by multiple regression analysis confirm that the best predictors of family size (dependent variable) were REPS and MINF, which between them explained over 85% of the total variation in FAMS (R2=0·853). In Lanciego, birth control seems to be present on the evidence of an increase in age at first maternity and a decrease in age at last parturition, indicating that the beginning of the reproductive span is delayed and its end is brought forward. Interaction between family size and infant mortality is discussed in the light of various hypotheses, including replacement of descendants, the so-called biological effect and the theory of r and k selection. (shrink)

According to the Principle of Sufficient Reason every event is determined down to the smallest detail. This principle entails a global determinism which is connected with the claim of uniformity: All things are basically one and differ only by degrees. Accordingly, Leibniz tries to explain the traditional distinction of necessity and contingency by the difference between a definite demonstration and an open, never ending analysis, that is a quantitative difference between the finite and infinite. It is controversial whether contingency can (...) be saved by this conception in the face of the thesis: Every predicate which can be truly attributed to a subject is included in the complete notion of this individual substance. The difficulties of the Lucky Proof can only be avoided by supposing: The infinity of analysis cannot be based on the fact that the complete notion is a simple conjunction of innumerable predicates which are not conceptually connected to each other. Then every predicate could be deduced from it in a finite number of steps; therefore, it would have been demonstrated and would consequently be necessary. The infinity of analysis cannot be either based on the fact that it is infinitely complex to prove that the subject is not contradictory. Conceptions like this or a superessentialism are not adequate, because they fail to distinguish between necessary and contingent statements about an individual within a single possible world. The complete notion and, therefore, the analysis of a contingent truth comprises an infinitely complex content, because the predicates of an individual are connected by infinitely complex relations. This corresponds to the idea that the perceptions of an individual mirror the infinitely complex connections by which the world is determined. (shrink)

Halldén complete modal logics are defined semantically. They have a nice characterization as they are determined by homogeneous Kripke frames.

RésuméL'héritage kantien dans la philosophie fregéenne de la connaissance est aujourd'hui largement reconnu. La présente analyse porte sur la point, déjà réputé central par J. Vuillemin , du jugement de recognition. On tente de montrer: °) le style transcendantal du traitement fregéen du problème des objets logiques, dont la nécessité s'introduit a partir des Grundlagen avec celle des extensions de concept, absentes de la première idéographie; style dont on tente d'expliquer les changements qu'il opére dans le modèle de la Begriffsbildung (...) kantienne. 2°) l'ambiguité de la recognition fondée par la source logique de connaissance d'objets logiques, ou par un principe d'image logique, qu'explicitera Wittgenstein, des invariants les plus généraux des opérations de pensée dans l'idéolographie. 3°) le lien du principe de recognition avec une supposition de détermination complète et son ultime formulation dans la théorie de la source géométrique; ses racines dans la formation mathématique de Frege. On conclut par la question posée par l'algébrisation de la logique, étrangére au style transcendantal de l'une des œuvres qui lui ont, fût‐ce de manière voilée par un principe de recognition, donné naissance. (shrink)

We define the notion of a completely determined Borel code in reverse mathematics, and consider the principle $CD - PB$, which states that every completely determined Borel set has the property of Baire. We show that this principle is strictly weaker than $AT{R_0}$. Any ω-model of $CD - PB$ must be closed under hyperarithmetic reduction, but $CD - PB$ is not a theory of hyperarithmetic analysis. We show that whenever $M \subseteq {2^\omega }$ is the second-order part of an ω-model (...) of $CD - PB$, then for every $Z \in M$, there is a $G \in M$ such that G is ${\rm{\Delta }}_1^1$-generic relative to Z. (shrink)

The method of calculating the degree of completeness presented below differs from methods discussed in [1] and [2] and is explicitly based on elementary properties of Lukasiewiczian valuations and reveals the character of possible enlargements of given n-valued Lukasiewicz logic. Above all it seems to be especially convenient for didactic purposes.

