Many theorists have proposed that we can use the principle of indifference to defeat the inductive sceptic. But any such theorist must confront the objection that different ways of applying the principle of indifference lead to incompatible probability assignments. Huemer offers the explanatory priority proviso as a strategy for overcoming this objection. With this proposal, Huemer claims that we can defend induction in a way that is not question-begging against the sceptic. But in this article, I argue (...) that the opposite is true: if anything, Huemer’s use of the principle of indifference supports the rationality of inductive scepticism. (shrink)

In The Problems of Philosophy, Bertrand Russell presents a justification of induction based on a principle he refers to as “the principle of induction”. Owing to the ambiguity of the notion of probability, the principle of induction may be interpreted in two different ways. If interpreted in terms of the subjective interpretation of probability, the principle of induction may be known a priori to be true. But it is unclear how this should (...) give us any confidence in our use of induction, since induction is applied to the external world outside our minds. If the principle is interpreted in light of the objective interpretation of induction, it cannot be known to be true a priori, since it applies to frequencies that occur in the world outside the mind, and these cannot be known without recourse to experience. Russell’s principle of induction therefore fails to provide a satisfactory justification of induction. (shrink)

I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act (...) as if one has substantive information about the world when one does not. I sketch the outlines of a solution in part I, showing how it differs from others, with full details to follow in subsequent parts. The solution is pragmatic in sentiment (though differs in specifics to arguments from, for example, William James); the conceptions we use to guide our actions are and should be at least partly determined by preferences. This is cashed out in a reformulation of decision theory motivated by a non-reductive formulation of hypotheses and logic. A distinction emerges between initial assumptions--that can be non-dogmatic--and effective assumptions that can simultaneously be substantive. An explanation is provided for the plausibility arguments used to explain assigned probabilities in BCT. -/- In subsequent parts, logic is constructed from principles independent of language and mind. In particular, propositions are defined to not have form. Probabilities are logical and uniquely determined by assumptions. The problems considered fatal to logical probabilities--Goodman's `grue' problem and the uniqueness of priors problem are dissolved due to the particular formulation of logic used. Other problems such as the zero-prior problem are also solved. -/- A universal theory of (non-linguistic) meaning is developed. Problems with counterfactual conditionals are solved by developing concepts of abstractions and corresponding pictures that make up hypotheses. Spaces of hypotheses and the version of Bayes' theorem that utilises them emerge from first principles. -/- Theoretical virtues for hypotheses emerge from the theory. Explanatory force is explicated. The significance of effective assumptions is partly determined by combinatoric factors relating to the structure of hypotheses. I conjecture that this is the origin of simplicity. (shrink)

My first goal is to motivate a distinctively metaphysical approach to the problem of induction. I argue that there is a precise sense in which the only way that orthodox Humean and non-Humean views can justify induction is by appealing to extremely strong and unmotivated probabilistic biases. My second goal is to sketch what such a metaphysical approach could possibly look like. After sketching such an approach, I consider a toy case that illustrates the way in which such (...) a metaphysics can help us make progress on the problem of induction. (shrink)

This paper explores the relationships between some the problems of the Fermi Paradox (FP), with its variety of possible answers; and the Problem of Induction, and thus the possibility of a Theory of Everything. We seek to improve the hierarchy of plausibility within answers to FP, given by what we call “preference criteria”, among which we particularly highlight culture-independence. We argue that, if the question of whether a Theory of Everything is possible is answered negatively, then FP becomes much (...) more serious than otherwise, and this makes many of FP’s solutions less preferable. This constitutes a further preference criterion. Armed with this tool, we try to outline a network of relative truths between FP and the Problem of Induction, in the form of a cross-answer table. Only two or three combinations of answers survive as preferable: 1) degenerate, pure solipsistic metaphysics; 2) accept Induction and the Anthropic Principle at the same time, thus saying that the human condition is a very rare one in the universe; or 3) that the Theory of Everything exists and its discovery is the Great Filter. This latter possibility is discussed with its implications for the current scientific and economic progress of our civilization. (shrink)

