Fallibilist a priori. Thought of the Day 127.0

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Kant’s ‘transcendental subject’ is pragmatized in this notion in Peirce, transcending any delimitation of reason to the human mind: the ‘anybody’ is operational and refers to anything which is able to undertake reasoning’s formal procedures. In the same way, Kant’s synthetic a priori notion is pragmatized in Peirce’s account:

Kant declares that the question of his great work is ‘How are synthetical judgments a priori possible?’ By a priori he means universal; by synthetical, experiential (i.e., relating to experience, not necessarily derived wholly from experience). The true question for him should have been, ‘How are universal propositions relating to experience to be justified?’ But let me not be understood to speak with anything less than profound and almost unparalleled admiration for that wonderful achievement, that indispensable stepping-stone of philosophy. (The Essential Peirce Selected Philosophical Writings)

Synthetic a priori is interpreted as experiential and universal, or, to put it another way, observational and general – thus Peirce’s rationalism in demanding rational relations is connected to his scholastic realism posing the existence of real universals.

But we do not make a diagram simply to represent the relation of killer to killed, though it would not be impossible to represent this relation in a Graph-Instance; and the reason why we do not is that there is little or nothing in that relation that is rationally comprehensible. It is known as a fact, and that is all. I believe I may venture to affirm that an intelligible relation, that is, a relation of thought, is created only by the act of representing it. I do not mean to say that if we should some day find out the metaphysical nature of the relation of killing, that intelligible relation would thereby be created. [ ] No, for the intelligible relation has been signified, though not read by man, since the first killing was done, if not long before. (The New Elements of Mathematics)

Peirce’s pragmatizing Kant enables him to escape the threatening subjectivism: rational relations are inherent in the universe and are not our inventions, but we must know (some of) them in order to think. The relation of killer to killed, is not, however, given our present knowledge, one of those rational relations, even if we might later become able to produce a rational diagram of aspects of it. Yet, such a relation is, as Peirce says, a mere fact. On the other hand, rational relations are – even if inherent in the universe – not only facts. Their extension is rather that of mathematics as such, which can be seen from the fact that the rational relations are what make necessary reasoning possible – at the same time as Peirce subscribes to his father’s mathematics definition: Mathematics is the science that draws necessary conclusions – with Peirce’s addendum that these conclusions are always hypothetical. This conforms to Kant’s idea that the result of synthetic a priori judgments comprised mathematics as well as the sciences built on applied mathematics. Thus, in constructing diagrams, we have all the possible relations in mathematics (which is inexhaustible, following Gödel’s 1931 incompleteness theorem) at our disposal. Moreover, the idea that we might later learn about the rational relations involved in killing entails a historical, fallibilist rendering of the a priori notion. Unlike the case in Kant, the a priori is thus removed from a privileged connection to the knowing subject and its transcendental faculties. Thus, Peirce rather anticipates a fallibilist notion of the a priori.

Metaphysical Would-Be(s). Drunken Risibility.

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If one were to look at Quine’s commitment to similarity, natural kinds, dispositions, causal statements, etc., it is evident, that it takes him close to Peirce’s conception of Thirdness – even if Quine in an utopian vision imagines that all such concepts in a remote future will dissolve and vanish in favor of purely microstructural descriptions.

A crucial difference remains, however, which becomes evident when one looks at Quine’s brief formula for ontological commitment, the famous idea that ‘to be is to be the value of a bound variable’. For even if this motto is stated exactly to avoid commitment to several different types of being, it immediately prompts the question: the equation, in which the variable is presumably bound, which status does it have? Governing the behavior of existing variable values, is that not in some sense being real?

This will be Peirce’s realist idea – that regularities, tendencies, dispositions, patterns, may possess real existence, independent of any observer. In Peirce, this description of Thirdness is concentrated in the expression ‘real possibility’, and even it may sound exceedingly metaphysical at a first glance, it amounts, at a closer look, to regularities charted by science that are not mere shorthands for collections of single events but do possess reality status. In Peirce, the idea of real possibilities thus springs from his philosophy of science – he observes that science, contrary to philosophy, is spontaneously realist, and is right in being so. Real possibilities are thus counterposed to mere subjective possibilities due to lack of knowledge on the part of the subject speaking: the possibility of ‘not known not to be true’.

