Carefully looking at the Brechtian article and unstitching it, herein lies the pence (this is reproduced via an email exchange and hence is too very basic in arguments!!):
Peirce’s famous ‘triadomania’ lets most of his decisive distinctions appear in threes, following the tripartition of his list of categories, the famous triad of First, Second, and Third, or Quality, Reaction, Representation, or Possibility, Actuality, Reality.
Firstness is the mode of being of that which is such as it is, positively and without reference to anything else.
Secondness is the mode of being of that which is such as it is, with respect to a second but regardless of any third.
Thirdness is the mode of being of that which is such as it is, in bringing a second and third into relation to each other.
Firstness constitutes the quality of experience: in order for something to appear at all, it must do so due to a certain constellation of qualitative properties. Peirce often uses sensory qualities as examples, but it is important for the understanding of his thought that the examples may refer to phenomena very far from our standard conception of ‘sensory data’, e.g. forms or the ‘feeling’ of a whole melody or of a whole mathematical proof, not to be taken in a subjective sense but as a concept for the continuity of melody or proof as a whole, apart from the analytical steps and sequences in which it may be, subsequently, subdivided. In short, all sorts of simple and complex Gestalt qualities also qualify as Firstnesses. Firstness tend to form continua of possibilities such as the continua of shape, color, tone, etc. These qualities, however, are, taken in themselves, pure possibilities and must necessarily be incarnated in phenomena in order to appear. Secondness is the phenomenological category of ‘incarnation’ which makes this possible: it is the insistency, then, with which the individuated, actualized, existent phenomenon appears. Thus, Secondness necessarily forms discontinuous breaks in Firstness, allowing for particular qualities to enter into existence. The mind may imagine anything whatever in all sorts of quality combinations, but something appears with an irrefutable insisting power, reacting, actively, yielding resistance. Peirce’s favorite example is the resistance of the closed door – which might be imagined reduced to the quality of resistance feeling and thus degenerate to pure Firstness so that his theory imploded into a Hume-like solipsism – but to Peirce this resistance, surprise, event, this thisness, ‘haecceity’ as he calls it with a Scotist term, remains irreducible in the description of the phenomenon (a Kantian idea, at bottom: existence is no predicate). About Thirdness, Peirce may directly state that continuity represents it perfectly: ‘continuity and generality are two names of the same absence of distinction of individuals’. As against Secondness, Thirdness is general; it mediates between First and Second. The events of Secondness are never completely unique, such an event would be inexperiencable, but relates (3) to other events (2) due to certain features (1) in them; Thirdness is thus what facilitates understanding as well as pragmatic action, due to its continuous generality. With a famous example: if you dream about an apple pie, then the very qualities of that dream (taste, smell, warmth, crustiness, etc.) are pure Firstnesses, while the act of baking is composed of a series of actual Secondnesses. But their coordination is governed by a Thirdness: the recipe, being general, can never specify all properties in the individual apple pie, it has a schematic frame-character and subsumes an indefinite series – a whole continuum – of possible apple pies. Thirdness is thus necessarily general and vague. Of course, the recipe may be more or less precise, but no recipe exists which is able to determine each and every property in the cake, including date, hour, place, which tree the apples stem from, etc. – any recipe is necessarily general. In this case, the recipe (3) mediates between dream (1) and fulfilment (2) – its generality, symbolicity, relationality and future orientation are all characteristic for Thirdness. An important aspect of Peirce’s realism is that continuous generality may be experienced directly in perceptual judgments: ‘Generality, Thirdness, pours in upon us in our very perceptual judgments’.
