The main objective of this PhD Thesis is to present a method of obtaining strong normalization via natural ordinal, which is applicable to natural deduction systems and typed lambda calculus. The method includes (a) the definition of a numerical assignment that associates each derivation (or lambda term) to a natural number and (b) the proof that this assignment decreases with reductions of maximal formulas (or redex). Besides, because the numerical assignment used coincide with the length of a specific sequence of (...) reduction - the worst reduction sequence - it is the lowest upper bound on the length of reduction sequences. The main commitment of the introduced method is that it is constructive and elementary, produced only through analyzing structural and combinatorial properties of derivations and lambda terms, without appeal to any sophisticated mathematical tool. Together with the exposition of the method, it is presented a comparative study of some articles in the literature that also get strong normalization by means we can identify with the natural ordinal methods. Among them we highlight Howard[1968], which performs an ordinal analysis of Godel’s Dialectica interpretation for intuitionistic first order arithmetic. We reveal a fact about this article not noted by the author himself: a syntactic proof of strong normalization theorem for the system of typified lambda calculus λ⊃ is a consequence of its results. This would be the first strong normalization proof in the literature. (written in Portuguese). (shrink)

Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on the (...) scope of quantifiers reveals a natural way out. (shrink)

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

In his 1927 Analysis of Matter and elsewhere, Russell argued that we can successfully infer the structure of the external world from that of our explanatory schemes. While nothing guarantees that the intrinsic qualities of experiences are shared by their objects, he held that the relations tying together those relata perforce mirror relations that actually obtain (these being expressible in the formal idiom of the Principia Mathematica). This claim was subsequently criticized by the Cambridge mathematician Max Newman as true but (...) trivial, insofar as from a closed body of observations (or “Ramsey sentence”) one can always generate other equally-satisfactory networks of relations, provided they respect the original set’s cardinality. Since any model thus generated will be empirically adequate, “[t]he defence is therefore driven back from the fairly safe fictitious-real classification to the much less tenable ‘trivial’ and ‘important’” (Newman 1928). Given the definitional rigour afforded by the initial appeal to isomorphism (via one-to-one correspondences in extension), the received assessment, shared by Russell himself, is that retreating to a pragmatic adjudication would betoken a fatal blow. However, I suggest that reliance on “importance” can be avoided if we incorporate an impersonal criterion of diachronic precedence. When collecting observations, an ordinality emerges alongside the cardinality which gives that underived structure an irrevocable epistemological privilege. Hence, I argue that, all other things being equal, any construct parasitic on an antecedent theory ought to be regarded as inferior/dispensable, since it was generated by an algorithm lacking the world-involving pedigree of its host structure. (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)

It is discerned what light can bring the recent historical reconstructions of maxwellian optics and electromagnetism unification on the following philosophical/methodological questions. I. Why should one believe that Nature is ultimately simple and that unified theories are more likely to be true? II. What does it mean to say that a theory is unified? III. Why theory unification should be an epistemic virtue? To answer the questions posed genesis and development of Maxwellian electrodynamics are elucidated. It is enunciated that the (...) Maxwellian Revolution is a far more complicated phenomenon than it may be seen in the light of Kuhnian and Lakatosian epistemological models. Correspondingly it is maintained that maxwellian electrodynamics was elaborated in the course of the old pre-maxwellian programmes’ reconciliation: the electrodynamics of Ampére-Weber, the wave theory of Young-Fresnel and Faraday’s programme. To compare the different theoretical schemes springing from the different language games James Maxwell had constructed a peculiar neutral language. Initially it had encompassed the incompressible fluid models; eventually – the vortices ones. The three programmes’ encounter engendered the construction of the hybrid theory at first with an irregular set of theoretical schemes. However, step by step, on revealing and gradual eliminating the contradictions between the programmes involved, the hybrid set is “put into order” (Maxwell’s term). A hierarchy of theoretical schemes starting from ingenious crossbreeds (the displacement current) and up to usual hybrids is set up. After the displacement current construction the interpenetration of the pre-maxwellian programmes begins that marks the commencement of theoretical schemes of optics, electricity and magnetism real unification. Maxwell’s programme surpassed that of Ampére-Weber because it did absorb the ideas of the Ampére-Weber programme, as well as the presuppositions of the programmes of Young-Fresnel and Faraday properly co-ordinating them with each other. But the opposite statement is not true. The Ampére-Weber programme did not assimilate the propositions of the Maxwellian programme. Maxwell’s victory over his rivals became possible because the gist of Maxwell’s unification strategy was formed by Kantian epistemology looked in the light of William Whewell and such representatives of Scottish Enlightenment as Thomas Reid and Sir William Hamilton. Maxwell did put forward as basic synthetic principles the ideas that radically differed from that of Ampére-Weber approach by their open, flexible and contra-ontological, genuinly epistemological, Kantian character. For Maxwell, ether was not the ultimate building block of physical reality, from which all the charges and fields should be constructed. “Action at a distance”, “incompressible fluid”, “molecular vortices”, etc. were contrived analogies for Maxwell, capable only to direct the researcher at the “right” mathematical relations. Key words: J.C. Maxwell, unification of optics and electromagnetism, I. Kant, T. Reid, W. Hamilton . (shrink)