In a famous piece of self-critique from his late, realist period, Peirce attacks his earlier arguments (from ‘How to Make Our Ideas Clear’, in the late 1890s considered by himself the birth certificate of pragmatism after James’s reference to Peirce as pragmatism’s inventor). Then, he wrote

let us ask what we mean by calling a thing hard. Evidently that it will not be scratched by many other substances. The whole conception of this quality, as of every other, lies in its conceived effects. There is absolutely no difference between a hard thing and a soft thing so long as they are not brought to the test. Suppose, then, that a diamond could be crystallized in the midst of a cushion of soft cotton, and should remain there until it was finally burned up. Would it be false to say that that diamond was soft? […] Reflection will show that the reply is this: there would be no falsity in such modes of speech.

More than twenty-five years later, however, he attacks this argument as bearing witness to the nominalism of his youth. Now instead he supports the

scholastic doctrine of realism. This is usually defined as the opinion that there are real objects that are general, among the number being the modes of determination of existent singulars, if, indeed, these be not the only such objects. But the belief in this can hardly escape being accompanied by the acknowledgment that there are, besides, real vagues, and especially real possibilities. For possibility being the denial of a necessity, which is a kind of generality, is vague like any other contradiction of a general. Indeed, it is the reality of some possibilities that pragmaticism is most concerned to insist upon. The article of January 1878 endeavored to gloze over this point as unsuited to the exoteric public addressed; or perhaps the writer wavered in his own mind. He said that if a diamond were to be formed in a bed of cotton-wool, and were to be consumed there without ever having been pressed upon by any hard edge or point, it would be merely a question of nomenclature whether that diamond should be said to have been hard or not. No doubt this is true, except for the abominable falsehood in the word MERELY, implying that symbols are unreal. Nomenclature involves classification; and classification is true or false, and the generals to which it refers are either reals in the one case, or figments in the other. For if the reader will turn to the original maxim of pragmaticism at the beginning of this article, he will see that the question is, not what did happen, but whether it would have been well to engage in any line of conduct whose successful issue depended upon whether that diamond would resist an attempt to scratch it, or whether all other logical means of determining how it ought to be classed would lead to the conclusion which, to quote the very words of that article, would be ‘the belief which alone could be the result of investigation carried sufficiently far.’ Pragmaticism makes the ultimate intellectual purport of what you please to consist in conceived conditional resolutions, or their substance; and therefore, the conditional propositions, with their hypothetical antecedents, in which such resolutions consist, being of the ultimate nature of meaning, must be capable of being true, that is, of expressing whatever there be which is such as the proposition expresses, independently of being thought to be so in any judgment, or being represented to be so in any other symbol of any man or men. But that amounts to saying that possibility is sometimes of a real kind. (The Essential Peirce Selected Philosophical Writings, Volume 2)

In the same year, he states, in a letter to the Italian pragmatist Signor Calderoni:

I myself went too far in the direction of nominalism when I said that it was a mere question of the convenience of speech whether we say that a diamond is hard when it is not pressed upon, or whether we say that it is soft until it is pressed upon. I now say that experiment will prove that the diamond is hard, as a positive fact. That is, it is a real fact that it would resist pressure, which amounts to extreme scholastic realism. I deny that pragmaticism as originally defined by me made the intellectual purport of symbols to consist in our conduct. On the contrary, I was most careful to say that it consists in our concept of what our conduct would be upon conceivable occasions. For I had long before declared that absolute individuals were entia rationis, and not realities. A concept determinate in all respects is as fictitious as a concept definite in all respects. I do not think we can ever have a logical right to infer, even as probable, the existence of anything entirely contrary in its nature to all that we can experience or imagine. 