All these determinations remain purely phenomenological, even if the later semiotic and metaphysical interpretations clearly shine through. In a more general, non-Peircean terminology, his phenomenology can be seen as the description of minimum aspects inherent in any imaginable possible world – for this reason it is imaginability which is the main argument, and this might point in the direction that Peirce could be open to critique for subjectivism, so often aimed at Husserl’s project, in some respects analogous. The concept of consciousness is invoked as the basis of imaginability: phenomenology is the study of invariant properties in any phenomenon appearing for a mind. Peirce’s answer would here be, on the one hand, the research community which according to him defines reality – an argument which structurally corresponds to Husserl’s reference to intersubjectivity as a necessary ingredient in objectivity (an object is a phenomenon which is intersubjectively accessible). Peirce, however, has a further argument here, namely his consequent refusal to delimit his concept of mind exclusively to human subjects (a category the use of which he obviously tries to minimize), mind-like processes may take place in nature without any subject being responsible. Peirce will, for continuity reasons, never accept any hard distinction between subject and object and remains extremely parsimonious in the employment of such terms.
From Peirce’s New Elements of Mathematics (The New Elements of Mathematics Vol. 4),
But just as the qualities, which as they are for themselves, are equally unrelated to one other, each being mere nothing for any other, yet form a continuum in which and because of their situation in which they acquire more or less resemblance and contrast with one another; and then this continuum is amplified in the continuum of possible feelings of quality, so the accidents of reaction, which are waking consciousnesses of pairs of qualities, may be expected to join themselves into a continuum.
Since, then an accidental reaction is a combination or bringing into special connection of two qualities, and since further it is accidental and antigeneral or discontinuous, such an accidental reaction ought to be regarded as an adventitious singularity of the continuum of possible quality, just as two points of a sheet of paper might come into contact.
But although singularities are discontinuous, they may be continuous to a certain extent. Thus the sheet instead of touching itself in the union of two points may cut itself all along a line. Here there is a continuous line of singularity. In like manner, accidental reactions though they are breaches of generality may come to be generalized to a certain extent.
Secondness is now taken to actualize these quality possibilities based on an idea that any actual event involves a clash of qualities – in the ensuing argumentation Peirce underlines that the qualities involved in actualization need not be restrained to two but may be many, if they may only be ‘dissolved’ into pairs and hence do not break into the domain of Thirdness. This appearance of actuality, hence, has the property of singularities, spontaneously popping up in the space of possibilities and actualizing pairs of points in it. This transition from First to Second is conceived of along Aristotelian lines: as an actualization of a possibility – and this is expressed in the picture of a discontinuous singularity in the quality continuum. The topological fact that singularities must in general be defined with respect to the neighborhood of the manifold in which they appear, now becomes the argument for the fact that Secondness can never be completely discontinuous but still ‘inherits’ a certain small measure of continuity from the continuum of Firstness. Singularities, being discontinuous along certain dimensions, may be continuous in others, which provides the condition of possibility for Thirdness to exist as a tendency for Secondness to conform to a general law or regularity. As is evident, a completely pure Secondness is impossible in this continuous metaphysics – it remains a conceivable but unrealizable limit case, because a completely discon- tinuous event would amount to nothing. Thirdness already lies as a germ in the non-discontinuous aspects of the singularity. The occurrences of Secondness seem to be infinitesimal, then, rather than completely extensionless points.
Negation reveals more a neurotic attitude towards jouissance, denounced as a perverse desire, that dominates both political and social life. Negation presupposes the acquisition of the meaning of “No” and it suggests a vigorous and compromising attitude between an idea remaining unconscious (repressed) and conscious at the same time. Thus, to negate means to go against the law and succumb to jouissance in a concealed way. Negating castration releases a destructive force against the paternal function, a force fuelled with jouissance. It is not the symbolic reality, but the non-symbolic real as a threatening source that is being negated. This means that the real is actually expressed through symbolic means, but in a negative form. Disavowal, involves a sexualization of the object precluding the threat of castration as punishment. But the threat is still there in the unconscious, whereas negation means that castration is negated even in the unconscious. Negation does not suggest a compromise (in the form of a splitting of the ego) between the denial of something and its acceptance, as disavowal does. Rather, it maintains the repressed status of castration by allowing the latter to be unconsciously expressed in its negated status. So, negation has a more hostile and aggressive attitude (originating in the death drive) towards castration, whereas disavowal originates in Eros. Disavowal does not go against castration, but keeps it at bay by not acknowledging it, which is different from negating it. In this way, the sexualization of the object (the mother’s phallus) remains intact. Therefore, the responsibility for extracting jouissance is also negated.