This essay presents a point of view for looking at `free will', with the purpose of interpreting where exactly the freedom lies. For, freedom is what we mean by it. It compares the exercise of free will with the making of inferences, which usually is predominantly inductive in nature. The making of inference and the exercise of free will, both draw upon psychological resources that define our ‘selves’. I examine the constitution of the self of an individual, especially the involvement (...) of personal beliefs, personal memories, affects, emotions, and the hugely important psychological value-system, all of which distinguish the self of one individual from that of another. The foundational position that adopted in this essay is that all psychological processes are correlated with corresponding ones involving large scale neural aggregates in the brain, communicating with one another through wavelike modes of excitation and de-excitation. Of central relevance is the value-network around which the affect system is organized, the latter, in turn, being the axis around which is assembled the self, with all its emotional correlates. The self is a complex system. I include a brief outline of what complexity consists of. In reality all systems are complex, for complexity is ubiquitous, and certain parts of nature appear to us to be ‘simple’ only in certain specific contexts. It is in this background that the issue of determinism is viewed in this essay. Instead of looking at determinism as a grand principle entrenched in nature independent of our interpretation of it, I look at our ability to explain and to predict events and phenomena around us, which is made possible by the existence of causal links running in a complex course that set up correlations between diverse parts of nature, in this way putting the stamp of necessity on these events. However, the complexity of systems limits our ability to explain and to predict to within certain horizons defined by contexts. Our ability to explain and predict in matters relating to acts of free will is similarly limited by the operations of the self that remain hidden from our own awareness. The aspects of necessity and determinism appear to us in the form of reason and rationality that explain and predict only within a limited horizon, while the rest depends on the complex operation of self-linked psychological resources, where the latter appear as contingent in the context of the exercise of free will. The hallmark of complex systems is the existence of amplifying factors that operate as destabilizing ones, along with inhibiting or stabilizing factors as well that generally limit the destabilizing influences to local occurrences, while preserving the global integrity of a system. This complex interplay of destabilizing and stabilizing influences lead to the possibility of an enormous number of distinct modes of behavior that appear as emergent phenomena in complex systems. Looking at the particular case of the self of an individual that guide her actions and thoughts, it is the operation of our emotions, built around the psychological value-system, that provide for the amplifying and inhibiting factors mentioned above. The operation of these self-linked factors stamps our actions and thoughts as contingent ones that do not fit with our concepts of reason and rationality. And this is what provides the basis of our idea of free will. Free will is not ‘free’ in virtue of exemption from causal links running through all our self-based processes - ones that remain hidden from our awareness, but is free of what is perceived to be ‘reason and rationality’ based on knowledge and the common pool of beliefs and principles associated with a shared world-view. When we speak of the choice involved in an act of exercise of free will what we actually refer to is the commonly observed fact that various different individuals of a similar disposition respond differently when placed under similar circumstances. In other words, free will is ‘free’ precisely because it is not subject to constraints of a commonly accepted and shared set of principles, beliefs, and values. While it is possible that, in an exercise of free will, the self-linked psychological resources are brought into action when a number of alternatives are presented to the self by the operation of the ingredients of a commonly shared world-view, it seems likely that, that set of alternatives is not of primary relevance in the final response that the mind produces, since the latter is primarily a product of the operation of the self-based psychological resources. What is of greater relevance here is the operation of emotion-driven processes, guided by the psychological value-system based on the activity of the so-called reward-punishment network in the brain. These processes lead the individual to a response that appears to be free from the shackles of determinism precisely because their mechanisms, which are hidden from us, do not conform to commonly accepted and shared rules and principles. In contrast, inductive inference is a process that is based on the ‘cognitive face’ of self, where the self-based psychological resources play a supportive role to the commonly shared world-view of an individual. There is never any freedom from the all-pervading causal links representing correlations among all objects, entities, and events in nature. In the midst of all this, the closest thing to freedom that we can have in our life comes with self-examination and self-improvement. The possibility of self-examination appears in the form of specific conjunctions between our complex self-processes and the ceaseless changes of scenario in our external world. This actually makes the emergent phenomenon of self-examination a matter of chance, but one that keeps on appearing again and again in our life. Once realized, self examination creates possibilities that would not be there in the absence of it, and these possibilities include the enhancement of further self-enrichment and further diversity in the exercise of our free will. (shrink)

This paper has three interdependent aims. The first is to make Reichenbach’s views on induction and probabilities clearer, especially as they pertain to his pragmatic justification of induction. The second aim is to show how his view of pragmatic justification arises out of his commitment to extensional empiricism and moots the possibility of a non-pragmatic justification of induction. Finally, and most importantly, a formal decision-theoretic account of Reichenbach’s pragmatic justification is offered in terms both of the minimax (...) principle and the dominance principle. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be (...) accepted rather a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

I reconstruct J. H. Lambert’s views on how practical grounds relate to epistemic features, such as certainty. I argue, first, that Lambert’s account of moral certainty does not involve any distinctively practical influence on theoretical belief. However, it does present an interesting form of fallibilism about justification as well as a denial of a tight link between knowledge and action. Second, I argue that for Lambert, the persistence principle that underwrites induction is supported by practical reasons to believe; (...) this indicates that Lambert is a moderate pragmatist about reasons for theoretical belief. (shrink)

According to John D. Norton's Material Theory of Induction, all inductive inferences are justified by local facts, rather than their formal features or some grand principles of nature's uniformity. Recently, Richard Dawid (Found Phys 45(9):1101–1109, 2015) has offered a challenge to this theory: in an adaptation of Norton's own celebrated "Dome" thought experiment, it seems that there are certain inductions that are intuitively reasonable, but which do not have any local facts that could serve to justify them in accordance (...) with Norton's requirements. Dawid's suggestion is that “raw induction” might have a limited but important role for such inferences. I argue that the Material Theory can accommodate such inductions, because there are local facts concerning the combinatoric features of the induction’s target populations that can licence the inferences in an analogous way to existing examples of material induction. Since my arguments are largely independent of the details of the Dome, Norton's theory emerges as surprisingly robust against criticisms of excessive narrowness. (shrink)

The thesis of this paper is that we can justify induction deductively relative to one end, and deduction inductively relative to a different end. I will begin by presenting a contemporary variant of Hume ’s argument for the thesis that we cannot justify the principle of induction. Then I will criticize the responses the resulting problem of induction has received by Carnap and Goodman, as well as praise Reichenbach ’s approach. Some of these authors compare (...) class='Hi'>induction to deduction. Haack compares deduction to induction, and I will critically discuss her argument for the thesis that we cannot justify the principles of deduction next. In concluding I will defend the thesis that we can justify induction deductively relative to one end, and deduction inductively relative to a different end, and that we can do so in a non-circular way. Along the way I will show how we can understand deductive and inductive logic as normative theories, and I will briefly sketch an argument to the effect that there are only hypothetical, but no categorical imperatives. (shrink)

We propose and investigate an Analogy Principle in the context of Unary Inductive Logic based on a notion of support by structural similarity which is often employed to motivate scientific conjectures.

The principle of maximal entropy (further abbreviated as “MaxEnt”) can be founded on the formal mechanism, in which future transforms into past by the mediation of present. This allows of MaxEnt to be investigated by the theory of quantum information. MaxEnt can be considered as an inductive analog or generalization of “Occam’s razor”. It depends crucially on choice and thus on information just as all inductive methods of reasoning. The essence shared by Occam’s razor and MaxEnt is for the (...) relevant data known till now to be postulated as an enough fundament of conclusion. That axiom is the kind of choice grounding both principles. Popper’s falsifiability (1935) can be discussed as a complement to them: That axiom (or axiom scheme) is always sufficient but never necessary condition of conclusion therefore postulating the choice in the base of MaxEnt. Furthermore, the abstraction axiom (or axiom scheme) relevant to set theory (e.g. the axiom scheme of specification in ZFC) involves choice analogically. (shrink)

Aristotle's cognitive ideal is a form of understanding that requires a sophisticated grasp of scientific first principles. At the end of the Analytics, Aristotle tells us that we learn these principles by induction. But on the whole, commentators have found this an implausible claim: induction seems far too basic a process to yield the sort of knowledge Aristotle's account requires. In this paper I argue that this criticism is misguided. I defend a broader reading of Aristotelian induction, (...) on which there's good sense to be made of the claim that we come to grasp first principles inductively, and show that this reading is a natural one given Aristotle's broader views on scientific learning. (shrink)

We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity.