Here lies the core of Peirce’s metaphysical insistence on the reality of ‘would-be’s. Real possibilities, or would-bes, are vague to the extent that they describe certain tendential, conditional behaviors only, while they do not prescribe any other aspect of the single objects they subsume. They are, furthermore, represented in rationally interrelated clusters of concepts: the fact that the diamond is in fact hard, no matter if it scratches anything or not, lies in the fact that the diamond’s carbon structure displays a certain spatial arrangement – so it is an aspect of the very concept of diamond. And this is why the old pragmatic maxim may not work without real possibilities: it is they that the very maxim rests upon, because it is they that provide us with the ‘conceived consequences’ of accepting a concept. The maxim remains a test to weed out empty concepts with no conceived consequences – that is, empty a priori reasoning and superfluous metaphysical assumptions. But what remains after the maxim has been put to use, is real possibilities. Real possibilities thus connect epistemology, expressed in the pragmatic maxim, to ontology: real possibilities are what science may grasp in conditional hypotheses.

The question is whether Peirce’s revision of his old ‘nominalist’ beliefs form part of a more general development in Peirce from nominalism to realism. The locus classicus of this idea is Max Fisch (Peirce, Semeiotic and Pragmatism) where Fisch outlines a development from an initial nominalism (albeit of a strange kind, refusing, as always in Peirce, the existence of individuals determinate in all respects) via a series of steps towards realism, culminating after the turn of the century. Fisch’s first step is then Peirce’s theory of the real as that which reasoning would finally have as its result; the second step his Berkeley review with its anti-nominalism and the idea that the real is what is unaffected by what we may think of it; the third step is his pragmatist idea that beliefs are conceived habits of action, even if he here clings to the idea that the conditionals in which habits are expressed are material implications only – like the definition of ‘hard’; the fourth step his reading of Abbott’s realist Scientific Theism (which later influenced his conception of scientific universals) and his introduction of the index in his theory of signs; the fifth step his acceptance of the reality of continuity; the sixth the introduction of real possibilities, accompanied by the development of existential graphs, topology and Peirce’s changing view of Hegelianism; the seventh, the identification of pragmatism with realism; the eighth ‘his last stronghold, that of Philonian or material implication’. A further realist development exchanging Peirce’s early frequentist idea of probability for a dispositional theory of probability was, according to Fisch, never finished.

The issue of implication concerns the old discussion quoted by Cicero between the Hellenistic logicians Philo and Diodorus. The former formulated what we know today as material implication, while the latter objected on common-sense ground that material implication does not capture implication in everyday language and thought and another implication type should be sought. As is well known, material implication says that p ⇒ q is equivalent to the claim that either p is false or q is true – so that p ⇒ q is false only when p is true and q is false. The problems arise when p is false, for any false p makes the implication true, and this leads to strange possibilities of true inferences. The two parts of the implication have no connection with each other at all, such as would be the spontaneous idea in everyday thought. It is true that Peirce as a logician generally supports material (‘Philonian’) implication – but it is also true that he does express some second thoughts at around the same time as the afterthoughts on the diamond example.

Peirce is a forerunner of the attempts to construct alternatives such as strict implication, and the reason why is, of course, that real possibilities are not adequately depicted by material implication. Peirce is in need of an implication which may somehow picture the causal dependency of q on p. The basic reason for the mature Peirce’s problems with the representation of real possibilities is not primarily logical, however. It is scientific. Peirce realizes that the scientific charting of anything but singular, actual events necessitates the real existence of tendencies and relations connecting singular events. Now, what kinds are those tendencies and relations? The hard diamond example seems to emphasize causality, but this probably depends on the point of view chosen. The ‘conceived consequences’ of the pragmatic maxim may be causal indeed: if we accept gravity as a real concept, then masses will attract one another – but they may all the same be structural: if we accept horse riders as a real concept, then we should expect horses, persons, the taming of horses, etc. to exist, or they may be teleological. In any case, the interpretation of the pragmatic maxim in terms of real possibilities paves the way for a distinction between empty a priori suppositions and real a priori structures.

Transcendentally Realist Modality. Thought of the Day 78.1

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Let us start at the beginning first! Though the fact is not mentioned in Genesis, the first thing God said on the first day of creation was ‘Let there be necessity’. And there was necessity. And God saw necessity, that it was good. And God divided necessity from contingency. And only then did He say ‘Let there be light’. Several days later, Adam and Eve were introducing names for the animals into their language, and during a break between the fish and the birds, introduced also into their language modal auxiliary verbs, or devices that would be translated into English using modal auxiliary verbs, and rules for their use, rules according to which it can be said of some things that they ‘could’ have been otherwise, and of other things that they ‘could not’. In so doing they were merely putting labels on a distinction that was no more their creation than were the fishes of the sea or the beasts of the field or the birds of the air.

