Hooking up Logic

January 8, 2012 § Leave a comment

The million dollar question of any philosophy is

about the relation between logic and world, though it is probably not the only one. “World” shall subsume the sayable and the demonstrable here (in contrast to the Tractatus [1]). Thus, this would comprise, for instance, the relationship between practiced language and logic, but also, and in no way less problematic, the derivation of a particular reasoning about the world on the basis of diagnostic models. Another flavor of the same issue is concerned about the question why mathematics is applicable to the world. There was, for instance, the dream of some philosophers and logicians (some still dreaming this dream today) about analytical (=logical) conclusions that extend the empirical basis. This is, of course, even beyond utter nonsense.

Somehow it seems that the logical approach is completely unsuitable for getting in touch with the world. O.k., that’s not really surprising for anyone who understood Wittgenstein’s philosophical work, even if only partially. Nevertheless, up to date there is no applicable proposal about this relationship. Simply enforcing practiced language (or even the whole world) into the rigid brace of logic renders practiced language as well as the world inevitably into a deterministic machine. This is hardly acceptable, of course, despite the fact that large parts of philosophy, neurobiology and many sciences are proposing (doing?) exactly this.

Our investigation of this difficult problematics has to concern about three main parts:

  • (1) The transition from the realm of (probabilistic) description to logic.
  • (2) The transition from logic back into the world.
  • (3) The conditions for either of the two directions

In other parts of this collection of writings about machine-based epistemology we already met these transitions, yet without digging too far into the problematics of the relation between logics and world. Matters of appropriate levels of description, the status of similarity, and also of the duality between information and causality all relate to these transitions.

Yet, we not only want to get clear about the problematics posed by the transition across the gap between the indeterminate/world and logics. We also want to outline a possible path towards an implementation.

Consequences of an Irrevocable Choice

Elsewhere, we already argued that the empirical input into instances that are stuffed with the power for modeling through association needs to be probabilized. Neither words, nor objects, nor formalized descriptions can serve as a basis for the first steps of getting into contact with the world, because any of those requires (and hence: assumes) a two-fold apriori existence, both in the outside and the inside of the “understanding” subject.1 Yet, this is exactly what we try to explain (in the meaning of “trying to get clear about”), thus we should not, of course, assume it. Doing so instead, we would commit the infamous figure of petitio principii, which victimizes large parts of philosophy (e.g. Hegel and any sort of “analytic” philosophy), humanities (positivism in social sciences, formalization of semantics or even language as a whole) and even of science (computer science, and even biology concerning “genes” [2]). Here, we have to be very clear about our basic assumptions in order to be victimized by a petitio principii ourselves.

Philosophically spoken, we do not start with existence. We do not follow the related assumption of the primary role of identity2 and logics, symbolized as “a=a”3. This also excludes any sort of externalized realism, even regarding the “structure” of the world. As a consequence, we also tend towards a denial of the feasibility of ontology as a subject of (philosophical) thinking. In the introduction to his “Ethics without Ontology” [3] Putnam readily displayed the intention for the Hermes lecture in 2001 on which the book was based:

I […] present in public something I realized I had long wanted to say, namely that the renewed (and continuing) respectability of Ontology (the capital letter here is intentional!) following the publication of W. V. Quine’s “On What There Is” at the midpoint of the last century has had disastrous consequences for just about every part of analytic philosophy.

…and a bit later a bit more precise:

[…] the purpose of the Hermes Lectures was to criticize certain fallacious conceptions-conceptions linking ontology, metaphysics, and the theory of truth-that, in my view, have had deleterious effects on our thinking as much in philosophy of logic and philosophy of mathematics as in ethics.

For Putnam, among many others, and also, of course, us, it does not make sense to split off philosophy into disciplines like epistemology as the philosophy of knowing, or, more general, into any philosophy of ⟨..⟩. Ontology, often regarded as the science of being, such putting the idea of being before any other idea, is deleterious to any human thought, because it claims a necessity of truths that are to be found in the external viz. non-human (sphere of the) world, let it be physical, religious or idealistic. The direction of this argument can be reversed without loosing validity: Claiming the necessity of x-kind of truth directly results in an acceptance of the primacy of existence. A truth that is rooted outside of ethics and morality is nothing but a monster. Both directions open the doors wide for any “justification” of a-human activities. From this perspective, ontology is a atavistic remnant pre-historic mysticism. The idea of “ontology” is even deleterious in computer sciences, as it hides the important questions and supports self-delusionary concepts. Our opposition to “Ontology” does not mean that we deny that things, facts or humans exists. In some sense we even could agree to say that ideas “exist.” We just deny that Ontology and existence is an acceptable or even a possible starting point. Yet, an ontology that is not a starting point is not an Ontology any more. A biology that does not start with life and living beings is not a biology any more, at most biochemistry, biophysics etc.

The contrasting perspective is that of the transcendental difference. In physical terms it is probably more popular to speak about fluctuations. In the beginning there is not the word, nor the idea, in the beginning there are only fluctuations, yet indeterminate, while the notion of “beginning” refers to any individual being as well as to the Big Bang and its evolution towards crisp separations, which we sometimes call “particles” or “objects.” If in any beginning there are only fluctuations, every thing and so every being may establish itself only through interpretation5, or more precisely, in a volatile (probabilistic) network of transient, mutually superposing interpretations. We may well call this kind of a “String Theory” (of Generalized Reference). Language and meaning form only the tip of that iceberg. Last, but not least, we see that accepting the primacy of interpretation influences any activity, even that of interpreting and modeling itself.