We aim to compile some means for a rational reconstruction of a named part of the start-over of Baruch (Benedictus) de Spinoza's metaphysics in 'de deo' (which is 'pars prima' of the 'ethica, ordine geometrico demonstrata' ) in terms of 1st order model theory. In so far, as our approach will be judged successful, it may, besides providing some help in understanding Spinoza, also contribute to the discussion of some or other philosophical evergreen, e.g. 'ontological commitment'. For this text we (...) assume the reader familiar with 'de deo' as well as with some basic concepts and results of 1st order model theory. Before we start reconstruction, we will first revisit shortly the concept of 'attributum' (definitio IV) in it's setting in 'de deo' , next scan for formalizable aspects of 'in suo genere finita' ('de deo', definitio II), subsequently list the model theoretic constructs we will make use of. Then we begin reconstruction by stating "coordinative definitions" for the notions of 'attribute (of a substance)', 'modus (as conceived via an attribute)' and 'substance (as conceived via an attribute)', reasoning shortly for each of them. The "coordinative definitions", we will arrive at, must not be understood as literal translations of Spinoza's concepts - of course, there can't be such a thing as a literal translation - they are meant as formal analoga of these concepts, mapping some logical structure. But even with this caveat they may seem strange to the reader at this stage of discussion. Additional justification for them then should be found in our endeavour, to map some argumentation of Spinoza's proofs of some of his propositions from this starting point. -/- [ Version 1 of this paper originated from 2020-03-14. This is version 2 from 2021-09-12 with some readability amendments. ]. (shrink)

The purpose of this paper is to communicate - as a proposal - a general method of assigning a 'truthmaker' to any 1st order sentence in each of its models. The respective construct is derived from the standard model theoretic (recursive) satisfaction definition for 1st order languages and is a conservative extension thereof. The heuristics of the proposal (which has been somewhat idiosyncratic from the current point of view) and some more technical detail of the construction may be found in (...) my article on part I of Spinoza's 'ethica, ordine geometrico demonstrata', which is the context within which I elaborated the assignment. But this context need not be repeated here, the presentation of the truthmaker assignment will be comprehensible to anybody with solid basic knowledge in 1st order model theory, anything used is standard and no advanced techniques are required. (shrink)

Harry Wolfson’s celebrated two-volume study of Spinoza – The Philosophy of Spinoza: Unfolding the Latent Process of His Reasoning – appeared in 1934 with Harvard University Press. The book originated in a series of five studies Wolfson published in the Chronicon Spinozanum between 1921 and 1926. In the Chronicon, Wolfson announced that the studies published in the journal are instalments from a planned larger work, to be titled: “Spinoza, the Last of the Mediaevals: A Study of the Ethica Ordine Geometrico (...) Demonstrata in the light of a hypothetically constructed Ethica More Scholastico Rabbinicoque Demonstrata.” In the preface to the 1934 book, Wolfson notes that the original title “had to be abandoned, as it did not seem advisable to have the title begin with the word ‘Spinoza’”. Thus, whatever stylistic reasons motivated Wolfson to amend the title, he was clearly not withdrawing from his view of Spinoza’s Ethics as being “More Scholastico Rabbinicoque Demonstrata.”. (shrink)

An orbital simulation program is described that uses a geometrical approach to modeling gravitational and atomic orbits at the Planck scale. Orbiting objects A, B, C... are sub-divided into points, each point representing 1 unit of Planck mass, for example, a 1kg satellite would divide into 1kg/Planck mass = 45940509 points. Each point in object A then forms a rotating orbital pair with every corresponding point in objects B, C... resulting in a universe-wide, n-body network of rotating point-to-point orbital pairs. (...) Each orbital pair rotates 1 unit of Planck length per unit of Planck time at velocity c in hypersphere space co-ordinates, the results are then summed and averaged to give the new co-ordinates, the program then repeats. When these rotations are mapped over time on a 2-D plane (representing 3D space), objects A, B, C... appear to be orbiting each other. The basic simulation uses the fine structure constant alpha as an orbital constant to simulate gravitational orbit parameters. As each orbital comprises only 2 points, 1 at each orbital pole, information regarding the objects A, B, C... ; momentum, size, center of mass, barycenter etc ... is not required, instead only the start (x, y, z) co-ordinates of each point are defined. Each point, by having a mass of Planck mass, is itself a construct of multiple particles, and so we can also form individual particle to particle orbital pairs. The simulation uses only geometry, no dimensioned constants (G, h, c ...) are required, although the results can be measured in Planck units for comparison. Points are physically linked together by a unit of momentum (a graviton), the rationale for this is described in a subsequent article on atomic orbitals. (shrink)

Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty ordinal construction and his fundamental powerset description of the continuum, Cantor has also left to us his obsessive presumption that the universe of sets should be subjected to laws similar to those governing the set of natural numbers, including the universal principles of cardinal comparability (...) and well-ordering -- and implying an ordinal re-creation of the continuum. During the last hundred years, the mainstream set-theoretical research -- all insights and adjustments due to Kurt G\"odel's revolutionary insights and discoveries notwithstanding -- has compliantly centered its efforts on ad hoc axiomatizations of Cantor's intuitive transfinite design. We demonstrate here that the ontological and epistemic sustainability} of this design has been irremediably compromised by the underlying peremptory, Reductionist mindset of the XIXth century's ideology of science. (shrink)

A possible world is a junky world if and only if each thing in it is a proper part. The possibility of junky worlds contradicts the principle of general fusion. Bohn (2009) argues for the possibility of junky worlds, Watson (2010) suggests that Bohn‘s arguments are flawed. This paper shows that the arguments of both authors leave much to be desired. First, relying on the classical results of Cantor, Zermelo, Fraenkel, and von Neumann, this paper proves the possibility of junky (...) worlds for certain weak set theories. Second, the paradox of Burali-Forti shows that according to the Zermelo-Fraenkel set theory ZF, junky worlds are possible. Finally, it is shown that set theories are not the only sources for designing plausible models of junky worlds: Topology (and possibly other "algebraic" mathematical theories) may be used to construct models of junky worlds. In sum, junkyness is a relatively widespread feature among possible worlds. (shrink)

The concept of expression has always held an important place in Fernando Gil’s thought. The author’s reflection on the idea of expression is well reflected among his writings – either in his early essays or throughout his entire work –, attaining a special focus in the lectures that he gave at Johns Hopkins University during the years of 2002, 2003 and 2004. Actually, these lectures represent the strongest testimony of the relevancy given by Fernando Gil to this concept. However, despite (...) being a concept which crosses all his work, clearly having a central place in his thought, Fernando Gil never got to write a systematic theory on the concept of expression. Thus, closely following the author’s works, the main purpose of this study is to suggest a personal vision of what could have been Fernando Gil’s theory on expression. Combining some of the main ideas of Johns Hopkins lectures to some fundamental notions of Fernando Gil’s thought, we will try to show that Fernando Gil’s theory on expression is a theory on the ordination of thought, on cognitive construction and, above all, a theory on the elevation of thought to what shall be considered its higher modality, the aesthetical thought. In fact, our major hypothesis is that Fernando Gil’s theory on expression is not only a cognitive theory but also an aesthetical one. As such, its major guidelines shall be: to explain the adequacy of expression to its objects; to show how expression evolves according to the cognitive development of the subject; and, finally, to explain and to justify the elevation of thought to universality, harmony and beauty. (shrink)

It is widely held that under ordinal utility, utility differences are ill-defined. Allegedly, for these to be well-defined (without turning to choice under risk or the like), one should adopt as a new kind of primitive quaternary relations, instead of the traditional binary relations underlying ordinal utility functions. Correlatively, it is also widely held that the key structural properties of quaternary relations are entirely arbitrary from an ordinal point of view. These properties would be, in a nutshell, the hallmark of (...) cardinal utility. While much is obviously true in these two tenets, this note explains why, as stated, they should be abandoned. Any ordinal utility function induces a rich quaternary relation. There is such a thing as ordinal utility differences. Furthermore, this induced quaternary relation respects, apart from completeness, the most standard structural properties of quaternary relations. These properties are, from an ordinal point of view, anything but arbitrary; from a quaternary perspective only completeness should be considered the hallmark—if any—of cardinal utility. These facts are explained to be especially relevant to the critical appreciation of the ordinalist methodology. (shrink)

Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While STT, understood as (...) a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

Transfinite ordinal numbers enter mathematical practice mainly via the method of definition by transfinite recursion. Outside of axiomatic set theory, there is a significant mathematical tradition in works recasting proofs by transfinite recursion in other terms, mostly with the intention of eliminating the ordinals from the proofs. Leaving aside the different motivations which lead each specific case, we investigate the mathematics of this action of proof transforming and we address the problem of formalising the philosophical notion of elimination which (...) characterises this move. (shrink)

The aim of this paper is to bring recent work on metaphysical grounding to bear on the phenomenon of social construction. It is argued that grounding can be used to analyze social construction and that the grounding framework is helpful for articulating various claims and commitments of social constructionists, especially about social identities, e.g., gender and race. The paper also responds to a number of objections that have been leveled against the application of grounding to social construction from Elizabeth Barnes, (...) Mari Mikkola, and Jessica Wilson. (shrink)

Niche construction theory highlights the active role of organisms in modifying their environment. A subset of these modifications is the developmental niche, which concerns ecological, epistemic, social and symbolic legacies inherited by organisms as resources that scaffold their developmental processes. Since in this theory development is a situated process that takes place in a culturally structured environment, we may reasonably ask if implicit cultural biases may, in some cases, be responsible for maladaptive developmental niches. In this paper we wish to (...) argue for an affirmative answer. In order to do so, we first propose to conceptualize implicit bias as embodied perceptual habits, and then proceed to show that these habits are at least partially responsible for maladaptive developmental niches of children with Down syndrome and autism. With this framework we thus hope to bring together two fields of research that haven’t been explicitly connected: implicit bias and niche construction theory. Linking these two theories may bring benefits both to implicit bias researchers, who can extend this concept to characterize other sets of processes as biased, as well as to niche construction theorists, who will have a useful theoretical tool to diagnose maladaptive features of niches brought about by sociocultural biases. (shrink)

This is the commentary on John Baker, "H. P. Grice's Construction of Value", read at the 34th Annual Congress of the Canadian Philosophical Association, May 1990, Victoria, British Columbia.