This chapter has two objectives. The first is to clarify Aristotle’s view of the first principles of the sciences. The second is to stake out a critical position with respect to this view. The paper sketches an alternative to Aristotle’s intuitionism based in part on the use of quantitative inductive logics.

[English in PhilArchive, unpublished]. Ruđer Bošković's (Rogerius Joseph Boscovich, 1711-1787) induction is described as a reasoning procedure that combines abductive, generalizing and deductive forms of inference. According to Bošković, the application of inductive reasoning extends beyond natural science. Bošković's critique of the use of the principle of sufficient reason is discussed, and constructive rules of Bošković's inductive logic are proposed from the standpoint of contemporary justification logic. To that end, justification logic could be extended with Bošković's typology of (...) reasons. Hunter's result (1965) is conceived as a confirmation that the inference from the constructive defectus rationis is a necessary component of Bošković's induction. - English version in _PhilArchive_. (shrink)

This article develops a constructive criticism of methodological conventionalism. Methodological conventionalism asserts that standards of inductive risk ought to be justified in virtue of their ability to facilitate coordination in a research community. On that view, industry bias occurs when conventional methodological standards are violated to foster industry preferences. The underlying account of scientific conventionality, however, is problematically incomplete. Conventions may be justified in virtue of their coordinative functions, but often qualify for posterior empirical criticism as research advances. Accordingly, industry (...) bias does not only threaten existing conventions but may impede their empirically warranted improvement if they align with industry preferences. My empiricist account of standards of inductive risk avoids such a problem by asserting that conventional justification can be pragmatically warranted but has, in principle, only a provisional status. Methodological conventions, therefore, should not only be defended from preference-based infringements on their coordinative function but ought to be subjected to empirical criticism. (shrink)

The philosophical background important to Mill’s theory of induction has two major components: Richard Whately’s introduction of the uniformity principle into inductive inference and the loss of the idea of formal cause.

Ayurveda is considered one of the ancient systems of knowledge in India. Various compendiums of Ayurveda i.e., Charaka, Sushruta, or Vagbhatta have enumerated an education system based on Gurukuls i.e., An Educator and their pupils. It is evident from them that a very systematized and organized form of medical education starting from selection to induction and then to effective teaching and training were given during that ancient era. The triad of education viz. Adhyayan (studying), Adhyapan (teaching) and Sambhasha (an (...) argument based on logic) is key to knowledge and the learning process as per Charaka. The selection of students and teachers was based on some set of fixed criteria necessary to be fulfilled. Induction was done prior to admission and proper disciplinary, and ethical rules were practiced. For the development of knowledge and skills in branches of Ayurveda, problems-based case discussion, identification, causes, and treatment of diseases, their principles were taught. Yogya (a set of dummy objects) was used to practice prior to the final surgery. (shrink)

Roger White (2015) sketches an ingenious new solution to the problem of induction. He argues from the principle of indifference for the conclusion that the world is more likely to be induction- friendly than induction-unfriendly. But there is reason to be skeptical about the proposed indifference-based vindication of induction. It can be shown that, in the crucial test cases White concentrates on, the assumption of indifference renders induction no more accurate than random guessing. After (...) discussing this result, the paper explains why the indifference-based argument seemed so compelling, despite ultimately being unsound. (shrink)

Most social policies cannot be defended without making inductive inferences. For example, consider certain arguments for racial profiling and affirmative action, respectively. They begin with statistics about crime or socioeconomic indicators. Next, there is an inductive step in which the statistic is projected from the past to the future. Finally, there is a normative step in which a policy is proposed as a response in the service of some goal—for example, to reduce crime or to correct socioeconomic imbalances. In comparison (...) to the normative step, the inductive step of a policy defense may seem trivial. We argue that this is not so. Satisfying the demands of the inductive step is difficult, and doing so has important but underappreciated implications for the normative step. In this paper, we provide an account of induction in social contexts and explore its implications for policy. Our account helps to explain which normative principles we ought to accept, and as a result it can explain why it is acceptable to make inferences involving race in some contexts (e.g., in defense of affirmative action) but not in others (e.g., in defense of racial profiling). (shrink)

Karl Popper, in "The Logic of Scientific Discovery" Section *vii, argues that if you find that some objecta a,b, c ... have a specific property P, then this discovery by itself does not increase the probability that some other object also has P. He concludes that there can be no effective principle of induction. My paper disproves Popper's claim, using very elementary considerations..

Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A.. Giving the boot to the bootstrap: How not to learn the natural numbers. Cognition, 101, B51–B60.] argue that such an inductive inference is consistent with a representational system that (...) clearly does not express the natural numbers and that possession of the natural numbers requires further principles that make the inductive inference superfluous. We argue that their critique is unsuccessful. Provided that children have access to a suitable initial system of representation, the sort of inductive inference that Rips et al. call into question can in fact facilitate the acquisition of larger integer concepts without the addition of any further principles. (shrink)

Inductive conclusions rest upon the Uniformity Principle, that similar events lead to similar results. The principle derives from three fundamental axioms: Existence, that the observed object has an existence independent of the observer; Identity, that the objects observed, and the relationships between them, are what they are; and Continuity, that the objects observed, and the relationships between them, will continue unchanged absent a sufficient reason. Together, these axioms create a statement sufficiently precise to be falsified. -/- Simple enumeration (...) of successful observations is ineffective to support an inductive conclusion. First, as its analytical device, induction uses the contrapositive form of the hypothesis; a successful observation merely represents the denial of the antecedent, from which nothing follows. Second, simple enumeration uses an invalid syllogism that fails to distribute its middle term. -/- Instead, the inductive syllogism identifies its subject by excluding nonuniform results, using the contrapositive form of the hypotheses. The excluded data allows an estimate of the outer boundaries of the subject under examination. But an estimate of outer boundaries is as far as the inductive process may proceed; an affirmative identification of the content of the subject never becomes possible. (shrink)