And here is the rival view. The failure of Genesis to mention any command ‘Let there be necessity’ is to be explained simply by the fact that no such command was issued. We have no reason to suppose that the language in which God speaks to the angels contains modal auxiliary verbs or any equivalent device. Sometime after the Tower of Babel some tribes found that their purposes would be better served by introducing into their language certain modal auxiliary verbs, and fixing certain rules for their use. When we say that this is necessary while that is contingent, we are applying such rules, rules that are products of human, not divine intelligence.

This theological language would have been the natural way for seventeenth or eighteenth century philosophers, who nearly all were or professed to be theists or deists, to discuss the matter. For many today, such language cannot be literally accepted, and if it is only taken metaphorically, then at least better than those who speak figuratively and frame the question as that of whether the ‘origin’ of necessity lies outside us or within us. So let us drop the theological language, and try again.

Well, here the first view: Ultimately reality as it is in itself, independently of our attempts to conceptualize and comprehend it, contains both facts about what is, and superfacts about what not only is but had to have been. Our modal usages, for instance, the distinction between the simple indicative ‘is’ and the construction ‘had to have been’, simply reflect this fundamental distinction in the world, a distinction that is and from the beginning always was there, independently of us and our concerns.

And here is the second view: We have reasons, connected with our various purposes in life, to use certain words, including ‘would’ and ‘might’, in certain ways, and thereby to make certain distinctions. The distinction between those things in the world that would have been no matter what and those that might have failed to be if only is a projection of the distinctions made in our language. Our saying there were necessities there before us is a retroactive application to the pre-human world of a way of speaking invented and created by human beings in order to solve human problems.

Well, that’s the second try. With it even if one has gotten rid of theology, unfortunately one has not gotten rid of all metaphors. The key remaining metaphor is the optical one: reflection vs projection. Perhaps the attempt should be to get rid of all metaphors, and admit that the two views are not so much philosophical theses or doctrines as ‘metaphilosophical’ attitudes or orientations: a stance that finds the ‘reflection’ metaphor congenial, and the stance that finds the ‘projection’ metaphor congenial. So, lets try a third time to describe the distinction between the two outlooks in literal terms, avoiding optics as well as theology.

To begin with, both sides grant that there is a correspondence or parallelism between two items. On the one hand, there are facts about the contrast between what is necessary and what is contingent. On the other hand, there are facts about our usage of modal auxiliary verbs such as ‘would’ and ‘might’, and these include, for instance, the fact that we have no use for questions of the form ‘Would 29 still have been a prime number if such-and- such?’ but may have use for questions of the form ‘Would 29 still have been the number of years it takes for Saturn to orbit the sun if such-and-such?’ The difference between the two sides concerns the order of explanation of the relation between the two parallel ranges of facts.

And what is meant by that? Well, both sides grant that ‘29 is necessarily prime’, for instance, is a proper thing to say, but they differ in the explanation why it is a proper thing to say. Asked why, the first side will say that ultimately it is simply because 29 is necessarily prime. That makes the proposition that 29 is necessarily prime true, and since the sentence ‘29 is necessarily prime’ expresses that proposition, it is true also, and a proper thing to say. The second side will say instead that ‘29 is necessarily prime’ is a proper thing to say because there is a rule of our language according to which it is a proper thing to say. This formulation of the difference between the two sides gets rid of metaphor, though it does put an awful lot of weight on the perhaps fragile ‘why’ and ‘because’.

Note that the adherents of the second view need not deny that 29 is necessarily prime. On the contrary, having said that the sentence ‘29 is necessarily prime’ is, per rules of our language, a proper thing to say, they will go on to say it. Nor need the adherents of the first view deny that recognition of the propriety of saying ‘29 is necessarily prime’ is enshrined in a rule of our language. The adherents of the first view need not even deny that proximately, as individuals, we learn that ‘29 is necessarily prime’ is a proper thing to say by picking up the pertinent rule in the course of learning our language. But the adherents of the first view will maintain that the rule itself is only proper because collectively, as the creators of the language, we or our remote answers have, in setting up the rule, managed to achieve correspondence with a pre-existing fact, or rather, a pre-existing superfact, the superfact that 29 is necessarily prime. The difference between the two views is, in the order of explanation.