Contemporary philosophers commonly suppose that any fundamental entities there may be are maximally determinate. More generally, they commonly suppose that, whether or not there are fundamental entities, any determinable entities there may be are grounded in, hence less fundamental than, more determinate entities. So, for example, Armstrong takes the physical objects constituting the presumed fundamental base to be “determinate in all respects” (1961, 59), and Lewis takes the properties characterizing things “completely and without redundancy” to be “highly specific” (1986, 60). (...) Here I look at the usually cited reasons for these suppositions as directed against the case of determinable properties, in particular, and argue that none is compelling (Sections 1 to 3). The discussion in Section 3 moreover identifies positive reason for taking some determinable properties to be part of a fundamental (or relatively fundamental) base. I close (Section 4) by noting certain questions arising from the possibility of fundamental determinables, as directions for future research. (shrink)

The paper discusses methodological guidelines for evaluating mechanistic explanations. According to current accounts, a satisfactory mechanistic explanation should include all of the relevant features of the mechanism, its component entities and activities, and their properties and organization, as well as exhibit productive continuity. It is not specified, however, how this kind of mechanistic completeness can be demonstrated. I argue that parameter sufficiency inferences based on mathematical model simulations provide a way of determining whether a mechanism capable of producing the phenomenon (...) of interest can be constructed from mechanistic components organized, acting, and having the properties described in the mechanistic explanation. (shrink)

I argue that the completeness of physics is composed of two distinct claims. The first is the commonly made claim that, roughly, every physical event is completely causally determined by physical events. The second has rarely, if ever, been explicitly stated in the literature and is the claim that microphysics provides a complete inventory of the fundamental categories that constitute both the causal features and intrinsic nature of all the events that causally affect the physical universe. After showing that (...) these claims are distinct, I argue that they can be used to solve a difficulty with existing responses to the exclusion problem—namely, that these existing responses also undermine the powerful causal argument for physicalism. Recognizing that there are two kinds of completeness opens up room for the nonreductive physicalist to solve the exclusion problem while also endorsing a modified, cogent causal argument for a kind of physicalism compatible with her position. (shrink)

The determination of the past and the future of a physical system are complementary aims of measurements. An optimal determination of the past of a system can be achieved by an informationally complete set of physical quantities. Such a set is always strongly noncommutative. An optimal determination of the future of a physical system can be obtained by a Boolean complete set of quantities. The two aims can be reconciled to a reasonable degree with using (...) unsharp measurements. (shrink)

A propositional logic is defined which in addition to propositional language contains a list of probabilistic operators of the form P ≥s (with the intended meaning ‘‘the probability is at least s’’). The axioms and rules syntactically determine that ranges of probabilities in the corresponding models are always finite. The completeness theorem is proved. It is shown that completeness cannot be generalized to arbitrary theories.

In December 1990, an empirical study assessing hospital ethics committee (HEC) success was completed. Success was measured in terms of the number of interventions undertaken by the committees in four functional areas: education, guidelines development, prospective and retrospective case review. Some commonly quoted success determinants, such as multidisciplinarity, physician chairpersons, and a high institutional status of the chairperson were found not to foster success; the latter two, actually decreased committee success.

We show how to encode, by classical structures, both the objects and the morphisms of the category of complete metric spaces and uniformly continuous maps. The result is a category of, what we call, cognate metric spaces and cognate maps. We show this category relativizes to all models of set theory. We extend this encoding to an encoding of complete metric structures by classical structures. This provide us with a general technique for translating results about infinitary logic on (...) classical structures to the setting of infinitary continuous logic on continuous structures. Our encoding will also allow us to talk about not only the relations between complete metric structures, but also the potential relations between complete metric structures, i.e. those which are satisfied in some larger model of set theory. For example we will show that given any two complete metric structures we can determine if they are potentially isomorphic by looking at any admissible set which contains them both. (shrink)

Many of the major self-determination movements of the 20th and early 21st Centuries did not go smoothly, but resulted in forced or semi-forced transfers of groups of people from one country to another. Forced population transfers are not, of course, supported by major theorists of self-determination and secession. However, the problems that make population transfers extremely common in actual cases of self-determination and secession, are not squarely faced in many theories of self-determination. And, I shall argue, (...) certain leading theories of self-determination and secession would make population transfers almost inevitable in practice, even if not called for or sanctioned in theory. This is a major stumbling block for any attempt to move from an abstract account of self-determination towards a working theory. In this paper I take a first step towards addressing this problem. I shall show how any approach to dealing with secession, including “primary rights” accounts, “remedial rights only” accounts, and even “consensual” accounts, must be able to deal with the inevitable problem of population transfers, if it is to be a complete and plausible theory. I shall also show how population transfers, to the extent that we can always expect them to take place, can be made as just as possible, in light of any approach to the problem of secession. I will not here attempt to adjudicate between different approaches to secession and self-determination. To that extent, my argument may be seen as a friendly addition to all of the above approaches, showing how they may try to meet an objection which they have not yet faced. (shrink)

