In this chapter, I discuss some lesser-known aspects of Husserl’s concept of the phenomenological reduction in relation to his use of the notion of reflection, and indicate how these topics connect to concerns in contemporary philosophy after the analytic-continental divide. Empathy, collective intentionality, non-representationalism, non-cognitivism, and the focus on the lived body as a source of sense-making and knowing-how are all domains in which Husserl’s conception of the reduction anticipates recent philosophical trends after the analytic-continental divide. (...) They are also interconnected parts of a unified conception of philosophy that arises from the phenomenological reduction when we reflect radically on experience in its full breadth as an embodied phenomenon that is both historical and communal. (shrink)

Three distinctly different interpretations of Aristotle’s notion of a sullogismos in Prior Analytics can be traced: (1) a valid or invalid premise-conclusion argument (2) a single, logically true conditional proposition and (3) a cogent argumentation or deduction. Remarkably the three interpretations hold similar notions about the logical relationships among the sullogismoi. This is most apparent in their conflating three processes that Aristotle especially distinguishes: completion (A4-6)reduction(A7) and analysis (A45). Interpretive problems result from not sufficiently recognizing Aristotle’s remarkable degree of (...) metalogical sophistication to distinguish logical syntax from semantics and, thus, also from not grasping him to refine the deduction system of his underlying logic. While it is obvious that Aristotle most often uses ‘sullogimos’ to denote a valid argument of a certain kind, we show that at Prior Analytics A4-6, 7, 45 Aristotle specifically treats a sullogismos as an elemental argument pattern having only valid instances and that such a pattern then serves as a rule of deduction in his syllogistic logic. By extracting Aristotle’s understanding of three proof-theoretic processes, this paper provides new insight into what Aristotle thinks reasoning syllogistically is and, moreover, it resolves three problems in the most recent interpretation that takes a sullogismos to be a deduction. (shrink)

Studies of Aristotle’s syllogistic system, since Corcoran’s deductionist interpretation supplanted Łukasiewicz’ axiomaticist interpretation, misrepresent Aristotle’s logic in two important respects. Following Corcoran, they take indirect deduction to occur only once in a deduction discourse; they then obviate the system having a reductio rule. Second, they represent reduction as a deductive process for deriving ‘imperfect’ syllogisms from ‘perfect’ syllogisms to impose an axiomatic interpretation on the logic. Denying that Aristotle's logic admits of a reductio rule results from this misrepresentation of (...) reduction. This discussion shows that the defects imputed to Aristotle's logic, and systems devised to resolve them, result from misunderstanding reduction, which itself results from misapprehending Prior Analytics expressly to identify in a metadiscourse deduction rules and not deductions per se. (shrink)

Reduction and reductionism have been central philosophical topics in analytic philosophy of science for more than six decades. Together they encompass a diversity of issues from metaphysics and epistemology. This article provides an introduction to the topic that illuminates how contemporary epistemological discussions took their shape historically and limns the contours of concrete cases of reduction in specific natural sciences. The unity of science and the impulse to accomplish compositional reduction in accord with a layer-cake vision (...) of the sciences, the seminal contributions of Ernest Nagel on theory reduction and how they strongly conditioned subsequent philosophical discussions, and the detailed issues pertaining to different accounts of reduction that arise in both physical and biological science (e.g., limit-case and part-whole reduction in physics, the difference-making principle in genetics, and mechanisms in molecular biology) are explored. The conclusion argues that the epistemological heterogeneity and patchwork organization of the natural sciences encourages a pluralist stance about reduction. (shrink)

In previous work, I described several examples combining reduction and emergence: where reduction is understood a la Ernest Nagel, and emergence is understood as behaviour that is novel. Here, my aim is again to reconcile reduction and emergence, for a case which is apparently more problematic than those I treated before: renormalization. My main point is that renormalizability being a generic feature at accessible energies gives us a conceptually unified family of Nagelian reductions. That is worth saying (...) since philosophers tend to think of scientific explanation as only explaining an individual event, or perhaps a single law, or at most deducing one theory as a special case of another. Here we see a framework in which there is a space of theories endowed with enough structure that it provides a family of reductions. (shrink)