The focus on experience ensures that Whitehead’s metaphysics is grounded. Otherwise the narrowness of approach would only culminate in sterile measurement. This becomes especially evident with regard to the science of history. Whitehead gives a lucid example of such ‘sterile measurement’ lacking the immediacy of experience.
Consider, for example, the scientific notion of measurement. Can we elucidate the turmoil of Europe by weighing its dictators, its prime ministers, and its editors of newspapers? The idea is absurd, although some relevant information might be obtained. (Alfred North Whitehead – Modes of Thought)
The wealth of experience leaves us with the problem of how to cope with it. Selection of data is required. This selection is done by a value judgment – the judgment of importance. Although Whitehead opposes the dichotomy of the two notions ‘importance’ and ‘matter of fact’, it is still necessary to distinguish grades and types of importance, which enables us to structure our experience, to focus it. This is very similar to hermeneutical theories in Schleiermacher, Gadamer and Habermas: the horizon of understanding structures the data. Therefore, we not only need judgment but the process of concrescence implicitly requires an aim. Whitehead explains that
By this term ‘aim’ is meant the exclusion of the boundless wealth of alternative potentiality and the inclusion of that definite factor of novelty which constitutes the selected way of entertaining those data in that process of unification.
The other idea that underlies experience is “matter of fact.”
There are two contrasted ideas which seem inevitably to underlie all width of experience, one of them is the notion of importance, the sense of importance, the presupposition of importance. The other is the notion of matter of fact. There is no escape from sheer matter of fact. It is the basis of importance; and importance is important because of the inescapable character of matter of fact.
By stressing the “alien character” of feeling that enters into the privately felt feeling of an occasion, Whitehead is able to distinguish the responsive and the supplemental stages of concrescence. The responsive stage being a purely receptive phase, the latter integrating the former ‘alien elements’ into a unity of feeling. The alien factor in the experiencing subjects saves Whitehead’s concept from being pure Spirit (Geist) in a Hegelian sense. There are more similarities between Hegelian thinking and Whitehead’s thought than his own comments on Hegel may suggest. But, his major criticism could probably be stated with Peirce, who wrote that
The capital error of Hegel which permeates his whole system in every part of it is that he almost altogether ignores the Outward clash. (The Essential Peirce 1)
Whitehead refers to that clash as matter of fact. Although, even there, one has to keep in mind that matter-of-fact is an abstraction.
Matter of fact is an abstraction, arrived at by confining thought to purely formal relations which then masquerade as the final reality. This is why science, in its perfection, relapses into the study of differential equations. The concrete world has slipped through the meshes of the scientific net.
Whitehead clearly keeps the notion of prehension in his late writings as developed in Process and Reality. Just to give one example,
I have, in my recent writings, used the word ‘prehension’ to express this process of appropriation. Also I have termed each individual act of immediate self-enjoyment an ‘occasion of experience’. I hold that these unities of existence, these occasions of experience, are the really real things which in their collective unity compose the evolving universe, ever plunging into the creative advance.
Process needs an aim in Process and Reality as much as in Modes of Thought:
We must add yet another character to our description of life. This missing characteristic is ‘aim’. By this term ‘aim’ is meant the exclusion of the boundless wealth of alternative potentiality, and the inclusion of that definite factor of novelty which constitutes the selected way of entertaining those data in that process of unification. The aim is at that complex of feeling which is the enjoyment of those data in that way. ‘That way of enjoyment’ is selected from the boundless wealth of alternatives. It has been aimed at for actualization in that process.
Constructivism, as portrayed by its adherents, “is the idea that we construct our own world rather than it being determined by an outside reality”. Indeed, a common ground among constructivists of different persuasion lies in a commitment to the idea that knowledge is actively built up by the cognizing subject. But, whereas individualistic constructivism (which is most clearly enunciated by radical constructivism) focuses on the biological/psychological mechanisms that lead to knowledge construction, sociological constructivism focuses on the social factors that influence learning.