The Laws of Thought is an exploration of the deductive and inductive foundations of rational thought. The author here clarifies and defends Aristotle’s Three Laws of Thought, called the Laws of Identity, Non-contradiction and Exclusion of the Middle – and introduces two more, which are implicit in and crucial to them: the Fourth Law of Thought, called the Principle of Induction, and the Fifth Law of Thought, called the Principle of Deduction. This book is a thematic compilation (...) drawn from past works by the author over a period of twenty-three years (1990-2013). (shrink)

Logic has a fundamental role in the philosophy of Franjo Marković (1845-1914). His theory of concepts and reasoning is analyzed, especially with respect to the essential role of the principle of sufficient reason and in connection with the concept of causality. The interplay of various types of evidence in Marković's inductive-deductive logic is analysed by means of contemporary justification logic tools.

The pessimistic induction is built upon the uniformity principle that the future resembles the past. In daily scientific activities, however, scientists sometimes rely on what I call the disuniformity principle that the future differs from the past. They do not give up their research projects despite the repeated failures. They believe that they will succeed although they failed repeatedly, and as a result they achieve what they intended to achieve. Given that the disuniformity principle is useful (...) in certain cases in science, we might reasonably use it to infer that present theories are true unlike past theories. Hence, pessimists have the burden to show that our prediction about the fate of present theories is more likely to be true if we use the uniformity principle than if we use the disuniformity principle. (shrink)

Measures of inductive risk and of safety-principle violation help us to operationalize concerns about theological assertions or a sort which, as we saw in Part I, aggravate or intensify problems of religious luck. Our overall focus in Part II will remain on a) responses to religious multiplicity, and b) sharply asymmetrical religious trait-ascriptions to religious insiders and outsiders. But in Part II formal markers of inductive norm violation will supply an empirically-based manner of distinguishing strong from moderate fideism. As (...) we develop these markers we will elaborate their more specific connections with comparative study of religious fundamentalisms (chapters 3 and 4), with exclusivist responses to religious multiplicity (chapter 5), and with working hypotheses in cognitive science of religion (chapter 6). In Chapters 3 the special focus is on the need for comparative fundamentalism (hereafter CF), and on how a better inductive risk ‘toolkit’ can empower its development. The “Enemy in the Mirror” is a metaphor which researchers of CF have sometimes used to describe a phenomena of special concern. This allows that religious fundamentalism per se need not be morally or socially problem, and that the terms such as “fundamentalism” and “fideism should not be over-used by scholars. But the enemy-in-the-mirror phenomena, which gives rise to what I term “bias-mirroring” attributions of good/bad traits to religious insiders and outsiders, carries enormous moral risks. I argue that this is something researchers would do well to study. On the view to be developed, the enemy in the mirror phenomenon is a direct consequent of counter-inductive thinking when applied to a multiplicity of narrative testimonial traditions. (shrink)

In a previous paper, an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for (...) “n = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the two linked semigroups originating from addition and multiplication and from the Peano axioms in the final analysis can be postulated algebraically as independent of each other in a “Hamilton” modification of arithmetic supposedly equivalent to Peano arithmetic. The inductive proof of FLT can be deduced absolutely precisely in that Hamilton arithmetic and the pransfered as a corollary in the standard Peano arithmetic furthermore in a way accessible in Fermat’s epoch and thus, to himself in principle. A future, second part of the paper is outlined, getting directed to an eventual proof of the case “n=3” based on the qubit Hilbert space and the Kochen-Specker theorem inferable from it. (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)

Arthur Clark and Michael Kube–McDowell (“The Triger”, 2000) suggested the sci-fi idea about the direct transformation from a chemical substance to another by the action of a newly physical, “Trigger” field. Karl Brohier, a Nobel Prize winner, who is a dramatic persona in the novel, elaborates a new theory, re-reading and re-writing Pauling’s “The Nature of the Chemical Bond”; according to Brohier: “Information organizes and differentiates energy. It regularizes and stabilizes matter. Information propagates through matter-energy and mediates the interactions of (...) matter-energy.” Dr Horton, his collaborator in the novel replies: “If the universe consists of energy and information, then the Trigger somehow alters the information envelope of certain substances –“. “Alters it, scrambles it, overwhelms it, destabilizes it” Brohier adds. There is a scientific debate whether or how far chemistry is fundamentally reducible to quantum mechanics. Nevertheless, the fact that many essential chemical properties and reactions are at least partly representable in terms of quantum mechanics is doubtless. For the quantum mechanics itself has been reformulated as a theory of a special kind of information, quantum information, chemistry might be in turn interpreted in the same terms. Wave function, the fundamental concept of quantum mechanics, can be equivalently defined as a series of qubits, eventually infinite. A qubit, being defined as the normed superposition of the two orthogonal subspaces of the complex Hilbert space, can be interpreted as a generalization of the standard bit of information as to infinite sets or series. All “forces” in the Standard model, which are furthermore essential for chemical transformations, are groups [U(1),SU(2),SU(3)] of the transformations of the complex Hilbert space and thus, of series of qubits. One can suggest that any chemical substances and changes are fundamentally representable as quantum information and its transformations. If entanglement is interpreted as a physical field, though any group above seems to be unattachable to it, it might be identified as the “Triger field”. It might cause a direct transformation of any chemical substance by from a remote distance. Is this possible in principle? (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation (...) needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. A comparison to Mach’s doctrine is used to be revealed the fundamental and philosophical reductionism of Husserl’s phenomenology leading to a kind of Pythagoreanism in the final analysis. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. Thus the problem which of the two mathematics is more relevant to our being is discussed. An information interpretation of the Schrödinger equation is involved to illustrate the above problem. (shrink)