Constructive empiricism implies that if van Fraassen does not believe that scientific theories and his positive philosophical theories, including his contextual theory of explanation, are empirically adequate, he cannot accept them, and hence he cannot use them for scientific and philosophical purposes. Moreover, his epistemic colleagues, who embrace epistemic reciprocalism, would not believe that his positive philosophical theories are empirically adequate. This epistemic disadvantage comes with practical disadvantages in a social world.

This paper looks at the question of what it means for a psychological test to have construct validity. I approach this topic by way of an analysis of recent debates about the measurement of implicit social cognition. After showing that there is little theoretical agreement about implicit social cognition, and that the predictive validity of implicit tests appears to be low, I turn to a debate about their construct validity. I show that there are two questions at stake: First, what (...) level of detail and precision does a construct have to possess such that a test can in principle be valid relative to it? And second, what kind of evidence needs to be in place such that a test can be regarded as validated relative to a given construct? I argue that construct validity is not an all-or-nothing affair. It can come in degrees, because both our constructs and our knowledge of the explanatory relation between constructs and data can vary in accuracy and level of detail, and a test can fail to measure all of the features associated with a construct. I conclude by arguing in favor of greater philosophical attention to processes of construct development. (shrink)

Inspired by Rudolf Carnap's Der Logische Aufbau Der Welt, David J. Chalmers argues that the world can be constructed from a few basic elements. He develops a scrutability thesis saying that all truths about the world can be derived from basic truths and ideal reasoning. This thesis leads to many philosophical consequences: a broadly Fregean approach to meaning, an internalist approach to the contents of thought, and a reply to W. V. Quine's arguments against the analytic and the a priori. (...) Chalmers also uses scrutability to analyze the unity of science, to defend a conceptual approach to metaphysics, and to mount a structuralist response to skepticism. Based on the 2010 John Locke lectures, Constructing the World opens up debate on central philosophical issues involving language, consciousness, knowledge, and reality. This major work by a leading philosopher will appeal to philosophers in all areas. This entry contains uncorrected proofs of front matter, chapter 1, and first excursus. (shrink)

There is a widely held view on measurement inferences, that goes back to Stevens’s ([1946]) theory of measurement scales and ‘permissible statistics’. This view defends the following prohibition: you should not make inferences from averages taken with ordinal scales (versus quantitative scales: interval or ratio). This prohibition is general—it applies to all ordinal scales—and it is sometimes endorsed without qualification. Adhering to it dramatically limits the research that the social and biomedical sciences can conduct. I provide a Bayesian analysis of (...) this inferential problem, determining when measurements from ordinal scales can be used to confirm hypotheses about relative group averages. The prohibition, I conclude, cannot be upheld, even in a qualified sense. The beliefs needed to make average comparisons are less demanding than those appropriate for quantitative scales. I illustrate with the alleged paradigm ordinal scale, Mohs’ scale of mineral hardness, arguing that the literature has mischaracterized it. (shrink)

Georg Cantor's absolute infinity, the paradoxical Burali-Forti class Ω of all ordinals, is a monstrous non-entity for which being called a "class" is an undeserved dignity. This must be the ultimate vexation for mathematical philosophers who hold on to some residual sense of realism in set theory. By careful use of Ω, we can rescue Georg Cantor's 1899 "proof" sketch of the Well-Ordering Theorem––being generous, considering his declining health. We take the contrapositive of Cantor's suggestion and add Zermelo's choice (...) function. This results in a concise and uncomplicated proof of the Well-Ordering Theorem. (shrink)

It is argued that, contrary to prevailing opinion, Bas van Fraassen nowhere uses the argument from underdetermination in his argument for constructive empiricism. It is explained that van Fraassen’s use of the notion of empirical equivalence in The Scientific Image has been widely misunderstood. A reconstruction of the main arguments for constructive empiricism is offered, showing how the passages that have been taken to be part of an appeal to the argument from underdetermination should actually be interpreted.