Earlier in this century, many philosophers of science (for example, Rudolf Carnap) drew a fairly sharp distinction between theory and observation, between theoretical terms like 'mass' and 'electron', and observation terms like 'measures three meters in length' and 'is _2° Celsius'. By simply looking at our instruments we can ascertain what numbers our measurements yield. Creatures like mass are different: we determine mass by calculation; we never directly observe a mass. Nor an electron: this term is introduced in order to (...) explain what we observe. This (once standard) distinction between theory and observation was eventually found to be wanting. First, if the distinction holds, it is difficult to see what can characterize the relationship between theory :md observation. How can theoretical terms explain that which is itself in no way theorized? The second point leads out of the first: are not the instruments that provide us with observational material themselves creatures of theory? Is it really possible to have an observation language that is entirely barren of theory? The theory-Iadenness of observation languages is now an accept ed feature of the logic of science. Many regard such dependence of observation on theory as a virtue. If our instruments of observation do not derive their meaning from theories, whence comes that meaning? Surely - in science - we have nothing else but theories to tell us what to try to observe. (shrink)

Drawing on 10 sets of data gathered in the General Social Survey between 2000 and 2018, this study examined whether confidence in the press mediated political party affiliation as a determinant of attitudes toward the scientific community. The study observed full mediation effects in three of five instances in which Republicans occupied the White House, with partial or no mediation observed at other points. Overall findings showed that males, White respondents, and those who had completed more years of school, as (...) well as Democrats and those who indicated higher levels of confidence in the press, tended to report greater levels of confidence in the scientific community. The study discusses quantitative results in light of increased partisanship and derisive attacks on news media. (shrink)

This thesis offers a re-definition of Kantian a priorism by expanding the notions surrounding it from within a Piagetian genetic epistemological viewpoint. ;In particular, the notion of "noumenon" is re-examined from within this viewpoint, and extended to all structural facets of the genetic epistemological knowing "situation". ;By means of these re-examinations of classical epistemological notions, the various forms of knowledge characteristically produced from within the bounds of that knowing "situation" can then be structurally located with respect to intent and focus (...) of the knowing activity, thereby making it possible to show the phenomenological connection between all these forms of knowledge, as well as to legitimize each form under the canopy of a common set of functional principles, such as truth, objectivity, progress, etc. This in turn allows for a re-definition of the Piagetian scientifically oriented "epistemic subject" into what I call the "complete epistemic subject", which takes account of all the forms of knowing occurring within the structure of the genetic epistemological "situation". ;Particularly are art and science focused upon as test cases for the re-oriented a priorism presented. ;Following the epistemological argument, the classical Progressive educational argument will be re-examined to determine whether any altered approaches and educational ideals result from analyzing the meaning of the "natural man" and "democratic man" and how these analyses can be seen to refer to an expanded type of knowing subject, the "complete epistemic subject". (shrink)

John Morrison has argued that confidences are assigned in perceptual experience. For example, when you perceive a figure in the distance, your experience might assign a 55-percent confidence to the figure’s being Isaac. Morrison’s argument leans on the phenomenon of ‘completely trusting your experience’. I argue that Morrison presupposes a problematic ‘importation model’ of this familiar phenomenon, and propose a very different way of thinking about it. While the article’s official topic is whether confidences are assigned in perceptual experience, it (...) is also about two more general issues: how we can determine which properties are assigned in perceptual experience; and how we transition from perception to belief. (shrink)

It is important to define and practice ethical rules and codes for professionalisation. Several national and international associations have determined midwifery ethical codes. In Turkey, ethical rules and codes that would facilitate midwifery becoming professionalised have not yet been determined. This study was planned to contribute to the professionalisation of midwifery by determining national ethical values and codes. A total of 1067 Turkish midwives completed the survey. The most prevalent values of Turkish midwives were care for mother–child health, responsibility and (...) professional adequacy. The preferred professional codes chosen by Turkish midwives were absence of conflicts of interest, respect for privacy, avoidance of deception, reporting of faulty practices, consideration of mothers and newborns as separate beings and prevention of harm. In conclusion, cultural values, beliefs and expectations of society cannot be underestimated, although the international professional values and codes of ethics contribute significantly to professionalisation of the midwifery profession. (shrink)

A simple Henkin-style completeness proof for Gödel 3-valued propositional logic G3 is provided. The idea is to endow G3 with an under-determined semantics of the type defined by Dunn. The key concept in u-semantics is that of “under-determined interpretation”. It is shown that consistent prime theories built upon G3 can be understood as u-interpretations. In order to prove this fact we follow Brady by defining G3 as an extension of Anderson and Belnap’s positive fragment of First Degree Entailment Logic.