Many philosophers have been attracted to a restricted version of the principle of indifference in the case of self‐locating belief. Roughly speaking, this principle states that, within any given possible world, one should be indifferent between different hypotheses concerning who one is within that possible world, so long as those hypotheses are compatible with one's evidence. My first goal is to defend a more precise version of this principle. After responding to several existing criticisms of such a (...) principle, I argue that existing formulations of the principle are crucially ambiguous, and I go on to defend a particular disambiguation of the principle. According to the disambiguation I defend, how we should apply this restricted principle of indifference sensitively depends on our background metaphysical beliefs. My second goal is to apply this disambiguated principle to classical skeptical problems in epistemology. In particular, I argue that Eternalism threatens to lead us to external world skepticism, and Modal Realism threatens to lead us to inductive skepticism. (shrink)

Background: Smart sensors have been developed as diagnostic tools for rehabilitation to cover an increasing number of geriatric patients. They promise to enable an objective assessment of complex movement patterns. -/- Objective: This research aimed to identify and analyze the conflicting ethical values associated with smart sensors in geriatric rehabilitation and provide ethical guidance on the best use of smart sensors to all stakeholders, including technology developers, health professionals, patients, and health authorities. -/- Methods: On the basis of a systematic (...) literature search of the scientific databases PubMed and ScienceDirect, we conducted a qualitative document analysis to identify evidence-based practical implications of ethical relevance. We included 33 articles in the analysis. The practical implications were extracted inductively. Finally, we carried out an ethical analysis based on the 4 principles of biomedical ethics: autonomy, beneficence, nonmaleficence, and justice. The results are reported in categories based on these 4 principles. -/- Results: We identified 8 conflicting aims for using smart sensors. Gains in autonomy come at the cost of patient privacy. Smart sensors at home increase the independence of patients but may reduce social interactions. Independent measurements performed by patients may result in lower diagnostic accuracy. Although smart sensors could provide cost-effective and high-quality diagnostics for most patients, minorities could end up with suboptimal treatment owing to their underrepresentation in training data and studies. This could lead to algorithmic biases that would not be recognized by medical professionals when treating patients. -/- Conclusions: The application of smart sensors has the potential to improve the rehabilitation of geriatric patients in several ways. It is important that patients do not have to choose between autonomy and privacy and are well informed about the insights that can be gained from the data. Smart sensors should support and not replace interactions with medical professionals. Patients and medical professionals should be educated about the correct application and the limitations of smart sensors. Smart sensors should include an adequate representation of minorities in their training data and should be covered by health insurance to guarantee fair access. (shrink)

Biomarker-based predictive tests for subjectively asymptomatic Alzheimer’s disease (AD) are utilized in research today. Novel applications of artificial intelligence (AI) promise to predict the onset of AD several years in advance without determining biomarker thresholds. Until now, little attention has been paid to the new ethical challenges that AI brings to the early diagnosis in asymptomatic individuals, beyond contributing to research purposes, when we still lack adequate treatment. The aim of this paper is to explore the ethical arguments put forward (...) for AI aided AD prediction in subjectively asymptomatic individuals and their ethical implications. The ethical assessment is based on a systematic literature search. Thematic analysis was conducted inductively of 18 included publications. The ethical framework includes the principles of autonomy, beneficence, non-maleficence, and justice. Reasons for offering predictive tests to asymptomatic individuals are the right to know, a positive balance of the risk-benefit assessment, and the opportunity for future planning. Reasons against are the lack of disease modifying treatment, the accuracy and explicability of AI aided prediction, the right not to know, and threats to social rights. We conclude that there are serious ethical concerns in offering early diagnosis to asymptomatic individuals and the issues raised by the application of AI add to the already known issues. Nevertheless, pre-symptomatic testing should only be offered on request to avoid inflicted harm. We recommend developing training for physicians in communicating AI aided prediction. (shrink)

Scientific realism is the position that the aim of science is to advance on truth and increase knowledge about observable and unobservable aspects of the mind-independent world which we inhabit. This book articulates and defends that position. In presenting a clear formulation and addressing the major arguments for scientific realism Sankey appeals to philosophers beyond the community of, typically Anglo-American, analytic philosophers of science to appreciate and understand the doctrine. The book emphasizes the epistemological aspects of scientific realism and contains (...) an original solution to the problem of induction that rests on an appeal to the principle of uniformity of nature. (shrink)

Physical laws are strikingly simple, although there is no a priori reason they must be so. I propose that nomic realists of all types (Humeans and non-Humeans) should accept that simplicity is a fundamental epistemic guide for discovering and evaluating candidate physical laws. This principle of simplicity clarifies and addresses several problems of nomic realism and simplicity. A consequence is that the oft-cited epistemic advantage of Humeanism over non-Humeanism disappears, undercutting an influential epistemological argument for Humeanism. Moreover, simplicity is (...) shown to be more tightly connected to lawhood than to mere truth. (shrink)

Logical and Spiritual Reflections is a collection of six shorter philosophical works, including: Hume’s Problems with Induction; A Short Critique of Kant’s Unreason; In Defense of Aristotle’s Laws of Thought; More Meditations; Zen Judaism; No to Sodom. Of these works, the first set of three constitutes the Logical Reflections, and the second set constitutes the Spiritual Reflections. Hume’s Problems with Induction, which is intended to describe and refute some of the main doubts and objections David Hume raised with (...) regard to inductive reasoning. It replaces the so-called problem of induction with a principle of induction. David Hume’s notorious skepticism was based on errors of observation and reasoning, with regard to induction, causation, necessity, the self and freewill. These are here pointed out and critically analyzed in detail – and more accurate and logical theories are proposed. The present work also includes refutations of Hempel’s and Goodman’s alleged paradoxes of induction. A Short Critique of Kant’s Unreason, which is a brief critical analysis of some of the salient epistemological and ontological ideas and theses in Immanuel Kant’s famous Critique of Pure Reason. It shows that Kant was in no position to criticize reason, because he neither sufficiently understood its workings nor had the logical tools needed for the task. Kant’s transcendental reality, his analytic-synthetic dichotomy, his views on experience and concept formation, and on the forms of sensibility (space and time) and understanding (his twelve categories), are here all subjected to rigorous logical evaluation and found deeply flawed – and more coherent theories are proposed in their stead. In Defense of Aristotle’s Laws of Thought, which addresses, from a phenomenological standpoint, numerous modern and Buddhist objections and misconceptions regarding the basic principles of Aristotelian logic. Many people seem to be attacking Aristotle’s Laws of Thought nowadays, some coming from the West and some from the East. It is important to review and refute such ideas as they arise. More Meditations, which is a sequel to the author’s earlier work, Meditations. It proposes additional practical methods and theoretical insights relating to meditation and Buddhism. It also discusses certain often glossed over issues relating to Buddhism – notably, historicity, idolatry, messianism, importation to the West. Zen Judaism, which is a frank reflection on the tensions between reason and faith in today’s context of knowledge, and on the need to inject Zen-like meditation into Judaism. This work also treats some issues in ethics and theodicy. No to Sodom, which is an essay against homosexuality, using biological, psychological, spiritual, ethical and political arguments. (shrink)