Reduction and reductionism have been central philosophical topics in analytic philosophy of science for more than six decades. Together they encompass a diversity of issues from metaphysics and epistemology. This article provides an introduction to the topic that illuminates how contemporary epistemological discussions took their shape historically and limns the contours of concrete cases of reduction in specific natural sciences. The unity of science and the impulse to accomplish compositional reduction in accord with a layer-cake vision (...) of the sciences, the seminal contributions of Ernest Nagel on theory reduction and how they strongly conditioned subsequent philosophical discussions, and the detailed issues pertaining to different accounts of reduction that arise in both physical and biological science (e.g., limit-case and part-whole reduction in physics, the difference-making principle in genetics, and mechanisms in molecular biology) are explored. The conclusion argues that the epistemological heterogeneity and patchwork organization of the natural sciences encourages a pluralist stance about reduction. (shrink)

Some time ago, the philosopher Luciano Floridi suggested that Western philosophy, and the mainstream contemporary approach to it traditionally called ‘analytic philosophy’, is in dire need of a reboot. The concern was that the discipline might be in a period of decadence. Analytic philosophy would be benefited by greater internationalization, wider and more transparent decision-making, and the reduction (as much as possible) of conflicts of interest as well as of its current habit of hiring and providing publication (...) opportunities on the basis of contacts, networking, and academic pedigree. If we are right, then we need a reconditioning of the institutional framework of analytic philosophy that adjusts it to the current global and interconnected world. (shrink)

Philosophers of modern logic have cherished no project more dearly than that of extensional reduction. Despite occasional protests that this project was ill-conceived from the start, or that it fails to account for important areas of experience and thought, the extensionalist mills have been grinding away anyhow. Their grinding has brought with it a number of important technical successes, replete with philosophical claims that light has finally been shed on areas hitherto buried in incomprehensible darkness.

Metaphor is commonly taken to be an elliptical simile. This article offers a rational reconstruction of two types of simile theories of metaphor: reductive and non-reductive. Careful analysis shows the differences between these theories, but in the end, neither does the explanatory work it sets out to do. In assimilating metaphor to simile and simile to literal comparison, the reductive simile theory obscures what is most important to an account of metaphor: an account of what it is to interpret a (...) bit of discourse metaphorically. The reductive simile theory fails because the reduction to literal comparison fails. The non-reductive simile theory faces most of the same problems that undermine the simile theory, particularly problems generating a corresponding simile when the metaphor contains quantificational terms and other linguistic complexities. Analysis of the non-reductive simile theory highlights the troublesome assumption (inherent in all simile theories) that metaphor and simile play the same linguistic role: making or prompting us to make comparisons. In both guises, the simile theory mistakes the task of explaining what a metaphor means with how metaphor (in general) has meaning; it confuses explanation with explication. In diagnosing and arguing against the simile theory, this article sets out a framework for understanding the difference between literal and metaphorical interpretation. (shrink)

Abstract Philosophers have paid little attention to the kind of reduction involved in transforming an analytically intractable equation into solvable form. I argue that this practice is important because it involves the design of a basic level theory for use in a specific domain. The design process can lead to the construction of a new theory. As a result of my analysis, theory design emerges as an important category of analysis for scientific methodology. Similarities between design in technology and (...) science are explored to illuminate the heuristic function of such reductions. (shrink)

In a recent paper, William K. Goosens objects to the arguments I set out some time ago attacking the logical empiricist analysis of reduction as applied to genetics. In these works I did not argue against the claim that Mendelian genetics was being reduced to molecular biology. Nor did I conclude, as Goosens asserts, that in the case of genetics, “reduction is insignificant”. To the contrary, I repeatedly stated that, “given our pre-analytic intuitions about reduction,” the (...) reduction of Mendelian to molecular genetics “is a case of reduction, a paradigm case”. And in agreement with Kenneth Schaffner I argued that reduction “in some very important, pre-analytic sense has taken place and is taking place in genetics”. The target of my objections to reduction in genetics was not “reduction” in some pre-analytic sense. Nor was it the various explications which have appeared since. Rather it was the notion of theory reduction set out a generation ago by such logical empiricists as Ernest Nagel, The particular version of this analysis which I chose to attack was that presented by Schaffner ; for Schaffner's later views, see his. I chose Schaffner's explication to attack because I thought it was the best of its kind and because it was the only defense of the logical empiricist analysis at the time which used genetics as one of its chief examples. Contrary to Goosens' assumption, in criticizing Schaffner's explication, I did not thereby “endorse” it. (shrink)