Let us briefly consider certain fundamental assumptions of individualistic constructivism. The first issue a constructivist theory of cognition ought to elucidate concerns of course the raw materials on which knowledge is constructed. On this issue, von Glaserfeld, an eminent representative of radical constructivism, gives a categorical answer: “from the constructivist point of view, the subject cannot transcend the limits of individual experience” (Michael R. Matthews Constructivism in Science Education_ A Philosophical Examination). This statement presents the keystone of constructivist epistemology, which conclusively asserts that “the only tools available to a ‘knower’ are the senses … [through which] the individual builds a picture of the world”. What is more, the so formed mental pictures do not shape an ‘external’ to the subject world, but the distinct personal reality of each individual. And this of course entails, in its turn, that the responsibility for the gained knowledge lies with the constructor; it cannot be shifted to a pre-existing world. As Ranulph Glanville confesses, “reality is what I sense, as I sense it, when I’m being honest about it” .
In this way, individualistic constructivism estranges the cognizing subject from the external world. Cognition is not considered as aiming at the discovery and investigation of an ‘independent’ world; it is viewed as a ‘tool’ that exclusively serves the adaptation of the subject to the world as it is experienced. From this perspective, ‘knowledge’ acquires an entirely new meaning. In the expression of von Glaserfeld,
the word ‘knowledge’ refers to conceptual structures that epistemic agents, given the range of present experience, within their tradition of thought and language, consider viable….[Furthermore] concepts have to be individually built up by reflective abstraction; and reflective abstraction is not a matter of looking closer but at operating mentally in a way that happens to be compatible with the perceptual material at hand.
To say it briefly, ‘knowledge’ signifies nothing more than an adequate organization of the experiential world, which makes the cognizing subject capable to effectively manipulate its perceptual experience.
It is evident that such insights, precluding any external point of reference, have impacts on knowledge evaluation. Indeed, the ascertainment that “for constructivists there are no structures other than those which the knower forms by its own activity” (Michael R. MatthewsConstructivism in Science Education A Philosophical Examination) yields unavoidably the conclusion drawn by Gerard De Zeeuw that “there is no mind-independent yardstick against which to measure the quality of any solution”. Hence, knowledge claims should not be evaluated by reference to a supposed ‘external’ world, but only by reference to their internal consistency and personal utility. This is precisely the reason that leads von Glaserfeld to suggest the substitution of the notion of “truth” by the notion of “viability” or “functional fit”: knowledge claims are appraised as “true”, if they “functionally fit” into the subject’s experiential world; and to find a “fit” simply means not to notice any discrepancies. This functional adaptation of ‘knowledge’ to experience is what finally secures the intended “viability”.
In accordance with the constructivist view, the notion of ‘object’, far from indicating any kind of ‘existence’, it explicitly refers to a strictly personal construction of the cognizing subject. Specifically, “any item of the furniture of someone’s experiential world can be called an ‘object’” (von Glaserfeld). From this point of view, the supposition that “the objects one has isolated in his experience are identical with those others have formed … is an illusion”. This of course deprives language of any rigorous criterion of objectivity; its physical-object statements, being dependent upon elements that are derived from personal experience, cannot be considered to reveal attributes of the objects as they factually are. Incorporating concepts whose meaning is highly associated with the individual experience of the cognizing subject, these statements form at the end a personal-specific description of the world. Conclusively, for constructivists the term ‘objectivity’ “shows no more than a relative compatibility of concepts” in situations where individuals have had occasion to compare their “individual uses of the particular words”.