The subject of the first section is Carnapian modal logic. One of the things I will do there is to prove that certain description principles, viz. the ''self-predication principles'', i.e. the principles according to which a descriptive term satisfies its own descriptive condition, are theorems and that others are not. The second section will be devoted to Carnapian modal arithmetic. I will prove that, if the arithmetical theory contains the standard weak principle of induction, modal truth collapses to (...) truth. Then I will propose a different formulation of Carnapian modal arithmetic and establish that it is free of collapse. Noteworthy is that one can retain the standard strong principle of induction. I will occupy myself in the third section with Carnapian epistemic logic and arithmetic. Here too it is claimed that the standard weak principle of induction is invalid and that the alternative principle is valid. In the fourth and last section I will get back to the self-predication principles and I will point to some of the consequences if one adds them to Carnapian Epistemic arithmetic. The interaction of self-predication principles and the strong principle of induction results in a collapse of de re knowability. (shrink)

Margaret MacDonald (1907–56) was a central figure in the history of early analytic philosophy in Britain due to both her editorial work as well as her own writings. While her later work on aesthetics and political philosophy has recently received attention, her early writings in the 1930s present a coherent and, for its time, strikingly original blend of common-sense and scientific philosophy. In these papers, MacDonald tackles the central problems of philosophy of her day: verification, the problem of induction, (...) and the relationship between philosophical and scientific method. MacDonald’s philosophy of science starts from the principle that we should carefully analyse the elements of scientific practice (particularly its temporal features) and the ways that scientists describe that practice. That is, she applies the techniques of ordinary language philosophy to actual scientific language. MacDonald shows how ‘scientific common-sense’ is inconsistent with both of the dominant schools of philosophy of her day. Bringing MacDonald back into the story of analytic philosophy corrects the impression that in early analytic philosophy, there are fundamental dichotomies between the style of Moore and Wittgenstein, on the one hand, and the Vienna Circle on the other. (shrink)

Among the most serious challenges to scientific realism are arguments for the underdetermination of theory by evidence. This paper defends a version of scientific realism against what is perhaps the most influential recent argument of this sort, viz. Kyle Stanford’s New Induction over the History of Science. An essential part of the defense consists in a probabilistic analysis of the slogan “absence of evidence is not evidence of absence”. On this basis it is argued that the likelihood of a (...) theory being underdetermined depends crucially on social and historical factors, such as the structure of scientific communities and the time that has passed since the theory first became accepted. This is then shown to serve as the epistemological foundation for a version of scientific realism which avoids Stanford’s New Induction in a principled and non-question-begging way. (shrink)

The inductive argument from evil to the non-existence of God contains the premise that, probably, there is gratuitous evil. Some skeptical theists object: one's justification for the premise that, probably, there is gratuitous evil involves an inference from the proposition that we don't see a good reason for some evil to the proposition that it appears that there is no good reason for that evil, and they use a principle, "CORNEA," to block that inference. The common sense problem of (...) evil threatens the CORNEA move, because the common sense problem of evil does not involve any inference to justify the belief that there is gratuitous evil. In this paper, I argue that the common sense problem of evil doesn't avoid CORNEA. CORNEA, or a reformulated version of it, can still prevent one from having justification for the belief that there is gratuitous evil. (shrink)

This book researches the thought of Jin Yuelin’s epistemology with some notions and methods of contemporary epistemology as the frame of reference. There are two kinds of academical significance in this book, one is that author has accurately comprehended the specific content, inadequacies and contradictions in Jin’ s epistemology, recognized the methods by which Jin Yuelin built his theory of knowledge. The other is that author has known about the differences in research objects and methods between Jin’s theory and contemporary (...) epistemology, and showed the position of Jin’s epistemology in the whole theory of knowledge through the comparative study. On the one hand, the book focuses on the core problem of Jin Yuelin’ epistemology that is how objective knowledge is produced. On the other hand, it is made up of seven chapters in accordance with the structure of Jin’s Theory of Knowledge. The first chapter introduces and comparatively analyzes the comprehensions about the concepts of “knowledge” and “epistemology” between Jin Yuelin and contemporary epistemologists. This chapter supplies the means and methods for following chapters. The second chapter describes Jin’s standpoint and criticism to idealism starting mode, analyzes the objective starting mode that belongs to Jin’s theory and reveals his negative attitude to skepticism. This chapter shows the essential characteristics of the Jin Yuelin’s epistemology. The given is the content of sensation, which is the most basic part of cognitive activity. Moreover Jin Yuelin regards sensation as foundation of knowledge, so the research on theory of the given is separated from the whole study of cognitive activity and treated as the third chapter, which presents Jin’s theory of the given and analyzes the problems of Jin’s theory, then introduces some kinds of theory of the given and theory of perception in the contemporary epistemology, finally comparatively investigates theories of the given between Jin Yuelin and contemporary epistemologists. From the perspective of cognitive activity, the fourth chapter describes the perceptual activity, the activity of knowing, the activity of thinking, means and outlines of reception in Jin’s epistemology, then exposes its contradictions and inadequacies; Induction is the important research object of the Western epistemologists, similarly Jin Yuelin paid more attention to induction and regards the principle of induction as outline of reception. In fact, his standpoint about the principle of induction is vital and creative, so the study of induction separately belongs to the fifth chapter. This chapter presents the Jin’s comprehension about the principle of induction and some answers to the problem of induction in contemporary epistemology, then comparatively analyzes two kinds of the thought about induction. The sixth chapter successively introduces being, nature and fact which all are objects of cognitive activity, then analyzes the problems within them. From the perspective of cognitive results, the last chapter presents the Jin’s standpoint about verification and demonstration of proposition, definition and criteria of truth, then simply describes the point views of contemporary epistemologists about verification and truth of proposition, finally comparatively investigates two kinds of thought. From the vertical, the thesis analyzes the fundamental sections of objective knowledge one by one, such as the given, experience, idea, proposition and truth. From the horizontal, the book focuses on the three main parts of knowledge event, for example, cognitive activity, objects of knowledge and the true proposition treated as knowledge. In a word, the whole book is coherent and organic unity. Through the comparative study, it can be concluded that it is reasonable for Jin Yuelin to enjoy a high academic status, because he is the first philosopher who specializes in the study of epistemology. At the same times, he improves transmission of logic, metaphysics and epistemology from the Western to China. So, his hard work enriches and expands the realm of Chinese philosophy. With the development of the study of epistemology, descriptive content of it, such as, perceptual activity and rational activity, will be regarded as the objects of psychology and cognitive science. Meanwhile, normative content will be retained. For example, analysis of conditions of knowledge, justification for belief claims, comprehension about the proofs of justification, as well as reactions to challenges of skepticism. The latter will continue to be objects of epistemology, of course, they must establish close relationships with psychology and cognitive science. According to this prospect, we should split Jin Yuelin’s theory of knowledge, of which the descriptive content would be allocated to psychology and cognitive science. On the contrary, the normative content would be kept as important resource for deeply studying epistemology. -/- Key words: Knowledge; Contemporary epistemology; Compare; The given; Idea; The principle of induction; Fact. (shrink)