From a logical viewpoint, object is never defined, even by a negative definition. This paper is a theoretical contribution about object using a new constructivist logical approach called Logic of Determination of Objects founded on a basic operation, called determination. This new logic takes into account cognitive problems such as the inheritance of properties by non typical occurrences or by indeterminate atypical objects in opposition to prototypes that are typical completely determinate objects. We show how extensional classes, intensions, (...) more and less determined objects, more or less typical representatives of a concept and prototypes are defined and organized, using a determination operation that constructs a class of indeterminate objects from an object representation of a concept called typical object. (shrink)

A recent surge of research has begun to examine music participation and well-being; however, a particular challenge with this work concerns theorizing around the associated well-being benefits of musical participation. Thus, the current research used Self-Determination Theory to consider the potential associations between basic psychological needs (competence, relatedness, and autonomy), self-determined autonomous motivation, and the perceived benefits to well-being controlling for demographic variables and the musical activity parameters. A sample of 192 Australian residents (17-85, Mage = 36.95), who were (...) currently participating in a musical activity at the time, completed an online questionnaire. Results indicated that females were more likely to perceive benefits to their well-being; and that how important an individual considers music in their life was positively related to perceived well-being. Importantly, the analyses also revealed that the basic needs of competency and relatedness were related to overall perceived well-being as well as specifically social, cognitive, and esteem dimensions of well-being. Autonomous motivation demonstrated significant associations with both an overall well-being score as well as four of five specific well-being subscales measured. Collectively, the findings indicate that Self-Determination Theory offers a useful theoretical framework to understanding the relationship between musical participation and well-being. Further, the pattern of findings reiterates the positive associations between musical participation and one’s psychosocial well-being, with broad implications for people involved in the facilitation of musical activity. (shrink)

Ross Cameron (2022) argues that metaphysical infinitists should reject the generally accepted idea that metaphysical determination relations back metaphysical explanations. Otherwise it won’t be possible for them to come up with successful explanations for the existence of dependent entities in non-wellfounded chains of dependence. I argue that his argument suffers from what he calls the finitist dogma, although indirectly so. However, there is a better way of motivating Cameron’s conclusion. Assuming Cameron’s principle of Essence, explanations for the existence of (...) dependent entities turn out to be circular if determination relations back explanations. This latter argument provides a stronger case as it puts the foundationalist under significant pressure, besides putting the infinitist under some pressure, to deny the idea that determination relations back explanations. (shrink)

In this paper, bi-intuitionistic multilattice logic, which is a combination of multilattice logic and the bi-intuitionistic logic also known as Heyting–Brouwer logic, is introduced as a Gentzen-type sequent calculus. A Kripke semantics is developed for this logic, and the completeness theorem with respect to this semantics is proved via theorems for embedding this logic into bi-intuitionistic logic. The logic proposed is an extension of first-degree entailment logic and can be regarded as a bi-intuitionistic variant of the original classical multilattice logic (...) determined by the algebraic structure of multilattices. Similar completeness and embedding results are also shown for another logic called bi-intuitionistic connexive multilattice logic, obtained by replacing the connectives of intuitionistic implication and co-implication with their connexive variants. (shrink)