From the viewpoint of radical constructivism, science, being a human enterprise, is amenable, by its very nature, to human limitations. It is then naturally inferred on constructivist grounds that “science cannot transcend [just as individuals cannot] the domain of experience” (von Glaserfeld). This statement, indicating that there is no essential differentiation between personal and scientific knowledge, permits, for instance, John Staver to assert that “for constructivists, observations, objects, events, data, laws and theory do not exist independent of observers. The lawful and certain nature of natural phenomena is a property of us, those who describe, not of nature, what is described”. Accordingly, by virtue of the preceding premise, one may argue that “scientific theories are derived from human experience and formulated in terms of human concepts” (von Glaserfeld).
In the framework now of social constructivism, if one accepts that the term ‘knowledge’ means no more than “what is collectively endorsed” (David Bloor Knowledge and Social Imagery), he will probably come to the conclusion that “the natural world has a small or non-existent role in the construction of scientific knowledge” (Collins). Or, in a weaker form, one can postulate that “scientific knowledge is symbolic in nature and socially negotiated. The objects of science are not the phenomena of nature but constructs advanced by the scientific community to interpret nature” (Rosalind Driver et al.). It is worth remarking that both views of constructivism eliminate, or at least downplay, the role of the natural world in the construction of scientific knowledge.
It is evident that the foregoing considerations lead most versions of constructivism to ultimately conclude that the very word ‘existence’ has no meaning in itself. It does acquire meaning only by referring to individuals or human communities. The acknowledgement of this fact renders subsequently the notion of ‘external’ physical reality useless and therefore redundant. As Riegler puts it, within the constructivist framework, “an external reality is neither rejected nor confirmed, it must be irrelevant”.
Convention is an invention that plays a distinctive role in Poincaré’s philosophy of science. In terms of how they contribute to the framework of science, conventions are not empirical. They are presupposed in certain empirical tests, so they are (relatively) isolated from doubt. Yet they are not pure stipulations, or analytic, since conventional choices are guided by, and modified in the light of, experience. Finally they have a different character from genuine mathematical intuitions, which provide a fixed, a priori synthetic foundation for mathematics. Conventions are thus distinct from the synthetic a posteriori (empirical), the synthetic a priori and the analytic a priori.
The importance of Poincaré’s invention lies in the recognition of a new category of proposition and its centrality in scientific judgment. This is more important than the special place Poincaré gives Euclidean geometry. Nevertheless, it’s possible to accommodate some of what he says about the priority of Euclidean geometry with the use of non-Euclidean geometry in science, including the inapplicability of any geometry of constant curvature in physical theories of global space. Poincaré’s insistence on Euclidean geometry is based on criteria of simplicity and convenience. But these criteria surely entail that if giving up Euclidean geometry somehow results in an overall gain in simplicity then that would be condoned by conventionalism.
The a priori conditions on geometry – in particular the group concept, and the hypothesis of rigid body motion it encourages – might seem a lingering obstacle to a more flexible attitude towards applied geometry, or an empirical approach to physical space. However, just as the apriority of the intuitive continuum does not restrict physical theories to the continuous; so the apriority of the group concept does not mean that all possible theories of space must allow free mobility. This, too, can be “corrected”, or overruled, by new theories and new data, just as, Poincaré comes to admit, the new quantum theory might overrule our intuitive assumption that nature is continuous. That is, he acknowledges that reality might actually be discontinuous – despite the apriority of the intuitive continuum.
The possibility of introducing magnitudes in a certain domain of concrete material objects is by no means immediate, granted or elementary. First of all, it is necessary to find a property of such objects that permits to compare them, so that a quasi-serial ordering be introduced in their set, that is a total linear ordering not excluding that more than one object may occupy the same position in the series. Such an ordering must then undergo a metrization, which depends on finding a fundamental measuring procedure permitting the determination of a standard sample to which the unit of measure can be bound. This also depends on the existence of an operation of physical composition, which behaves additively with respect to the quantity which we intend to measure. Only if all these conditions are satisfied will it be possible to introduce a magnitude in a proper sense, that is a function which assigns to each object of the material domain a real number. This real number represents the measure of the object with respect to the intended magnitude. This condition, by introducing an homomorphism between the domain of the material objects and that of the positive real numbers, transforms the language of analysis (that is of the concrete theory of real numbers) into a language capable of speaking faithfully and truly about those physical objects to which it is said that such a magnitude belongs.