ABSTRACT (ENG) One of the concerns of Greek philosophy centred on the question of how a manifold and ordered universe arose out of the primitive state of things. From the mythical accounts dating around the seventh century B.C. to the cosmologies of the Classical period in Ancient Greece, many theories have been proposed in order to answer to this question. How these theories differ in positing a “something” that pre-existed the ordered cosmos has been widely discussed. However, scholars have rarely (...) made explicit how they differ in style of thought. In the span of four centuries the first deductive arguments of the Eleatic philosophers culminated in the emergence of logical proof and a form of explanation of natural phenomena, which consisted of searching for the simplest and fewest premises and deducting implications. In this paper it will be discussed how, at distinct stages of its development, the deductive thinking informed the solutions proposed to solve the chaos-order problem, that of how an ordered universe has been possible. -/- ABSTRACT (ITA) Una delle più importanti questioni della filosofia greca è stata quella di comprendere come sia stato possibile un universo ordinato a partire da uno stato primordiale. Dalle teogonie del VII secolo a.C. fino alle cosmologie dei filosofi dell’età classica, sono state proposte diverse teorie per dare risposta a questa domanda. Come esse differiscano nel postulare l’esistenza di un “qualcosa” di primordiale che preesisteva all’ordine del cosmo è stato molto discusso. Pochi studiosi, però, le hanno esaminate sullo sfondo della lenta evoluzione del pensiero deduttivo, culminata nella dimostrazione in geometria e in una forma di spiegazione dei fenomeni che consisteva nel cercare semplici premesse e inferire conclusioni. In questo articolo si mostrerà come il lento affermarsi della spiegazione razionale prima, dell’argomento deduttivo e della dimostrazione in geometria poi, abbiano dato forma alle diverse risposte al problema caos-ordine, e in particolare alla domanda su come sia sorto un universo ordinato. (shrink)

Niche construction is a concept that captures a wide array of biological phenomena, from the environmental effects of metabolism to the creation of complex structures such as termite mounds and beaver dams. A central point in niche construction theory is that organisms do not just passively undergo developmental, ecological, or evolutionary processes, but are also active participants in them Evolution: From molecules to men, Cambridge University Press, Cambridge, 1983; Laland KN, Odling-Smee J, Feldman MW, In: KN Laland and T Uller (...) Evolutionary causation: Biological and philosophical reflections, MIT Press, Cambridge, MA, 2019). In this paper, we distinguish between two fundamentally different ways in which organisms are active participants: as agents and as contributors. Roughly, organisms act as agents when niche constructing effects are a result of a goal-directed behavior over which the organisms have some degree of control. Organisms act as contributors when the niche constructing effects do not arise from a goal to perform the constructive activity. As illustrative examples we discuss plants altering leaf-morphology to optimize light exposure as reported by Sultan and bacteria creating novel niches through excreting energy-rich metabolites. The difference between agential and contributional niche construction is important for understanding the different ways organisms can actively participate in development, ecology, and evolution. Additionally, this distinction can increase our understanding of how the capacity of agency is distributed across the tree of life and how agency influences developmental and evolutionary processes. (shrink)

With an extensive amount of research on the social lives of primates, Frans de Waal has been a pioneering advocate for the continuity of human and non-human minds, putting forward the idea that these creatures exhibit rudimentary political and moral behaviors. One of the traits which de Waal focuses on is animal normativity, a set of behaviors functionally defined as adherence to social standards. Recently, some philosophers have endorsed this position, holding that animals show a psychological capacity called normative cognition (...) underlying those and other social behaviors. In this paper, I assess whether advocacy for animal normativity is an exercise of theory construction in comparative cognition. To that end, I present three features of this kind of theory construction. First, the explanatory goal of building functional analyses of cognitive capacities. Second, the conceptual aid of comparative thinking for theory construction. Third, the heuristic value of theory in specifying possible roads of inquiry. Taking these features into account, I assess whether the claims advocates make regarding animal normativity consider them. My answer is negative. First, since some advocates focus on behavioral traits and not on psychological capacities, they are not producing theory in comparative cognition, although, as I argue, they should. Second, there is a disregard for hypothesis testing and no evolutionary considerations to support their views. Finally, the claim that non-human animals exhibit normativity does not seem to have heuristic value. (shrink)

How easy is it to construct life and consciousness from the building blocks of reality? Some philosophers seem to think both are pretty easy, whilst others take consciousness to be difficult but life to be no problem. In this paper I question whether we should in fact think this, could life after all be difficult to construct? I contend that the answer to this, much like the answer to how hard consciousness is to construct, largely depends on the nature of (...) life and the building blocks of reality. I will show that many of the considerations as to whether consciousness is hard to construct can be paralleled when thinking about the construction of life, and that given one prominent definition of life, it does in fact seem difficult to construct. I will conclude by offering a few suggestions for future research, and suggest that philosophers should be more hesitant in their affirmation that life is easy to construct. (shrink)

In this article, I explain why stabilizing constructs is important to the success of the Research Domain Criteria Project and identify one measure for facilitating such stability.