Creature consciousness provides a physicalist account of the first-person awareness. I argue that non-reductive consciousness is not about phenomenal qualia ; it is about the stream of awareness that makes any objects of perception epistemically available and ontologically present. This kind of consciousness is central, internally to one’s awareness. Externally, the feel about one’s significant other’s that “there is someone home” is quite important too. This is not substance dualism since creature consciousness and functional consciousness are both at different generality (...) levels of physicalism. Surprisingly, pre-Hegel philosophy of pure subject is more fitting with the current engineering approach than analytical phenomenalism. The complementary view of subject- and object-related perspectives, may come from Fichte’s Wissenschaftslehre; but here it is placed, securely within the physicalist paradigm. It is essential to the Engineering Thesis in Machine Consciousness, which helps us understand under what general conditions a machine would be first-person conscious, but when it is merely functionally conscious. (shrink)

Creature consciousness provides a physicalist account of the first-person awareness. I argue that non-reductive consciousness is not about phenomenal qualia ; it is about the stream of awareness that makes any objects of perception epistemically available and ontologically present. This kind of consciousness is central, internally to one’s awareness. Externally, the feel about one’s significant other’s that “there is someone home” is quite important too. This is not substance dualism since creature consciousness and functional consciousness are both at different generality (...) levels of physicalism. Surprisingly, pre-Hegel philosophy of pure subject is more fitting with the current engineering approach than analytical phenomenalism. The complementary view of subject- and object-related perspectives, may come from Fichte’s Wissenschaftslehre; but here it is placed, securely within the physicalist paradigm. It is essential to the Engineering Thesis in Machine Consciousness, which helps us understand under what general conditions a machine would be first-person conscious, but when it is merely functionally conscious. (shrink)

The syllogistic mnemonic known by its first two words Barbara Celarent introduced a constellation of terminology still used today. This concatenation of nineteen words in four lines of verse made its stunning and almost unprecedented appearance around the beginning of the thirteenth century, before or during the lifetimes of the logicians William of Sherwood and Peter of Spain, both of whom owe it their lasting places of honor in the history of syllogistic. The mnemonic, including the theory or theories it (...) encoded, was prominent if not dominant in syllogistics for the next 700 years until a new paradigm was established in the 1950s by the great polymath Jan Łukasiewicz, a scholar equally at home in philosophy, classics, mathematics, and logic. Perhaps surprisingly, the then-prominent syllogistic mnemonic played no role in the Łukasiewicz work. His 1950 masterpiece does not even mention the mnemonic or its two earliest champions William and Peter. The syllogistic mnemonic is equally irrelevant to the post-Łukasiewicz paradigm established in the 1970s and 1980s by John Corcoran, Timothy Smiley, Robin Smith, and others. Robin Smith’s comprehensive 1989 treatment of syllogistic does not even quote the mnemonic’s four verses. Smith’s work devotes only 2 of its 262 pages to the mnemonic. The most recent translation of Prior Analytics by Gisela Striker in 2009 continues the post-Łukasiewicz paradigm and accordingly does not quote the mnemonic or even refer to the code—although it does use the terminology. Full mastery of modern understandings of syllogistic does not require and is not facilitated by ability to decode the mnemonic. Nevertheless, an understanding of the history of logic requires detailed mastery of the syllogistic mnemonic, of the logical theories it spawned, and of the conflicting interpretations of it that have been offered over the years by respected logicians such as De Morgan, Jevons, Keynes, and Peirce. More importantly, an understanding of the issues involved in decoding the mnemonic might lead to an enrichment of the current paradigm—an enrichment so profound as to constitute a new paradigm. After presenting useful expository, bibliographic, hermeneutic, historical, and logical background, this paper gives a critical exposition of Smith’s interpretation. (shrink)

David Papineau's model of scientific reduction, contrary to his intent, appears to enable a naturalist realist account of the primitive normativity involved in a biological adaptation's being “for” this or that (say the eye's being for seeing). By disabling the crucial anti‐naturalist arguments against any such reduction, his model would support a cogni‐tivist semantics for normative claims like “The heart is for pumping blood, and defective if it doesn't.” No moral claim would follow, certainly. Nonetheless, by thus “pressing (...) from below” we may learn something about moral normativity. For instance, suppose non‐cognitivists like Mackie are right that the semantics of normative claims should be “unified”: if the semantics of moral claims is non‐cognitivist, so too is that of all normative claims. Then, assuming that a naturalist reduction does yield a sound cognitivist account of the primitive normativity, it would follow that our semantics of moral claims is cognitivist as well. (shrink)