Does the success of applying mathematics in the study of the physical world mean that this world has a mathematical structure in an ontological sense, or does it simply mean that we find in mathematics nothing but a convenient practical tool for putting order in our representations of the world? Neither of the answers to this question is right, and this is because the question itself is not correctly raised. Indeed it tacitly presupposes that the endeavour of our scientific investigations consists in facing the reality of “things” as it is, so to speak, in itself. But we know that any science is uniquely concerned with a limited “cut” operated in reality by adopting a particular point of view, that is concretely manifested by adopting a restricted number of predicates in the discourse on reality. Several skilful operational manipulations are needed in order to bring about a homomorphism with the structure of the positive real numbers. It is therefore clear that the objects that are studied by an empirical theory are by no means the rough things of everyday experience, but bundles of “attributes” (that is of properties, relations and functions), introduced through suitable operational procedures having often the explicit and declared goal of determining a concrete structure as isomorphic, or at least homomorphic, to the structure of real numbers or to some other mathematical structure. But now, if the objects of an empirical theory are entities of this kind, we are fully entitled to maintain that they are actually endowed with a mathematical structure: this is simply that structure which we have introduced through our operational procedures. However, this structure is objective and real and, with respect to it, the mathematized discourse is far from having a purely conventional and pragmatic function, with the goal of keeping our ideas in order: it is a faithful description of this structure. Of course, we could never pretend that such a discourse determines the structure of reality in a full and exhaustive way, and this for two distinct reasons: In the first place, reality (both in the sense of the totality of existing things, and of the ”whole” of any single thing), is much richer than the particular “slide” that it is possible to cut out by means of our operational manipulations. In the second place, we must be aware that a scientific object, defined as a structured set of attributes, is an abstract object, is a conceptual construction that is perfectly defined just because it is totally determined by a finite list of predicates. But concrete objects are by no means so: they are endowed with a great deal of attributes of an indefinite variety, so that they can at best exemplify with an acceptable approximation certain abstract objects that are totally encoding a given set of attributes through their corresponding predicates. The reason why such an exemplification can only be partial is that the different attributes that are simultaneously present in a concrete object are, in a way, mutually limiting themselves, so that this object does never fully exemplify anyone of them. This explains the correct sense of such common and obvious remarks as: “a rigid body, a perfect gas, an adiabatic transformation, a perfect elastic recoil, etc, do not exist in reality (or in Nature)”. Sometimes this remark is intended to vehiculate the thesis that these are nothing but intellectual fictions devoid of any correspondence with reality, but instrumentally used by scientists in order to organize their ideas. This interpretation is totally wrong, and is simply due to a confusion between encoding and exemplifying: no concrete thing encodes any finite and explicit number of characteristics that, on the contrary, can be appropriately encoded in a concept. Things can exemplify several concepts, while concepts (or abstract objects) do not exemplify the attributes they encode. Going back to the distinction between sense on the one hand, and reference or denotation on the other hand, we could also say that abstract objects belong to the level of sense, while their exemplifications belong to the level of reference, and constitute what is denoted by them. It is obvious that in the case of empirical sciences we try to construct conceptual structures (abstract objects) having empirical denotations (exemplified by concrete objects). If one has well understood this elementary but important distinction, one is in the position of correctly seeing how mathematics can concern physical objects. These objects are abstract objects, are structured sets of predicates, and there is absolutely nothing surprising in the fact that they could receive a mathematical structure (for example, a structure isomorphic to that of the positive real numbers, or to that of a given group, or of an abstract mathematical space, etc.). If it happens that these abstract objects are exemplified by concrete objects within a certain degree of approximation, we are entitled to say that the corresponding mathematical structure also holds true (with the same degree of approximation) for this domain of concrete objects. Now, in the case of physics, the abstract objects are constructed by isolating certain ontological attributes of things by means of concrete operations, so that they actually refer to things, and are exemplified by the concrete objects singled out by means of such operations up to a given degree of approximation or accuracy. In conclusion, one can maintain that mathematics constitutes at the same time the most exact language for speaking of the objects of the domain under consideration, and faithfully mirrors the concrete structure (in an ontological sense) of this domain of objects. Of course, it is very reasonable to recognize that other aspects of these things (or other attributes of them) might not be treatable by means of the particular mathematical language adopted, and this may imply either that these attributes could perhaps be handled through a different available mathematical language, or even that no mathematical language found as yet could be used for handling them.