Memory perspectives on past events allegedly take one of two shapes. In field memories, we recall episodes from a first-person point of view, while in observer memories, we look at a past scene from a third-person perspective. But this mere visuospatial dichotomy faces several practical and conceptual challenges. First, this binary distinction is not exhaustive. Second, this characterization insufficiently accounts for the phenomenology of observer memories. Third, the focus on the visual aspect of memory perspective neglects emotional, agential, and self-related (...) social aspects. Fourth, the focus on the time of recall neglects the fact that visual, emotional, agential, and social aspects of perspective can also be dissociated in the original experience. In this chapter, we move away from the standard visual dichotomy. Instead, we propose that memory perspective is better understood along four lines: visual, agential, emotional, and social. Drawing on empirical research, we argue that these dimensions predict a disposition to recall a past event based on the present situation of the memorizer. This account supports seeing episodic memory as a natural kind, supported by scenario construction mechanisms and minimal memory traces. By remapping the classic distinction between field and observer perspectives along four dimensions, our proposal provides explanatory advantages and secures practical gains by enabling testable hypotheses. (shrink)

The papers in this volume originated in a workshop on externalism and conceptual change held at the University of St. Andrews in June 2018. The discussion of conceptual change was driven largely by...

It is an integral part of the phenomenology of mature perceptual experience that it seems to present to us an experience-independent world. I shall call this feature 'perceptual intentionality'. In this paper, I argue that perceptual intentionality is constructed by the structure of more basic sensory features, features that are not intentional themselves. This theory can explain why the same sensory feature can figure both in presentational and non-presentational experiences. There is a fundamental difference between the intentionality of sensory experiences (...) and the intentionality of thoughts: unlike the former, the latter is not constructed. (shrink)

Part 1 of this exchange consists in a critique by Smith of Searle’s The Construction of Social Reality focusing on Searle’s use of the formula ‘X counts as Y in context C’. Smith argues that this formula works well for social objects such as dollar bills and presidents where the corresponding X terms (pieces of paper, human beings) are easy to identify. In cases such as debts and prices and money in a bank's computers, however, the formula fails, because these (...) are cases of what he calls ‘free-standing Y terms’, since there is here no X which can count as the corresponding Y. In his response in Part 2, Searle argues that Smith’s critique rests on three misunderstandings: 1. in wrongly presupposing that Searle is trying to analyze the nature of what he calls “social objects”, rather than of social facts; 2. in thinking that the counts as formula is intended as a definition, rather than as a mere mnemonic; and 3. in neglecting the naturalism of Searle’s account. (shrink)

A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems.

___MERGING of temporally distant events: One perceives a singular causal relation that c causes e whenever c instantiates a mental property C which anticipates a certain mental property E instantiated by e. Such a knowledge of future self is feasible by there being a common mental property D that is instantiated by both c and e. -/- ___SPLITTING to temporally distant events: In the action that is aimed to bring about E, the knowledge or perception or D (explained by the (...) anticipation of E by C) in turn causally explains an event cc instantiating C and then (via causing cc) event ee instantiating E. (shrink)

This paper offers a critique of an account of explanatory integration that claims that explanations of cognitive capacities by functional analyses and mechanistic explanations can be seamlessly integrated. It is shown that achieving such explanatory integration requires that the terms designating cognitive capacities in the two forms of explanation are stable but that experimental practice in the mind-brain sciences currently is not directed at achieving such stability. A positive proposal for changing experimental practice so as to promote such stability is (...) put forward and its implications for explanatory integration are briefly considered. (shrink)

Martin Heidegger devotes extensive discussion to medieval philosophers, particularly to their treatment of Truth and Being. On both these topics, Heidegger accuses them of forgetting the question of Being and of being responsible for subjugating truth to the modern crusade for certainty: ‘truth is denied its own mode of being’ and is subordinated ‘to an intellect that judges correctly’. Though there are some studies that discuss Heidegger’s debt to and criticism of medieval thought, particularly that of Thomas Aquinas, there is (...) no constructive reply to his assertions. As a result, Heidegger’s critique had an unprecedented effect on the credibility of medieval philosophy, whereby great portions of the philosophical community dismiss it altogether as an illegitimate Onto‐Theology. It is the aim of this study to offer a constructive reply that will fundamentally grapple with these allegations. By constructive reply we mean not only a reply that avoids the problems Heidegger raises regarding existence, essence and truth, but more importantly, one that uses Heidegger’s criticism in order to present a more insightful account of these notions. The present study is composed of two parts where the second serves as a sort of addendum. The first part, the core of this study, is an attempt to develop an understanding of the distinction between essence and existence that, on the one hand, accords with Heidegger’s criticism while on the other hand advances our understanding of how we think and understand reality. After presenting Heidegger’s depiction of Aquinas’s distinction between essence and existence (esse) as a real distinction, the study will present several views propounded by scholars of Aquinas regarding the status of this distinction. It will be argued that it is not clear whether the distinction is real, formal or conceptual, and that different types of distinction are applied in different places, particularly in regard to the phantasm that Aquinas considers essential to the human act of thinking. The second part diverges from the first part and focuses on Heidegger’s criticism of Aquinas’s conception of truth as adequation, i.e., what it is that grounds the possibility of truth as adequation. This divergence is necessary in order to present a full metaphysical response to Heidegger’s criticism. Since the aim of the present study is to argue that Aquinas’s philosophical system can contend with Heidegger’s criticism, a partial reply would greatly diminish its effectiveness. (shrink)