The adherents regarding labels for the two sides, or ‘metaphilosophical’ stances, rather than inventing new ones, will simply take two of the most overworked terms in the philosophical lexicon and give them one more job to do, calling the reflection view ‘realism’ about modality, and the projection view ‘pragmatism’. That at least will be easy to remember, since ‘realism’ and ‘reflection’ begin with the same first two letters, as do ‘pragmatism’ and ‘projection’. The realist/pragmatist distinction has bearing across a range of issues and problems, and above all it has bearing on the meta-issue of which issues are significant. For the two sides will, or ought to, recognize quite different questions as the central unsolved problems in the theory of modality.

For those on the realist side, the old problem of the ultimate source of our knowledge of modality remains, even if it is granted that the proximate source lies in knowledge of linguistic conventions. For knowledge of linguistic conventions constitutes knowledge of a reality independent of us only insofar as our linguistic conventions reflect, at least to some degree, such an ultimate reality. So for the realist the problem remains of explaining how such degree of correspondence as there is between distinctions in language and distinctions in the world comes about. If the distinction in the world is something primary and independent, and not a mere projection of the distinction in language, then how the distinction in language comes to be even imperfectly aligned with the distinction in the world remains to be explained. For it cannot be said that we have faculties responsive to modal facts independent of us – not in any sense of ‘responsive’ implying that if the facts had been different, then our language would have been different, since modal facts couldn’t have been different. What then is the explanation? This is the problem of the epistemology of modality as it confronts the realist, and addressing it is or ought to be at the top of the realist agenda.

As for the pragmatist side, a chief argument of thinkers from Kant to Ayer and Strawson and beyond for their anti-realist stance has been precisely that if the distinction we perceive in reality is taken to be merely a projection of a distinction created by ourselves, then the epistemological problem dissolves. That seems more like a reason for hoping the Kantian or Ayerite or Strawsonian view is the right one, than for believing that it is; but in any case, even supposing the pragmatist view is the right one, and the problems of the epistemology of modality are dissolved, still the pragmatist side has an important unanswered question of its own to address. The pragmatist account, begins by saying that we have certain reasons, connected with our various purposes in life, to use certain words, including ‘would’ and ‘might’, in certain ways, and thereby to make certain distinctions. What the pragmatist owes us is an account of what these purposes are, and how the rules of our language help us to achieve them. Addressing that issue is or ought to be at the top of the pragmatists’ to-do list.

While the positivist Ayer dismisses all metaphysics, the ordinary-language philosopher Strawson distinguishes good metaphysics, which he calls ‘descriptive’, from bad metaphysics, which he calls ‘revisionary’, but which rather be called ‘transcendental’ (without intending any specifically Kantian connotations). Descriptive metaphysics aims to provide an explicit account of our ‘conceptual scheme’, of the most general categories of commonsense thought, as embodied in ordinary language. Transcendental metaphysics aims to get beyond or behind all merely human conceptual schemes and representations to ultimate reality as it is in itself, an aim that Ayer and Strawson agree is infeasible and probably unintelligible. The descriptive/transcendental divide in metaphysics is a paradigmatically ‘metaphilosophical’ issue, one about what philosophy is about. Realists about modality are paradigmatic transcendental metaphysicians. Pragmatists must in the first instance be descriptive metaphysicians, since we must to begin with understand much better than we currently do how our modal distinctions work and what work they do for us, before proposing any revisions or reforms. And so the difference between realists and pragmatists goes beyond the question of what issue should come first on the philosopher’s agenda, being as it is an issue about what philosophical agendas are about.

Mathematical Reductionism: As Case Via C. S. Peirce’s Hypothetical Realism.