Background: The division of non-paid labor in heterosexual parents in the West is usually still gender-based, with mothers taking on the majority of direct caregiving responsibilities. However, in same-sex couples, gender cannot be the deciding factor. Inspired by Feinberg’s ecological model of co-parenting, this study investigated whether infant temperament, parent factors (biological relatedness to child, psychological adjustment, parenting stress, and work status), and partner relationship quality explained how first-time gay, lesbian, and heterosexual parents divided labor (childcare and family decision-making) when (...) their infants were four months and 12 months old. We also tested whether family type acted as a moderator. Method: Participants were drawn from [MASKED FOR REVIEW]. Only those who provided information about their biological relatedness (yes or no) to their child (N = 263 parents) were included. When infants were four months (T1), parents completed a password-protected online questionnaire exploring their demographic characteristics including work status and standardized online-questionnaires on task division (childcare and family decision-making), infant temperament, parental anxiety, parental depression, parental stress, and partner relationship satisfaction. When infants were 12-months-old (T2), parents provided information about task division and their biological relatedness to their children. Results: Linear mixed models showed that no factor explained the division of family decision making at T1 and T2. For relative time spent on childcare tasks at T1, biological relatedness mattered for lesbian mothers only: biologically related mothers appeared to spend more time on childcare tasks than did non-related mothers. Results showed that, regardless of family type, parents who were not working or were working part-time at T1 performed more childcare tasks at T1. This was still true at T2. The other factors did not significantly contribute to relative time spent on childcare tasks at T2. Conclusion: We had the opportunity to analyze the division of non-paid tasks in families where parenting was necessarily planned and in which gender could not affect that division. Although Feinberg’s model of co-parenting suggests that various factors are related to task division, we found that paid work outside the home was most important during the first year of parenthood in determining caregiving roles. (shrink)

A logic is said to admit an equational completeness theorem when it can be interpreted into the equational consequence relative to some class of algebras. We characterize logics admitting an equational completeness theorem that are either locally tabular or have some tautology. In particular, it is shown that a protoalgebraic logic admits an equational completeness theorem precisely when it has two distinct logically equivalent formulas. While the problem of determining whether a logic admits an equational completeness theorem is shown to (...) be decidable both for logics presented by a finite set of finite matrices and for locally tabular logics presented by a finite Hilbert calculus, it becomes undecidable for arbitrary logics presented by finite Hilbert calculi. (shrink)

Background Researchers are required to determine whether a person has capacity to consent to a research study before they are able to participate. The Mental Capacity Act and accompanying Code of Practice for England and Wales provide some guidance on this process, but researchers have identified that it can be difficult to determine capacity to consent when a person has complex cognitive or communication needs. This study aimed to understand the experiences and opinions of researchers who recruit people with dementia (...) to research projects, to inform the future development of training resources. Methods A mixed method, cross-sectional, electronic survey was circulated via social media and research networks in England and Wales. The survey remained open for ten weeks and included open and closed questions exploring respondents’ confidence in determining capacity in the context of recruiting people with dementia to consent, their views on training and support they have experienced and their suggestions for future training and support needs. Results 60 respondents completed the survey from across England and Wales. Although 75% of respondents had experience of determining capacity to consent with people with dementia to research, only 13% rated themselves as feeling ‘very confident’ in this. Qualitative content analysis of open responses led to the generation of six themes, explaining researchers’ confidence, competence and future training needs in this area: (1) Researcher uncertainties, (2) Lack of time, (3) Balancing information complexity with accessibility, (4) Gatekeepers, (5) Existing enablers and (6) Envisioning future training. Conclusions Researchers would benefit from specific training in undertaking conversations around consent with people with dementia. People with dementia may have fluctuating capacity, and despite support from caregivers, researchers have little practical guidance on methods of determining a person’s ability to understand or appreciate the information they have provided during the consent process. Given the development of large complex trials within dementia research, there is an urgency to develop specific and practical guidance and training for researchers working with people with dementia and their families. (shrink)

We introduce the notion of “δ-complete decision procedures” for solving SMT problems over the real numbers, with the aim of handling a wide range of nonlinear functions including transcendental functions and solutions of Lipschitz-continuous ODEs. Given an SMT problemϕ and a positive rational number δ, a δ-complete decision procedure determines either that ϕ is unsatisfiable, or that the “δ-weakening” of ϕ is satisfiable. Here, the δ-weakening of ϕ is a variant of ϕ that allows δ-bounded numerical perturbations on (...) ϕ. We establish the existence and complexity of δ-complete decision procedures for bounded SMT over reals with functions mentioned above. We propose to use δ-completeness as an ideal requirement for numerically-driven decision procedures. As a concrete example, we formally analyze the DPLL〈ICP〉 framework, which integrates Interval Constraint Propagation in DPLL, and establish necessary and sufficient conditions for its δ-completeness. We discuss practical applications of δ-complete decision procedures for correctness-critical applications including formal verification and theorem proving. (shrink)

In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder R, its rough set-based Nelson algebra can be obtained by applying Sendlewski’s well-known construction. We prove that if the set of all R-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by the quasiorder R forms (...) an effective lattice, that is, an algebraic model of the logic E 0, which is characterised by a modal operator grasping the notion of “to be classically valid”. We present a necessary and sufficient condition under which a Nelson algebra is isomorphic to a rough set-based effective lattice determined by a quasiorder. (shrink)