In this paper, I argue that Constructive Empiricism (CE) is ambiguous between two interpretations: CE as a normative epistemology of science and CE as a descriptive philosophy of science. When they present CE, constructive empiricists write as if CE is supposed to be more than a normative epistemology of science and that it is meant to be responsible to actual scientific practices. However, when they respond to objections, constructive empiricists fall back on a strictly normative interpretation of (...) CE. This ambiguity seems to make CE immune to objections in a rather ad hoc fashion. (shrink)

Usually, modular construction involves the off-site manufacturing of standard building components in a factory before the components are assembled on the construction site. It is common to use terms like "prefabrication," "off-site construction," and "modular construction" interchangeably. The construction of modular constructions nowadays is flourishing all over the globe. The roots of the Albanian prefabricated constructions are extended for the first time around the 1970s. This paper will indeed analyze some recently built modular construction in Albania, considering and comparing it (...) with international case studies. The demand for new construction in Albania is rising rapidly. Currently, the most common structures are cast-in-place beam-column designs, driven by both traditional mindsets and industrial capabilities. However, with Albania's economic growth, there is an increasing need for affordable, quickly built, and technologically advanced buildings. Modular construction, which assembles prefabricated modules on-site, offers a solution. This method aligns with bioclimatic design principles, reducing environmental impact and optimizing resources, marking a shift toward sustainability in the construction industry. The purpose of this article is to explore the potential integration of “modular construction techniques” with “bioclimatic design concepts” to create buildings that are environmentally friendly, energy-efficient, and multipurpose by function. This study explores the use of modular construction techniques in conjunction with bioclimatic techniques to increase “building sustainability”. Combining these tactics encourages energy efficiency and a reduced environmental effect, making people far more resilient and weather-adaptable. The synergy between the two of them is necessary. (shrink)

Visual imagery is a form of sensory imagination, involving subjective experiences typically described as similar to perception, but which occur in the absence of corresponding external stimuli. We used the Activation Likelihood Estimation algorithm (ALE) to identify regions consistently activated by visual imagery across 40 neuroimaging studies, the first such meta-analysis. We also employed a recently developed multi-modal parcellation of the human brain to attribute stereotactic co-ordinates to one of 180 anatomical regions, the first time this approach has been combined (...) with the ALE algorithm. We identified a total 634 foci, based on measurements from 464 participants. Our overall comparison identified activation in the superior parietal lobule, particularly in the left hemisphere, consistent with the proposed ‘top-down’ role for this brain region in imagery. Inferior premotor areas and the inferior frontal sulcus were reliably activated, a finding consistent with the prominent semantic demands made by many visual imagery tasks. We observed bilateral activation in several areas associated with the integration of eye movements and visual information, including the supplementary and cingulate eye fields (SCEFs) and the frontal eye fields (FEFs), suggesting that enactive processes are important in visual imagery. V1 was typically activated during visual imagery, even when participants have their eyes closed, consistent with influential depictive theories of visual imagery. Temporal lobe activation was restricted to area PH and regions of the fusiform gyrus, adjacent to the fusiform face complex (FFC). These results provide a secure foundation for future work to characterise in greater detail the functional contributions of specific areas to visual imagery. (shrink)

The (dis)continuism debate—the debate over whether remembering is a form of imagining—is a prominent one in contemporary philosophy of memory. In recent work, Langland-Hassan (2021) has argued that this debate is best understood as a dispute over whether remembering is a form of constructive imagining. In this paper, I argue that remembering is not a form of constructive imagining because constructive processes in remembering and imagining are constrained, and hence controlled, in different ways at the level of (...) consciousness. More specifically, I argue that remembering and imagining differ in terms of the interventions we can make on the constructive processes as they unfold. If this is correct, then a form of discontinuism is vindicated: remembering and imagining are, on this view, processes of different kinds. (shrink)

This article explores some open questions related to the problem of verification of theories in the context of empirical sciences by contrasting three epistemological frameworks. Each of these epistemological frameworks is based on a corresponding central metaphor, namely: (a) Neo-empiricism and the gambling metaphor; (b) Popperian falsificationism and the scientific tribunal metaphor; (c) Cognitive constructivism and the object as eigen-solution metaphor. Each of one of these epistemological frameworks has also historically co-evolved with a certain statistical theory and method for testing (...) scientific hypotheses, respectively: (a) Decision theoretic Bayesian statistics and Bayes factors; (b) Frequentist statistics and p-values; (c) Constructive Bayesian statistics and e-values. This article examines with special care the Zero Probability Paradox (ZPP), related to the verification of sharp or precise hypotheses. Finally, this article makes some remarks on Lakatos’ view of mathematics as a quasi-empirical science. (shrink)

An increasing number of philosophers argue that indeterminacy is metaphysical (or worldly) in the sense that indeterminacy has its source in the world itself (rather than how the world is represented or known). The standard arguments for metaphysical indeterminacy are centered around the sorites paradox. In this essay, I present a novel argument for metaphysical indeterminacy. I argue that metaphysical indeterminacy follows from the existence of constitutive social construction; there is indeterminacy in the social world because there is indeterminacy in (...) how the social world is constructed. (shrink)