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During the 20th century, the following epistemology of mathematics was predominant: a sufficient condition for the possibility of the cognition of objects is that these objects can be reduced to set theory. The conditions for the possibility of the cognition of the objects of set theory (the sets), in turn, can be given in various manners; in any event, the objects reduced to sets do not need an additional epistemological discussion – they “are” sets. Hence, such an epistemology relies ultimately on ontology. Frege conceived the axioms as descriptions of how we actually manipulate extensions of concepts in our thinking (and in this sense as inevitable and intuitive “laws of thought”). Hilbert admitted the use of intuition exclusively in metamathematics where the consistency proof is to be done (by which the appropriateness of the axioms would be established); Bourbaki takes the axioms as mere hypotheses. Hence, Bourbaki’s concept of justification is the weakest of the three: “it works as long as we encounter no contradiction”; nevertheless, it is still epistemology, because from this hypothetical-deductive point of view, one insists that at least a proof of relative consistency (i.e., a proof that the hypotheses are consistent with the frequently tested and approved framework of set theory) should be available.

Doing mathematics, one tries to give proofs for propositions, i.e., to deduce the propositions logically from other propositions (premisses). Now, in the reductionist perspective, a proof of a mathematical proposition yields an insight into the truth of the proposition, if the premisses are already established (if one has already an insight into their truth); this can be done by giving in turn proofs for them (in which new premisses will occur which ask again for an insight into their truth), or by agreeing to put them at the beginning (to consider them as axioms or postulates). The philosopher tries to understand how the decision about what propositions to take as axioms is arrived at, because he or she is dissatisfied with the reductionist claim that it is on these axioms that the insight into the truth of the deduced propositions rests. Actually, this epistemology might contain a short-coming since Poincaré (and Wittgenstein) stressed that to have a proof of a proposition is by no means the same as to have an insight into its truth.

Attempts to disclose the ontology of mathematical objects reveal the following tendency in epistemology of mathematics: Mathematics is seen as suffering from a lack of ontological “determinateness”, namely that this science (contrarily to many others) does not concern material data such that the concept of material truth is not available (especially in the case of the infinite). This tendency is embarrassing since on the other hand mathematical cognition is very often presented as cognition of the “greatest possible certainty” just because it seems not to be bound to material evidence, let alone experimental check.

The technical apparatus developed by the reductionist and set-theoretical approach nowadays serves other purposes, partly for the reason that tacit beliefs about sets were challenged; the explanations of the science which it provides are considered as irrelevant by the practitioners of this science. There is doubt that the above mentioned sufficient condition is also necessary; it is not even accepted throughout as a sufficient one. But what happens if some objects, as in the case of category theory, do not fulfill the condition? It seems that the reductionist approach, so to say, has been undocked from the historical development of the discipline in several respects; an alternative is required.

Anterior to Peirce, epistemology was dominated by the idea of a grasp of objects; since Descartes, intuition was considered throughout as a particular, innate capacity of cognition (even if idealists thought that it concerns the general, and empiricists that it concerns the particular). The task of this particular capacity was the foundation of epistemology; already from Aristotle’s first premisses of syllogism, what was aimed at was to go back to something first. In this traditional approach, it is by the ontology of the objects that one hopes to answer the fundamental question concerning the conditions for the possibility of the cognition of these objects. One hopes that there are simple “basic objects” to which the more complex objects can be reduced and whose cognition is possible by common sense – be this an innate or otherwise distinguished capacity of cognition common to all human beings. Here, epistemology is “wrapped up” in (or rests on) ontology; to do epistemology one has to do ontology first.

Peirce shares Kant’s opinion according to which the object depends on the subject; however, he does not agree that reason is the crucial means of cognition to be criticised. In his paper “Questions concerning certain faculties claimed for man”, he points out the basic assumption of pragmatist philosophy: every cognition is semiotically mediated. He says that there is no immediate cognition (a cognition which “refers immediately to its object”), but that every cognition “has been determined by a previous cognition” of the same object. Correspondingly, Peirce replaces critique of reason by critique of signs. He thinks that Kant’s distinction between the world of things per se (Dinge an sich) and the world of apparition (Erscheinungswelt) is not fruitful; he rather distinguishes the world of the subject and the world of the object, connected by signs; his position consequently is a “hypothetical realism” in which all cognitions are only valid with reservations. This position does not negate (nor assert) that the object per se (with the semiotical mediation stripped off) exists, since such assertions of “pure” existence are seen as necessarily hypothetical (that means, not withstanding philosophical criticism).