: In the first edition of his book on the completeness of Kant’s table of judgments, Klaus Reich shortly indicates that the B-version of the metaphysical exposition of space in the Critique of pure reason is structured following the inverse order of the table of categories. In this paper, I develop Reich’s claim and provide further evidence for it. My argumentation is as follows: Through analysis of our actually given representation of space as some kind of object, the metaphysical exposition (...) will show that this representation is secondary to space considered as an original, undetermined and as such unrepresentable intuitive manifold. Now, following Kant, the representation of any kind of object involves diversity, synthesis and unity. In the case of our representation of space as formal intuition, this involves, firstly, a manifold a priori, i.e. space as pure form, delivered by the transcendental Aesthetic, secondly, a figurative, productive synthesis of that manifold, and, thirdly, the unity provided by the categories. Analysing our given representation of space – the task of the metaphysical exposition – amounts to dismantling its unity and determine its characteristics with respect to the categories. (shrink)

Given a regular cardinal κ such that κ<κ=κ (e.g., if the generalized continuum hypothesis holds), we develop a proof system for classical infinitary logic that includes heterogeneous quantification (i.e., infinite alternating sequences of quantifiers) within the language Lκ+,κ, where there are conjunctions and disjunctions of at most κ many formulas and quantification (including the heterogeneous one) is applied to less than κ many variables. This type of quantification is interpreted in Set using the usual second-order formulation in terms of strategies (...) for games, and the axioms are based on a stronger variant of the axiom of determinacy for game semantics. With respect to this axiom system we prove the soundness and completeness theorem with respect to a class of set-valued structures that we call well determined. We also investigate intuitionistic systems with heterogeneous quantifiers for Lκ+,κ,κ (when only conjunctions of less than κ many formulas are allowed), and prove analogously a completeness theorem with respect to well-determined structures in categories in general, in κ-Grothendieck topoi in particular, and, when κ<κ=κ, also in Kripke models. Finally, we consider an extension of our system in which heterogeneous quantification with bounded quantifiers is expressible, and extend our completeness results to that case. (shrink)

In this paper I study the variants of the notion of completeness Husserl pre-sented in “Ideen I” and two lectures he gave in Göttingen in 1901. Introduced primarily in connection with the problem of imaginary numbers, this notion found eventually a place in the answer Husserl provided for the philosophically more im-portant problem of the logico-epistemological foundation of formal knowledge in sci-ence. I also try to explain why Husserl said that there was an evident correlation between his and Hilbert’s notion (...) of completeness introduced in connection with the axiomatisation of geometry and the theory of real numbers when, as many commen-tators have already observed, these two notions are independent. I show in this paper that if a system of axioms is complete in Husserl’s sense, then its formal domain, the manifold of formal objects it determines, does not admit any extension. This is precisely the idea behind Hilbert’s notion of completeness in question. Therefore, the correlation Husserl noted indeed exists. But, in order to see it, we must consider the formal domain determined by a formal theory, not its models. (shrink)

For each vertex of a simple polygon P an integer valued weight is given. We consider the path p1, p2, ..., pk in P which is created according to the following strategy: p1 is a designated start vertex s and pi+1 is obtained by choosing the vertex with smallest weight among all vertices visible from pi and different from p1, p2, ..., pi. If there is no such vertex the path is finished. This path is called geometric lexicographic dead end (...) path. We shall prove the problem of determining whether a distinguished vertex t of P is on the geometric lexicographic dead end path or not to be P-complete. (shrink)

Recent work has shown that the input-output behavior of some common machine learning classifiers can be captured in symbolic form, allowing one to reason about the behavior of these classifiers using symbolic techniques. This includes explaining decisions, measuring robustness, and proving formal properties of machine learning classifiers by reasoning about the corresponding symbolic classifiers. In this work, we present a theory for unveiling the _reasons_ behind the decisions made by Boolean classifiers and study some of its theoretical and practical implications. (...) At the core of our theory is the notion of a _complete reason,_ which can be viewed as a necessary and sufficient condition for why a decision was made. We show how the complete reason can be used for computing notions such as sufficient reasons (also known as PI-explanations and abductive explanations), how it can be used for determining decision and classifier bias and how it can be used for evaluating counterfactual statements such as “a decision will stick even if...because....” We present a linear-time algorithm for computing the complete reasoning behind a decision, assuming the classifier is represented by a Boolean circuit of appropriate form. We then show how the computed complete reason can be used to answer many queries about a decision in linear or polynomial time. We finally conclude with a case study that illustrates the various notions and techniques we introduced. (shrink)