David Papineau’s model of scientific reduction, contrary to his intent, appears to enable a naturalist realist account of the primitive normativity involved in a biological adaptation’s being “for” this or that (say the eye’s being for seeing). By disabling the crucial anti-naturalist arguments against any such reduction, his model would support a cognitivist semantics for normative claims like “The heart is for pumping blood, and defective if it doesn’t.” No moral claim would follow, certainly. Nonetheless, by thus “pressing (...) from below” we may learn something about moral normativity. For instance, suppose non-cognitivists like Mackie are right that the semantics of normative claims should be “unified”: if the semantics of moral claims is non-cognitivist, so too is that of all normative claims. Then, assuming that a naturalist reduction does yield a sound cognitivist account of the primitive normativity, it would follow that our semantics of moral claims is cognitivist as well. (shrink)

It can be argued (cf. Dizadji‑Bahmani et al. 2010) that an increase in coherence is one goal that drives reductionist enterprises. Consequently, the question if or how well this goal is achieved can serve as an epistemic criterion for evaluating both a concrete case of a purported reduction and our model of reduction : what conditions on the model allow for an increase in coherence ? In order to answer this question, I provide an analysis of the relation (...) between the reduction and the coherence of two theories. The underlying model of reduction is a (generalised) Nagelian model (cf. Nagel 1970, Schaffner 1974, Dizadji‑Bahmani et al. 2010). For coherence, different measures have been put forward (e.g. Shogenji 1999, Olsson 2002, Fitelson 2003, Bovens & Hartmann 2003). However, since there are counterexamples to each proposed coherence measure, we should be careful that the analysis be sufficiently stable (in a sense to be specified). It will turn out that this can be done. (shrink)

This chapter describes the application of reduction concepts in emergence and self organization of complex dynamical system. Condition-dependent laws compress and dynamical equation sets provide implicit compressed representations even when most of that information is not explicitly available without decompression. And, paradoxically, there is still the determined march of fundamental analytical dynamics expanding its compression reach toward a Theory of Everything—even while the more rapidly expanding domain of complex systems dynamics confronts its assumptions and its monolithicity. Nor does science (...) fall apart into a disunified aggregate of particular cases since, with fundamental dynamics as a backbone, complex matching up of models across theoretical and empirical domains then articulates its model-structured skeleton. Discussion provides the delicately entwined dance of emergence and reduction providing constraints on compression that also permit its expansion. However, while the vision is not dead, it is currently substantially more complexly structured through model similarities and differences than that initially envisaged and individuals are left with deep questions about compression unresolved. (shrink)

In his influential paper ‘‘Essence and Modality’’, Kit Fine argues that no account of essence framed in terms of metaphysical necessity is possible, and that it is rather metaphysical necessity which is to be understood in terms of essence. On his account, the concept of essence is primitive, and for a proposition to be metaphysically necessary is for it to be true in virtue of the nature of all things. Fine also proposes a reduction of conceptual and logical necessity (...) in the same vein: a conceptual necessity is a proposition true in virtue of the nature of all concepts, and a logical necessity a proposition true in virtue of the nature of all logical concepts. I argue that the plausibility of Fine's view crucially requires that certain apparent explanatory links between essentialist facts be admitted and accounted for, and I make a suggestion about how this can be done. I then argue against the reductions of conceptual and logical necessity proposed by Fine and suggest alternative reductions, which remain nevertheless Finean in spirit. (shrink)

The point of the present article is to investigate whether the key conceptions of epochē and reduction as found in Husserl's phenomenology can be brought to bear in a fruitful rereading of the speech of Socrates in Plato's Symposium.1 In pursuit of this goal, I will begin by revisiting the traditional reading of this speech in terms of a scala amoris in which the erotic subject is guided from attachment to a series of inferior objects to the Beautiful and (...) Good itself such that the value of all preceding attachments is suspended. The critique that this approach to love instrumentalizes all but the transcendent Good is one that is found both within and without the text. In opposition to this reading, however, I will suggest that Husserl's notions of epochē and reduction enable us to read the speech not as an instrumentalizing scala but in terms of a reflective distance in which our immersion in and with the erotic object is suspended so that we might reappropriate the real meaning of erotic engagement. According to this reading, Plato does not negate the particular or lower forms of eros but reinscribes them with a value derived from their position in relation to the ultimate. The suspension of the lower forms, then, is not final but is merely employed in order to let what occurs in erotic engagement show itself. (shrink)