By his basic assumption, Peirce was led to reveal a problem concerning the subject matter of epistemology, since this assumption means in particular that there is no intuitive cognition in the classical sense (which is synonymous to “immediate”). Hence, one could no longer consider cognitions as objects; there is no intuitive cognition of an intuitive cognition. Intuition can be no more than a relation. “All the cognitive faculties we know of are relative, and consequently their products are relations”. According to this new point of view, intuition cannot any longer serve to found epistemology, in departure from the former reductionist attitude. A central argument of Peirce against reductionism or, as he puts it,

the reply to the argument that there must be a first is as follows: In retracing our way from our conclusions to premisses, or from determined cognitions to those which determine them, we finally reach, in all cases, a point beyond which the consciousness in the determined cognition is more lively than in the cognition which determines it.

Peirce gives some examples derived from physiological observations about perception, like the fact that the third dimension of space is inferred, and the blind spot of the retina. In this situation, the process of reduction loses its legitimacy since it no longer fulfills the function of cognition justification. At such a place, something happens which I would like to call an “exchange of levels”: the process of reduction is interrupted in that the things exchange the roles performed in the determination of a cognition: what was originally considered as determining is now determined by what was originally considered as asking for determination.

The idea that contents of cognition are necessarily provisional has an effect on the very concept of conditions for the possibility of cognitions. It seems that one can infer from Peirce’s words that what vouches for a cognition is not necessarily the cognition which determines it but the livelyness of our consciousness in the cognition. Here, “to vouch for a cognition” means no longer what it meant before (which was much the same as “to determine a cognition”), but it still means that the cognition is (provisionally) reliable. This conception of the livelyness of our consciousness roughly might be seen as a substitute for the capacity of intuition in Peirce’s epistemology – but only roughly, since it has a different coverage.

Whitehead’s Non-Anthropocentric Quantum Field Ontology. Note Quote.

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Whitehead builds also upon James’s claim that “The thought is itself the thinker”.

Either your experience is of no content, of no change, or it is of a perceptible amount of content or change. Your acquaintance with reality grows literally by buds or drops of perception. Intellectually and on reflection you can divide them into components, but as immediately given they come totally or not at all. — William James.