Organ donation after the circulatory determination of death requires the permanent cessation of circulation while organ donation after the brain determination of death requires the irreversible cessation of brain functions. The unified brain-based determination of death connects the brain and circulatory death criteria for circulatory death determination in organ donation as follows: permanent cessation of systemic circulation causes permanent cessation of brain circulation which causes permanent cessation of brain perfusion which causes permanent cessation of brain function. (...) The relevant circulation that must cease in circulatory death determination is that to the brain. Eliminating brain circulation from the donor ECMO organ perfusion circuit in thoracoabdominal NRP protocols satisfies the unified brain-based determination of death but only if the complete cessation of brain circulation can be proved. Despite its medical and physiologic rationale, the unified brain-based determination of death remains inconsistent with the Uniform Determination of Death Act. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free topology) (...) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

In a trio of recent articles, Johnson and Nado defend a form of metasemantic dispositionalism, arguing for a novel approach to the “error”-problem, based on speakers’ dispositional states under what they call a state of “full information”. In this article, I argue that their brand of dispositionalism fails to solve the “error”-problem, because of what I think of as counterexamples to it. In the final sections, I propose a way to amend the theory to shield it from some of the (...) counterexamples, based on the idea that what determines meaning is not only dispositions to apply words under full information, but also dispositions to evaluate one’s prior usage, under full information. (shrink)

Generally, ontological categories are understood to express the most general features of reality; however, obtaining a complete category list is difficult. This volume examines how Aquinas establishes the list of categories through a technique of identifying diversity—in how predicates are related to their subjects. A sophisticated critique by Scotus is also examined—a rejection which is fundamentally grounded in the idea that no real distinction can be made from a logical one. It is argued Aquinas's approach can be rehabilitated in (...) that real distinctions are possible when specifically considering modes of predication. This discussion between Aquinas and Scotus bears fruit in a contemporary context insofar as it bears upon, strengthens, and seeks to correct Lowe's four-category ontology view regarding the identity and relation of the categories. (shrink)

The fundamental determinant of death in donation after circulatory determination of death is the cessation of brain circulation and function. We therefore propose the term donation after brain circulation determination of death [DBCDD]. In DBCDD, death is determined when the cessation of circulatory function is permanent but before it is irreversible, consistent with medical standards of death determination outside the context of organ donation. Safeguards to prevent error include that: 1] the possibility of auto-resuscitation has elapsed; 2] (...) no brain circulation may resume after the determination of death; 3] complete circulatory cessation is verified; and 4] the cessation of brain function is permanent and complete. Death should be determined by the confirmation of the cessation of systemic circulation; the use of brain death tests is invalid and unnecessary. Because this concept differs from current standards, consensus should be sought among stakeholders. The patient or surrogate should provide informed consent for organ donation by understanding the basis of the declaration of death. In cases of circulatory cessation, such as occurs in DBCDD, death can be defined as the permanent cessation of brain functions, determined by the permanent cessation of brain circulation. (shrink)

In a previous article on cosmological arguments, I have put forward a few examples of complete infinite and circular explanations, and argued that complete non-wellfounded explanations such as these might explain the present state of the world better than their well-founded theistic counterparts (Billon, 2021). Although my aim was broader, the examples I gave there implied merely causal explanations. In this article, I would like to do three things: • Specify some general informative conditions for complete and (...) incomplete non-wellfounded causal explanations that can be used to assess candidate explanations and to generate new examples of complete non-wellfounded explanations. • Show that these conditions, which concern chains of causal explanations, easily generalize to chains of metaphysical, grounding explanations and even to chains involving other “determination relations” such as supervenience. • Apply these general conditions to the recent debates against the existence of nonwellfounded chains of grounds and show, with a couple of precise examples, that the latter can be complete, and that just like in the case of causal explanations, non-wellfoundedness can in fact be an aset rather than a liability. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free topology) (...) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator Int. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the modal operators K and B holds such that a completeness theorem for weak KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge Int comes along with a complete Heyting algebra of belief operators N° that all fit the knowledge operator Int in the sense that the pairs (Int, N°) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist that can be compared with each other. (shrink)