The objective of the paper is the methodological presentation of the basic principles towards a critical interdisciplinary approach for studying the history of monuments restoration, valid for different cultures. The proposed integrated framework offers the possibility to study and document monuments restoration in various spatial levels e.g. global, continental, international, national, regional, and local. The conceptual and methodological aspects are based on the following fundamental pillars a) the development of science and technology, including relevant history of education, b) the evolution (...) of the restoration philosophy, c) the incorporation of the above in restoration projects at a lower level, d) the infiltration of the above in restoration interventions at the lowest level. The author expects that the above successive and/or parallel levels of scientific branches can contribute effectively to the analysis, synthesis and comparative assessment of the aspects and criteria that influenced monuments restoration timeline. The challenge for the researcher of the monuments restoration history is the adjustment of the whole process to his own –under research- level in such a way as to take advantage of all theinterdisciplinary inputs creating, thus, inventive links and stimulating new information and knowledge. The above are briefly tested in the case study of Thessaloniki, Macedonia, Greece. Such an inductive approach will enable all disciplines to devote their finest efforts towards understanding, documenting and studying monuments restoration history and, thus, support effectively a sustainable future for the world’s cultural heritagel audience. (shrink)

Judaic Logic is an original inquiry into the forms of thought determining Jewish law and belief, from the impartial perspective of a logician. Judaic Logic attempts to honestly estimate the extent to which the logic employed within Judaism fits into the general norms, and whether it has any contributions to make to them. The author ranges far and wide in Jewish lore, finding clear evidence of both inductive and deductive reasoning in the Torah and other books of the Bible, and (...) analyzing the methodology of the Talmud and other Rabbinic literature by means of formal tools which make possible its objective evaluation with reference to scientific logic. The result is a highly innovative work – incisive and open, free of clichés or manipulation. Judaic Logic succeeds in translating vague and confusing interpretative principles and examples into formulas with the clarity and precision of Aristotelean syllogism. Among the positive outcomes, for logic in general, are a thorough listing, analysis and validation of the various forms of a-fortiori argument, as well as a clarification of dialectic logic. However, on the negative side, this demystification of Talmudic/Rabbinic modes of thought (hermeneutic and heuristic) reveals most of them to be, contrary to the boasts of orthodox commentators, far from deductive and certain. They are often, legitimately enough, inductive. But they are also often unnatural and arbitrary constructs, supported by unverifiable claims and fallacious techniques. Many other thought-processes, used but not noticed or discussed by the Rabbis, are identified in this treatise, and subjected to logical review. Various more or less explicit Rabbinic doctrines, which have logical significance, are also examined in it. In particular, this work includes a formal study of the ethical logic (deontology) found in Jewish law, to elicit both its universal aspects and its peculiarities. With regard to Biblical studies, one notable finding is an explicit formulation (which, however, the Rabbis failed to take note of and stress) of the principles of adduction in the Torah, written long before the acknowledgement of these principles in Western philosophy and their assimilation in a developed theory of knowledge. Another surprise is that, in contrast to Midrashic claims, the Tanakh (Jewish Bible) contains a lot more than ten instances of qal vachomer (a-fortiori) reasoning. In sum, Judaic Logic elucidates and evaluates the epistemological assumptions which have generated the Halakhah (Jewish religious jurisprudence) and allied doctrines. Traditional justifications, or rationalizations, concerning Judaic law and belief, are carefully dissected and weighed at the level of logical process and structure, without concern for content. This foundational approach, devoid of any critical or supportive bias, clears the way for a timely reassessment of orthodox Judaism (and incidentally, other religious systems, by means of analogies or contrasts). Judaic Logic ought, therefore, to be read by all Halakhists, as well as Bible and Talmud scholars and students; and also by everyone interested in the theory, practise and history of logic. (shrink)