If difference is the ground of being qua becoming, it is not difference as contradiction (Hegel), but as infinitesimal difference (Leibniz). Accordingly, the world is an ideal continuum or transfinite totality (Fold: Leibniz and the Baroque) of compossibilities and incompossibilities analyzable into an infinity of differential relations (Desert Islands and Other Texts). As the physical world is merely composed of contiguous parts that actually divide until infinity, it finds its sufficient reason in the reciprocal determination of evanescent differences (dy/dx, i.e. the perfectly determinable ratio or intensive magnitude between indeterminate and unassignable differences that relate virtually but never actually). But what is an evanescent difference if not a speculation or fiction? Leibniz refuses to make a distinction between the ontological nature and the practical effectiveness of infinitesimals. For even if they have no actuality of their own, they are nonetheless the genetic requisites of actual things.
Moreover, infinitesimals are precisely those paradoxical means through which the finite understanding is capable of probing into the infinite. They are the elements of a logic of sense, that great logical dream of a combinatory or calculus of problems (Difference and Repetition). On the one hand, intensive magnitudes are entities that cannot be determined logically, i.e. in extension, even if they appear or are determined in sensation only in connection with already extended physical bodies. This is because in themselves they are determined at infinite speed. Is not the differential precisely this problematic entity at the limit of sensibility that exists only virtually, formally, in the realm of thought? Isn’t the differential precisely a minimum of time, which refers only to the swiftness of its fictional apprehension in thought, since it is synthesized in Aion, i.e. in a time smaller than the minimum of continuous time and hence in the interstitial realm where time takes thought instead of thought taking time?
Contrary to the Kantian critique that seeks to eliminate the duality between finite understanding and infinite understanding in order to avoid the contradictions of reason, Deleuze thus agrees with Maïmon that we shouldn’t speak of differentials as mere fictions unless they require the status of a fully actual reality in that infinite understanding. The alternative between mere fictions and actual reality is a false problem that hides the paradoxical reality of the virtual as such: real but not actual, ideal but not abstract. If Deleuze is interested in the esoteric history of differential philosophy, this is as a speculative alternative to the exoteric history of the extensional science of actual differences and to Kantian critical philosophy. It is precisely through conceptualizing intensive, differential relations that finite thought is capable of acquiring consistency without losing the infinite in which it plunges. This brings us back to Leibniz and Spinoza. As Deleuze writes about the former: no one has gone further than Leibniz in the exploration of sufficient reason [and] the element of difference and therefore [o]nly Leibniz approached the conditions of a logic of thought. Or as he argues of the latter, fictional abstractions are only a preliminary stage for thought to become more real, i.e. to produce an expressive or progressive synthesis: The introduction of a fiction may indeed help us to reach the idea of God as quickly as possible without falling into the traps of infinite regression. In Maïmon’s reinvention of the Kantian schematism as well as in the Deleuzian system of nature, the differentials are the immanent noumena that are dramatized by reciprocal determination in the complete determination of the phenomenal. Even the Kantian concept of the straight line, Deleuze emphasizes, is a dramatic synthesis or integration of an infinity of differential relations. In this way, infinitesimals constitute the distinct but obscure grounds enveloped by clear but confused effects. They are not empirical objects but objects of thought. Even if they are only known as already developed within the extensional becomings of the sensible and covered over by representational qualities, as differences they are problems that do not resemble their solutions and as such continue to insist in an enveloped, quasi-causal state.