Memories of our personal past are the building blocks of our narrative identity. So, when we depend on objects and other people to remember and construct our personal past, our narrative identity is distributed across our embodied brains and an ecology of environmental resources. This paper uses a cognitive niche construction approach to conceptualise how we engineer our memory ecology and construct our distributed narrative identities. It does so by identifying three types of niche construction processes that govern how we (...) interact with our memory ecology, namely creating, editing, and using resources in our memory ecology. It also conceptualises how identity-relevant information in objects and (family) stories is transmitted vertically, i.e., across different generations of people. Identifying these processes allows us to better understand the cultural information trajectories that constitute our memory ecologies. Thus, what I’ll argue is that our memory ecology distributes our narrative identity and that engineering our memory ecology is a form of narrative niche construction. (shrink)

One of the most common criticisms one hears of the idea of granting a legitimate role for social values in theory choice in science is that it just doesn’t make sense to regard social preferences as relevant to the truth or to the way things are. “What is at issue,” wrote Susan Haack, is “whether it is possible to derive an ‘is’ from an ‘ought.’ ” One can see that this is not possible, she concludes, “as soon as one expresses (...) it plainly: that propositions about what states of affairs are desirable or deplorable could be evidence that things are, or are not, so” (Haack 1993a, 35, emphasis in original). The purpose of this chapter is not to determine whether this widespread view is correct, but rather to show that even if we grant it (which I do), we may still consistently believe that social values have a legitimate role in theory choice in science. I will defend this conclusion by outlining a view about social values and theory choice that is available to a Constructive Empiricist anti-realist, but not to a realist. (shrink)

A naturalistic theory of intentionality is proposed that differs from previous evolutionary and tracking theories. Full-blown intentionality is constructed through a series of evolvable refinements. A first, minimal version of intentionality originates from a conjectured internal process that estimates an organism’s own fitness and that continually modifies the organism. This process produces the directedness of intentionality. The internal estimator can be parsed into intentional components that point to components of the process that produces fitness. It is argued that such intentional (...) components can point to mistaken or non-existing entities. Different Fregian senses of the same reference correspond to different components that have different roles in the estimator. Intentional components that point to intentional components in other organisms produce directedness towards semi-abstract entities. Finally, adding a general, population-wide means of communication enables intentional components that point to fully abstract entities. Intentionality thus naturalized has all of its expected properties: being directed; potentially making errors; possibly pointing to non-existent, abstract, or rigid entities; capable of pointing many-to-one and one-to-many; distinguishing sense and reference; having perspective and grain; and having determinate content. Several examples, such as ‘swampman’ and ‘brain-in-a-vat’, illustrate how the theory can be applied. (shrink)

Bas van Fraassen’s Constructive Empiricism (CE) has been much discussed. There is, however, a curious feature of van Fraassen’s writings that has been overlooked up until now. This is that he sometimes capitalises certain key terms, notably “Induction”. This is done to differentiate a pragmatic small ‘i’ induction (which has epistemic import) from a rule-bound capital ‘I’ induction (which does not). In this paper, I argue that van Fraassen’s small letter/capital letter distinction reveals an underlying dualism, one that is (...) reminiscent of the notoriously problematic semantic dualism in Logical Positivism (between a theoretical language and an observation language). Despite partly developing CE to overcome Logical Positivism’s kind of dualism, van Fraassen seems to have tacitly endorsed it anyway. If so, then CE requires revision. It is, however, not clear how to conduct such a revision. It is not clear what the way forward should be once CE is understood as innately dualistic. (shrink)

Gauthier and Hobbes reduce Prisoners Dilemmas to co-ordination problems (CPs). Many think rational, face-to-face agents can solve any CP by agreed fiat. But though an agent can rationally use a symmetry-breaking technique (ST) to decide between equal options, groups cannot unless their members' STs luckily converge. Failing this, the CP is escapable only by one agent's non-rational stubbornness, or by the group's "conquest" by an outside force. Implications: one's strategic rationality is group-relative; there are some optimums groups in principle cannot (...) rationally choose; thus justice cannot always be a rationally contracted optimum. Howard Sobel provides the point of departure. (shrink)

The incorporation of post-event testimonial information into an agent’s memory representation of the event via constructive memory processes gives rise to the misinformation effect, in which the incorporation of inaccurate testimonial information results in the formation of a false memory belief. While psychological research has focussed primarily on the incorporation of inaccurate information, the incorporation of accurate information raises a particularly interesting epistemological question: do the resulting memory beliefs qualify as knowledge? It is intuitively plausible that they do not, (...) for they appear to be only luckily true. I argue, however, that, despite its intuitive plausibility, this view is mistaken: once we adopt an adequate (modal) conception of epistemic luck and an adequate (adaptive) general approach to memory, it becomes clear that memory beliefs resulting from the incorporation of accurate testimonial information are not in general luckily true. I conclude by sketching some implications of this argument for the psychology of memory, suggesting that the misinformation effect would better be investigated in the context of a broader “information effect”. (shrink)