The primary aim of this paper is to critically evaluate the deductive model of ethical applications, which is based on normative ethical theories like deontology and consequentialism, and to show why a number of models have failed to furnish appropriate resolutions to practical moral problems. Here, for the deductive model, I want to call it a “Linear Mechanical Model” because the basic assumption of this model is that if a normative theory is sacrosanct, then the case is as it is. (...) The conclusion derived from the case will also be correct, true and acceptable. However, traditional ethicists used to apply their ethical theories, but they did not know which moral theory was effective on the ground level of reality. The study will show readers how ethical theories are in conflict with each other in the case of euthanasia. In more precise words, “which ethical theories are said to be applied, meta-ethical or normative, or both for the resolution of ethical problems? If normative theories are said to be applied, how the application can take place when it is contrary to our experience, that (then) in a situation of moral crises, no one really applies a theory?” For that, my argument is the linear model has failed because it is rigid, often ignores the agents’ intrinsic values, and has no space to amend it, no matter how bizarre the consequence is. Its alternative is the Inductive model. For that, the paper will take three moral principles (autonomy, beneficence including maleficence, and justice) of Beauchamp & Childress. This suggests us for resolving value-laden moral problems, we should consider some steps such as a) recognising moral issues to start with; b) developing the moral imagination; c) sharpening analytical/critical skills; d) testing out disagreements; e) effecting decisions and behavior; and f) implementation, closure, and process are of vital importance, in other words, it starts with the free and informed consensus of all interested parties, but this model also has been failed because the model could not give a systematic organization to their way of resolution. Here, my argument is that the inductive model provides resolution of the practical problem but ignores what is ethically obligatory, permissible, or wrong in that situation, and there are no appropriate suggestions in the case of a moral crisis. (shrink)

In this paper intuitionistic set theory INC# in infinitary set theoretical language is considered. External induction principle in nonstandard intuitionistic arithmetic were derived. Non trivial application in number theory is considered.

My paper builds on the conceptual tools from three interrelated philosophical debates that—as I believe—may help structure important if chaotic discussions about surrogates for living human brains and resolve some practical issues related to regulatory matters. In particular, I refer to the discussions about the “moral precautionary principle” in research ethics (Koplin and Wilkinson 2019); about normative uncertainty in ethics (MacAskill, Bykvist, and Ord 2020), and about the inductive risk problem for animal welfare scientists (Birch 2018). I elucidate upon (...) the possible meanings of the phrase “a too good human brain surrogate” used by Henry T. Greely (2021), and I demonstrate that the evaluation of the practical and regulatory implications of the “goodness” of such surrogates created for research purposes should be sensitive to the possible consequences of two types of errors: the under-attribution and over-attribution of moral status to such beings. Many authors writing about this topic (including Greely 2021, but see also, e.g., Koplin and Savulescu 2019) concentrate only on the first type of error, neglecting the negative consequences of the second type, i.e., over-attribution. (shrink)

The article discusses the actual problem of social support for people with mental health problems, which has an important place in the study field of social psychology and social work.The article also deals with the definition of the concept of “mental health”, the problem of introducing the term “mental health problems” as a way to avoid stigmatization, and the spread of a humanistic attitude to persons with a psychiatric diagnosis. It also discussed modern theoretical approaches that offer an understanding of (...) the contribution of biological, social, and psychological factors into the cause of mental health problems. -/- The problem of mental illness is common to all countries of the world, as WHO data evidenced the number of people with mental disorders among the world’s population, ranging from 4–5 %. According to researchers P. Voloshin and N. Maruta, the spread of mental and behavioral disorders in Ukraine is characterized by a slow increase of about 2.9 % in every 10 years. Researchers argue that in subsequent years, according to the prognostic data, there will be an increase in these indicators. The issue of providing social support to people with PDS in Ukrainian society is very relevant, which is complicated by their social isolation in the process of recovery after the treatment. The results of scientific research in the context of different cultures and relatively diverse life events (hospitalization, mental illness, unemployment, old age) generally confirm the positive results of using social support to promote mental and physical health. Instead, there are no studies in Ukrainian science related to the phenomenon of social support of people with mental health problems. -/- It is important to define the concepts of “mental health” and “mental health problems” in the process of studying the features of social support for people with mental health problems. The term “mental health” combines the medical and psychological fields of science and practice, but modern psychology offers a comprehensive approach to assessing the psychological health of a person, the psychological norm, its limits, taking into account the criteria of mental health. The description of the mental health given by the Psychological Dictionary points out the components of awareness and the sense of continuity, continuity and identity of their physical and mental “I”; sense of continuity and identity of experiences in similar situations; critical to yourself and your mental activity and its results; the adequacy of psychic reactions of force and frequency of environmental influences; the ability to manage their behavior in accordance with social norms; planning personal activities and implementing them; changing the way of behavior depending on the changing circumstances of life. -/- The concept of “mental health problem” was taken as a term that denotes all the symptoms classified in ICD-10 and DSM-IV, which are recommended by experts to clients for appropriate treatment and care. Scientists and mental health practitioners point out that mental health problems can affect the way an individual thinks, feels, and behaves; affects self-service, fulfills professional duties, social, family roles, and household behavior, which is usually deeply affected by the quality of life of the individual. Numerous results of the research show that there are specific psychological and personality factors apart from the biological causes of mental disorders (genetic factors that contribute to the imbalance of chemicals in the brain) that make people vulnerable to occurrences of the mental health problems. -/- Several modern theoretical approaches offer an understanding of the contribution of biological, social, and psychological factors to the induction of mental health problems: the traditional medical model, the rehabilitation model, the interface model, the social model, and the biopsychosocial approach. Only biopsychosocial and social models are consistent with the definition of WHO disability and emphasize the impact social aspects of mental health and the quality of life of people with mental health problems. -/- Individuals with PPP, as a social community, have specific needs that differentiate them from other members of society, one of which is the need for constant socio-psychological support. So, the contribution of psychology and social work to the quality of life of people with mental disorder lies in the application of professional approaches and methods based on the biopsychosocial (social) model, which emphasize the need for socio-psychological support. An example of such a technique is the model of modern social work practice “people-in-environment”, which serves as a guiding principle of social work and emphasizes the importance of understanding the persons with disorder and their behavior in the light of the multiple context of the social environment in which these persons live and act. Specialists of social work and psychology make interventions at three levels: individual, at the family level, and at the community level, by means of intensifying the support of the environment within the cognitive-behavioral and other approaches, which contribute to the process of reintegrating people with mental health problems into community. (shrink)