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The most common version of empirical equivalence discussed by philosophers is the case of exact empirical equivalence for all models of two theories. The potential interest of such a scenario is evident: obviously there is no chance in any nomologically possible world that experimental progress will resolve the debate, while settling it on theoretical grounds might also be difficult. However, this scenario runs the risk that the two supposedly rival theories are in fact one and the same theory in different guises. Such identification was often made by those influenced by logical empiricism. A related weaker claim is made today by John Norton, namely, that for theories for which the
observational equivalence can be demonstrated by arguments brief enough to be included in a journal article . . . we cannot preclude the possibility that the theories are merely variant formulations of the same theory.
Norton evidently has in mind journal articles in the philosophy of science, not physics or some other science. While Norton aims to deny that the underdetermination of theories by data is generic and that philosophers’ algorithmic rivals carry much force, there are some serious candidates for underdetermination that arise from within real physics and that have not been discussed much, if at all, by philosophers. However, the examples available from real physics do seem sufficiently widespread and interesting that it might well frequently be the case that scientific, or rather physical, theories are permanently underdetermined by data…..
Apart from some exceptions of perhaps little physical importance (such as solutions of an Ashtekar formulation with a degenerate metric, for example), the various sets of variables for GTR (broadly construed in the fashion of physicists) are empirically equivalent in the sense that all or most solutions of one set of equations are suitably related (not always one-to-one) with solutions in other sets of variables. Physicists are generally not tempted to regard the resulting theory formulations as distinct theories, partly because their criteria for physical reality are attuned to this mathematical interrelation. Each description comes with an adequate recipe for distinguishing the physically meaningful from the descriptive fluff, and no further ontological questions are typically asked or answered. Physicists are also quite comfortable with a certain amount of vagueness or merely implicit specificity. For example, is a given energy condition, such as the weak energy condition, part of General Relativity or not? The answer to that question depends, at least, on whether ‘realistic’ matter fields satisfy the condition; but whether a certain kind of matter is realistic is malleable in light of both empirical factors (such as the apparent observation of dark energy in the late 1990s) and theoretical factors (such as recognition that seemingly tame matter fields or quantum fields violate an energy condition hitherto regarded as important). GTR for physicists is in effect a cluster of theories sharing a hard core including Einstein’s equations, while partially overlapping in including or failing to include various additional claims with various degrees of importance, not unlike a Lakatosian research program. Perhaps Arthur Fine (Arthur Fine-The shaky game_ Einstein, realism, and the quantum theory) would commend to philosophers the physicists’ approach, which sounds something like his Natural Ontological Attitude that there is no distinctively philosophical question about the real existence of entities employed in scientific theories, so neither realism nor anti-realism is an appropriate doctrine. Physicists typically assume some sort of mathematical equivalence as necessary and sufficient for two formulations to be the same theory (though strict equivalence is not always required).
One of the reasons Marxism fails is because its cognitive model of the world – which even low IQ knuckleheads can grasp – does not map adequately on the reality of human nature and the means of production. But it would be a huge mistake to think that cognitive simplification is of exclusive domain of the liberal temperament, Conservatives are quite capable of “intuitively simplifying” as well. Which brings us to the psuedo-Right. If I had to define the Pseudo-Right, I would define it as those of a conservative disposition who refuse to acknowledge reality. Reality, in this instance, is not rhetorical “reality” but objective Truth, since it makes them feel bad – The Social Pathologist
Many of the Alt-Right, for instance, are quite happy with moral degeneracy provided its ethnically pure. The problem is that even an elementary understanding of history will show that no stable or prosperous society has ever been built on moral degeneracy. It’s a belief that is miscalibrated to reality. But lounging poolside in a white brothel sure feelz good. Likewise those of a traditionalist disposition wondering why it all went to Hell in a handbasket fail to understand that many of their “traditional beliefs” were miscalibrated to reality, and had the rug pulled out from them when reality intervened. Change induces bad feelings and these feelings must be avoided. Hence no change.