The point of the present article is to investigate whether the key conceptions of epochē and reduction as found in Husserl's phenomenology can be brought to bear in a fruitful rereading of the speech of Socrates in Plato's Symposium.1 In pursuit of this goal, I will begin by revisiting the traditional reading of this speech in terms of a scala amoris in which the erotic subject is guided from attachment to a series of inferior objects to the Beautiful and (...) Good itself such that the value of all preceding attachments is suspended. The critique that this approach to love instrumentalizes all but the transcendent Good is one that is found both within and without the text. In opposition to this reading, however, I will suggest that Husserl's notions of epochē and reduction enable us to read the speech not as an instrumentalizing scala but in terms of a reflective distance in which our immersion in and with the erotic object is suspended so that we might reappropriate the real meaning of erotic engagement. According to this reading, Plato does not negate the particular or lower forms of eros but reinscribes them with a value derived from their position in relation to the ultimate. The suspension of the lower forms, then, is not final but is merely employed in order to let what occurs in erotic engagement show itself. (shrink)

In this paper, I will discuss three arguments which have been advanced by three of the most important recent analytic philosophers: Willard Van Orman Quine, Hilary Putnam, and Michael Dummett. Each argument is central to the views of the philosopher in question, and each leads to sweeping and, to my mind, highly implausible conclusions concerning the content of our thoughts about the world. The philosophers in question claim, of course, that these implications should be accepted, but few others have (...) been willing to follow them in this. At the same time, however, there has been no very widespread agreement on where and how the arguments go wrong. My view is that they are best viewed as reductions to absurdity of their premises and of one underlying premise in particular. [1] But just which premise is at fault is not, perhaps, immediately obvious. I will have more to say about that after we have had an initial look at the arguments. (shrink)

Based on some reflections found on Husserl’s C-manuscripts, the article focuses on the methodical path toward the disclosure of what I call the “primal-intentional-tension” (PIT)—namely, the differential relation between the I and the Not-I, at the most fundamental level of the constitution of time. In order to reach this essential structure of experience, I address the method of the reduction and its radicalization. I argue: first, that intentionality is for Husserl not only act-intentionality, since there are also other intentional (...) modes, such as the stream-intentionality; second, that the reduction is the leading method to the discovery of the operating and unthematic transcendental dimension of experience as well as to the disclosure of the multiple phenomenological dimensions and, by means of a radicalization, of the living present as primal-mode of transcendental life; third, that the reduction to the most fundamental level is an analytic and abstractive “deconstruction” (Abbau) of the concrete transcendental life of the living present; fourth, that the primal-phenomenal dimension shows itself as a PIT between the I (primal-I) and the Not-I (the primal-temporalization of primal-hyle) as the most intimate strangeness in me; and, fifth, I finally show that this PIT might be understood as a primal-difference in the originality of my experience. (shrink)

Scientists employ a variety of procedures to eliminate degrees of freedom from computationally and/or analytically intractable equations. In the process, they often construct new models and discover new concepts, laws and functional relations. I argue these procedures embody a central notion of reduction, namely, the containment of one structure within another. However, their inclusion in the philosophical concept of reduction necessitates a reevaluation of many standard assumptions about the ontological, epistemological and functional features of a reduction. On (...) the basis of the reevaluation, I advocate a continuum of reduction which proceeds from the eliminative to the constructive. The metaphysical aspects of theory use in constructive reductions are sketched. (shrink)

A clear understanding of the notion of phenomenological reduction is crucial for any evaluation of the claims of Husserlian phenomenology. The phenomenological reduction is said to be the distinctive step one has to take if one is to enter the realm of phenomenology proper. Husserl labored all his life to find the best way which would lead the nonphenomenologist into the new land which he thought he had discovered. Commentators have classified the ways discussed by Husserl under at (...) least three main headings: the Cartesian way, the way through psychology, and the way through ontology. In each of these ways, one is urged to perform a phenomenological reduction. But since the ways are different, the step also of the phenomenological reduction varies somewhat for each approach. Husserl and his interpreters tried hard to clarify these subtle distinctions, but up to now their ways of speaking have proven rather opaque, especially to philosophers accustomed to the standards of clarity of Analytic Philosophy. (shrink)