If the quantum vacuum displays features that make it resemble a material, albeit a really special one, we can immediately ask: then what is this material made of? Is it a continuum, or are the “atoms” of vacuum? Is vacuum the primordial substance of which everything is made of? Let us start by decoupling the concept of vacuum from that of spacetime. The concept of vacuum as accepted and used in standard quantum field theory is tied with that of spacetime. This is important for the theory of quantum fields, because it leads to observable effects. It is the variation of geometry, either as a change in boundary conditions or as a change in the speed of light (and therefore the metric) which is responsible for the creation of particles. Now, one can legitimately go further and ask: which one is the fundamental “substance”, the space-time or the vacuum? Is the geometry fundamental in any way, or it is just a property of the empty space emerging from a deeper structure? That geometry and substance can be separated is of course not anything new for philosophers. Aristotle’s distinction between form and matter is one example. For Aristotle the “essence” becomes a true reality only when embodied in a form. Otherwise it is just a substratum of potentialities, somewhat similar to what quantum physics suggests. Immanuel Kant was even more radical: the forms, or in general the structures that we think of as either existing in or as being abstracted from the realm of noumena are actually innate categories of the mind, preconditions that make possible our experience of reality as phenomena. Structures such as space and time, causality, etc. are a priori forms of intuition – thus by nature very different from anything from the outside reality, and they are used to formulate synthetic a priori judgments. But almost everything that was discovered in modern physics is at odds with Kant’s view. In modern philosophy perhaps Whitehead’s process metaphysics provides the closest framework for formulating these problems. For Whitehead, potentialities are continuous, while the actualizations are discrete, much like in the quantum theory the unitary evolution is continuous, while the measurement is non-unitary and in some sense “discrete”. An important concept is the “extensive continuum”, defined as a “relational complex” containing all the possibilities of objectification. This continuum also contains the potentiality for division; this potentiality is effected in what Whitehead calls “actual entities (occasions)” – the basic blocks of his cosmology. The core issue for both Whiteheadian Process and Quantum Process is the emergence of the discrete from the continuous. But what fixes, or determines, the partitioning of the continuous whole into the discrete set of subsets? The orthodox answer is this: it is an intentional action of an experimenter that determines the partitioning! But, in Whiteheadian process the world of fixed and settled facts grows via a sequence actual occasions. The past actualities are the causal and structural inputs for the next actual occasion, which specifies a new space-time standpoint (region) from which the potentialities created by the past actualities will be prehended (grasped) by the current occasion. This basic autogenetic process creates the new actual entity, which, upon becoming actual, contributes to the potentialities for the succeeding actual occasions. For the pragmatic physicist, since the extensive continuum provides the space of possibilities from which the actual entities arise, it is tempting to identify it with the quantum vacuum. The actual entities are then assimilated with events in spacetime, as resulting from a quantum measurement, or simply with particles. The following caveat is however due: Whitehead’s extensive continuum is also devoid of geometrical content, while the quantum vacuum normally carries information about the geometry, be it flat or curved. Objective/absolute actuality consist of a sequence of psycho-physical quantum reduction events, identified as Whiteheadian actual entities/occasions. These happenings combine to create a growing “past” of fixed and settled “facts”. Each “fact” is specified by an actual occasion/entity that has a physical aspect (pole), and a region in space-time from which it views reality. The physical input is precisely the aspect of the physical state of the universe that is localized along the part of the contemporary space-like surface σ that constitutes the front of the standpoint region associated with the actual occasion. The physical output is reduced state ψ(σ) on this space-like surface σ. The mental pole consists of an input and an output. The mental inputs and outputs have the ontological character of thoughts, ideas, or feelings, and they play an essential dynamical role in unifying, evaluating, and selecting discrete classically conceivable activities from among the continuous range of potentialities offered by the operation of the physically describable laws. The paradigmatic example of an actual occasion is an event whose mental pole is experienced by a human being as an addition to his or her stream of conscious events, and whose output physical pole is the neural correlate of that experiential event. Such events are “high-grade” actual occasions. But the Whitehead/Quantum ontology postulates that simpler organisms will have fundamentally similar but lower-grade actual occasions, and that there can be actual occasions associated with any physical systems that possess a physical structure that will support physically effective mental interventions of the kind described above. Thus the Whitehead/Quantum ontology is essentially an ontologicalization of the structure of orthodox relativistic quantum field theory, stripped of its anthropocentric trappings. It identifies the essential physical and psychological aspects of contemporary orthodox relativistic quantum field theory, and lets them be essential features of a general non-anthropocentric ontology.

quantum_veda

It is reasonable to expect that the continuous differentiable manifold that we use as spacetime in physics (and experience in our daily life) is a coarse-grained manifestation of a deeper reality, perhaps also of quantum (probabilistic) nature. This search for the underlying structure of spacetime is part of the wider effort of bringing together quantum physics and the theory of gravitation under the same conceptual umbrella. From various the- oretical considerations, it is inferred that this unification should account for physics at the incredibly small scale set by the Planck length, 10−35m, where the effects of gravitation and quantum physics would be comparable. What happens below this scale, which concepts will survive in the new description of the world, is not known. An important point is that, in order to incorporate the main conceptual innovation of general relativity, the the- ory should be background-independent. This contrasts with the case of the other fields (electromagnetic, Dirac, etc.) that live in the classical background provided by gravitation. The problem with quantizing gravitation is – if we believe that the general theory of relativity holds in the regime where quantum effects of gravitation would appear, that is, beyond the Planck scale – that there is no underlying background on which the gravitational field lives. There are several suggestions and models for a “pre-geometry” (a term introduced by Wheeler) that are currently actively investigated. This is a question of ongoing investigation and debate, and several research programs in quantum gravity (loops, spinfoams, noncommutative geometry, dynamical triangulations, etc.) have proposed different lines of attack. Spacetime would then be an emergent entity, an approximation valid only at scales much larger than the Planck length. Incidentally, nothing guarantees that background-independence itself is a fundamental concept that will survive in the new theory. For example, string theory is an approach to unifying the Standard Model of particle physics with gravitation which uses quantization in a fixed (non-dynamic) background. In string theory, gravitation is just another force, with the graviton (zero mass and spin 2) obtained as one of the string modes in the perturbative expansion. A background-independent formulation of string theory would be a great achievement, but so far it is not known if it can be achieved.