In this paper, the author compares passages from two philosophically important texts and concludes that they have fundamental ideas in common. What makes this comparison and conclusion interesting is that the texts come from two different traditions in philosophy, the analytic and the phenomenological. In 1912, Ernst Mally published *Gegenstandstheoretische Grundlagen der Logik und Logistik*, an analytic work containing a combination of formal logic and metaphysics. In 1913, Edmund Husserl published *Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie*, a seminal (...) work in phenomenology in which noemata are defined and given a crucial role in directing our mental states. In the passages from these two texts reproduced below, the author shows that the abstract `determinates' postulated by Mally in 1912 are assigned much the same role that Husserl assigned to noemata in 1913. Though Mally's determinates are not as highly structured as Husserl's noemata, they have a feature that explains how they manage to play the role assigned to them. The corresponding feature is missing, or at least, not emphasized in Husserl's account of noemata. Therefore, insights from both philosophers, and thus from both the analytic and phenomenological traditions, are needed to give a more complete account of directed mental states. (shrink)

The purpose of the present study was to evaluate the effectiveness of a physical activity intervention program designed to enhance levels of engagement in PA. Despite robust evidence supporting the beneficial effects of PA on overall health, only about 22% of individuals engage in the recommended minimum amount of PA. Recent surveys suggested that most individuals express intentions to be physically active, though the psychological state of amotivation dismissed these struggles. In the current study, we pilot-tested a new intervention program, (...) aimed at enhancing engagement in PA among sedentary individuals. The intervention was based on two behavioral change and motivational psychological frameworks: Self-Determination Theory and Acceptance and Commitment Therapy. During a 14-week intervention program, 94 sedentary Israeli college students were randomly assigned into one of three groups: SDT and ACT-based intervention, traditional intervention, and a non-treatment group. Prior to and following the intervention, participants completed the Behavioral Regulation in Exercise Questionnaire-3 to examine motivation to exercise and the International Physical Activity Measurement IPAQ to evaluate their training frequency. Results showed that the SDT and ACT-based intervention group exhibited a significant increase in motivation to exercise between time 1 and time 2, while the other two groups showed insignificant differences in motivation to exercise. Furthermore, neither of the groups showed significant differences in their training frequency per week. However, those in the SDT and ACT-based groups reported an increase in activity intensity from time 1 to time 2 compared to the two other groups. Further, exercise psychology consultants and scholars can use the intervention protocol and utilize these findings to improve PA behaviors and promote health in the general population. Limitations, future directions, and implications are discussed in detail. (shrink)

This book offers a new interpretation of Hermann von Helmholtz's work on the epistemology of geometry. A detailed analysis of the philosophical arguments of Helmholtz's Erhaltung der Kraft shows that he took physical theories to be constrained by a regulative ideal. They must render nature "completely comprehensible", which implies that all physical magnitudes must be relations among empirically given phenomena. This conviction eventually forced Helmholtz to explain how geometry itself could be so construed. Hyder shows how Helmholtz answered this question (...) by drawing on the theory of magnitudes developed in his research on the colour-space. He argues against the dominant interpretation of Helmholtz's work by suggesting that for the latter, it is less the inductive character of geometry that makes it empirical, and rather the regulative requirement that the system of natural science be empirically closed. (shrink)

Causal discovery becomes especially challenging when the possibility of latent confounding and/or selection bias is not assumed away. For this task, ancestral graph models are particularly useful in that they can represent the presence of latent confounding and selection effect, without explicitly invoking unobserved variables. Based on the machinery of ancestral graphs, there is a provably sound causal discovery algorithm, known as the FCI algorithm, that allows the possibility of latent confounders and selection bias. However, the orientation rules used in (...) the algorithm are not complete. In this paper, we provide additional orientation rules, augmented by which the FCI algorithm is shown to be complete, in the sense that it can, under standard assumptions, discover all aspects of the causal structure that are uniquely determined by facts of probabilistic dependence and independence. The result is useful for developing any causal discovery and reasoning system based on ancestral graph models. (shrink)

The aim of this paper is to present a strongly complete first order functional predicate calculus generalized to models containing not only ordinary classical total functions but also arbitrary partial functions. The completeness proof follows Henkin’s approach, but instead of using maximally consistent sets, we define saturated deductively closed consistent sets . This provides not only a completeness theorem but a representation theorem: any SDCCS defines a canonical model which determine a unique partial value for every predicate symbol and (...) any function symbol. Any SDCCS can thus be interpreted as an epistemic state. (shrink)