This paper defends the view that Frege’s reduction of arithmetic to logic would, if successful, have shown that arithmetical knowledge is analytic in essentially Kant’s sense. It is argued, as against Paul Benacerraf, that Frege’s apparent acceptance of multiple reductions is compatible with this epistemological thesis. The importance of this defense is that (a) it clarifies the role of proof, definition, and analysis in Frege’s logicist works; and (b) it demonstrates that the Fregean style of reduction is (...) a valuable tool for those who would investigate the nature of arithmetical knowledge. (shrink)

How to think a unique and determinative turn in analytic philosophy of mind? To answer this question this article first presents an attempt to render clear that analytic phenomenology, by contrast with conceptions of phenomenology of the XXth century, beneficially dispenses with several methodological and conceptual assumptions that were assumed to be compulsory, as phenomenological reduction, a notion of synthesis, and a philosophical notion of the a priori. It then presents some eventual difficulties to the achievement of (...) a phenomenological turn within analytic philosophy, which are, the neglect of historicity, abstractionism, the acknowledgement of the place of language in our lives, and solipsism. It finally presents several demands that concern the felicity of contemporary analytic phenomenologies, namely, anti-abstractionism, fallibilism, attention to polyadic relations, and the integration of ecological and decolonial concerns of our cultures. (shrink)

This article explores some fundamental issues of definition-based lexical semantic research through a critique of the Natural Semantic Metalanguage (NSM) theory of semantic and grammatical description (Wierzbicka 1996, Semantics. Primes and Universals, Oxford University Press, Oxford). NSM is criticized for attaching excessive importance to explanatory definition, for its adoption of the reductive requirement that a definiens be simpler than a definiendum, and for its use of ‘canonical contexts’ to disambiguate meaning. The principle of substitutability, according to which a definition of (...) a term is accepted if it can be substituted for the term itself, is also critically examined, and the theory’s use of syntactic phenomena as evidence for polysemy is shown to be inconsistent. Finally, suggestions that NSM may be a valid analytical method for only a subpart of the lexicon are rejected. (shrink)

Is social science ‘reducible’ to individual psychology, and ultimately to some physical theory? If a sociological theory, that is, a theory dealing with group phenomena, is ‘reduced’ in a relevant and appropriate sense to individual psychology, could we then say that the social phenomena in the domain of the sociological theory are just psychological phenomena of individuals? Conversely, if social events and processes are just individual psychological events and processes, then does it follow that any theory dealing with the former (...) is ‘reducible’ to some theory dealing with the latter? Analogously, if psychological theory is ‘reducible’ to physical theory, say the neurological theory of the brain and the associated organs, could we say that psychological phenomena are just neurological phenomena in the brain? What of the converse of this question? Further, what is the bearing on these questions of the thesis that there are laws correlating types of social phenomena with types of individual psychological phenomena, or types of psychological phenomena with types of neurological phenomena? (shrink)

This paper attempts a critical reappraisal of Nagel's (1961, 1970) model of reduction taking into account both traditional criticisms and recent defenses. This model treats reduction as a type of explanation in which a reduced theory is explained by a reducing theory after their relevant representational items have been suitably connected. In accordance with the deductive-nomological model, the explanation is supposed to consist of a logical deduction. Nagel was a pluralist about both the logical form of the connections (...) between the reduced and reducing theories (which could be conditionals or biconditionals) and their epistemological status (as analytic connections, conventions, or synthetic claims). This paper defends Nagel's pluralism on both counts and, in the process, argues that the multiple realizability objection to reductionism is misplaced. It also argues that the Nagel model correctly characterizes reduction as a type of explanation. However, it notes that logical deduction must be replaced by a broader class of inferential techniques that allow for different types of approximation. Whereas Nagel (1970), in contrast to his earlier position (1961), recognized the relevance of approximation, he did not realize its full import for the model. Throughout the paper two case studies are used to illustrate the arguments: the putative reduction of classical thermodynamics to the kinetic theory of matter and that of classical genetics to molecular biology. (shrink)

We show that every analytic filter is generated by a Π 0 2 prefilter, every Σ 0 2 filter is generated by a Π 0 1 prefilter, and if $P \subseteq \mathscr{P}(\omega)$ is a Σ 0 2 prefilter then the filter generated by it is also Σ 0 2 . The last result is unique for the Borel classes, as there is a Π 0 2 -complete prefilter P such that the filter generated by it is Σ 1 1 (...) -complete. Also, no complete coanalytic filter is generated by an analytic prefilter. The proofs use König's infinity lemma, a normal form theorem for monotone analytic sets, and Wadge reductions. (shrink)