Preferring difference in favor of identity, and so interpretation in favor of existence as starting points should not be misinterpreted as a denial of existence, as we already mentioned above, or as a denial of the possibility of identity. I am not denying that we exist, that is it is feasible to say that something like an idea or properties of things exists6, nor do I think that we are living in a matrix, in a brain vat or anything comparable.7 Of course, the concept of “reality” remains meaningful for us. Yet, the reference of this “existing,” or this “reality” is, in our perspective, not outside the human sphere, definitely not, and not a tiny bit. Hence it is not possible to do a science of existence (ontology), because as soon as one would start with it, it would vanish. (The rest of the argument can be met in Putnam’s book.)

Both of these alternatives are, however, still based on assumptions, necessarily so. One may call these assumptions “metaphysical,” the label does not matter. If there would not be metaphysical assumptions inside them, everything about the origin could be formulated (formally explicated), which of course is not possible. There is no such thing as an explication that does not need external conditions. Such, albeit there seem to be good reasons for choosing the second alternative we nevertheless you may also call these assumptions “non-justifiable beliefs.” Later, we will see that it is well possible to identify the “nature” of this dependence to external conditions and also how we can speak about it without internal contradiction, without “silly” self-contradictory performance. Yet, preferring the primacy of interpretation against the primacy of identity is justified by a larger degree consistency, in other words it remains being based on a belief.

The common issue about both alternatives is that there is no “intermediate” for them. They are mutually exclusive and together they are exhaustive, there is no other possibility, except, perhaps, revelation that by definition is not only outside of the sayable, but even outside of the world. It is simply there, without any possibility for (a) preceding reason. Besides that, there are only two possible primacies, logics or interpretation. We may call them strong abstract attractors. Switching between them forth and back would corroborate any possibility even for the simplest argument, which is not acceptable for any stance emerging from the two alternatives.

The difference between both alternatives is, indeed, really a large one. Starting with identity not only means starting with logics, but even to equate the world with logics, or, in more favorable words, to claim the direct applicability of truth functions in the world. Yet, today we know that the programs of Carnap [4] and Stegmüller [5] heading for a “language of/for science”, or “scientific language” failed, that there is no possible definition of knowledge that would obey to the logical frame (cf. Gettier [6], Peschard[7]). The failure of the logical approach in artificial intelligence we already mentioned above.

So, the question about the relationship between logics and the world itself turns away from the possibility for a formal foundation, even from formal arguments. This relationship is one of pure practical concerns.

The Theory of Transit

Unexpected Allies, and a Break

Even if we accept the primacy of interpretation for any feasibly distinguished activity, it is undeniable that there is something like logics. Before we start trying to link into the fields of the propositional we have to get clear about the status of logic itself.

Following Wittgenstein, Johnston [8] supports the position that logical form is available only a posteriori. We can’t have apriori knowledge of atomic forms, e.g. of “relation,” where “apriori” means “in advance to the application of logic”. The “application of logic” precedes the possibility to distinguish logical forms and it is understood by Wittgenstein as a truth-functional analysis; this brings in aspects of interpretation. In other words, it is a performance that actualizes a particular logical form. No doubt, there is now a certain tension that we have to resolve.

Johnston [8] captures it in the following way (p.155):

And in a 1929 discussion with Waismann entitled ‘Objects’ Wittgenstein says: “Only when we analyse phenomena logically shall we know what form elementary propositions have. (Wittgenstein 1979b, p. 42)8” It is, Wittgenstein held, only through the performance of analysis that we may develop a clear symbolism, substituting it for the unprecise one of everyday. A concept script will encode the elementary propositional forms and uncovering what these are is a principal ambition of the project of analysis. Wittgenstein is fundamentally opposed to the idea that one first constructs a concept script and only subsequently turns one’s attention to particular propositions of everyday, attempting to see how they might be written in the constructed symbolism. One does not first work out what propositional forms there are and then subsequently decide which of these forms is had by some English sentence. Those are not the two steps of giving logic and applying it. The two steps of giving logic and applying it are rather first to characterise truth functionality, and subsequently to uncover truth functional structuring within propositions. And it is only through the second of these that the elementary forms will become apparent, that a concept-script will become available.

The distinction between (universal) “particulars” and (truly universal) universals (by Frege or Russell) is a misunderstanding. Johnston (p.159) cites Ramsey that in “the historical theories of universals and particulars are ‘muddles’ predicated upon the false presumption that we have knowledge of atomic forms.”

Tractarian objects of logic do not have a particular form. As Johnston compiled it, Wittgenstein wrote in the Tractatus (TLP 2.0141):

The possibility of its occurring in states of affairs is the form of an object.

But he also asserts that there is nothing accidental in logic. Wittgenstein does not refer to probability or possibility here, as it is to be understood regarding empirical relations. Thus the possibility in TLP 2.0141 could not be related to immanence either. It is much more appealing to interpret the Tractarian possibility as potential, or virtuality, maybe almost in the Aristotelian sense. Logic gets attached the notion of transcendentality.

Even more significant for our endeavor of machine-based epistemology, he proceeds with

If two objects have the same logical form, the only distinction between them, apart from their external properties, is that they are different. (TLP 2.0233)

External properties are properties that emerge due to the application of the logic that comprises them. The potential of building relations is the form of an object of logic, and the only thing that we can say about different such potentials is that they are different. That difference can’t be described, of course. It is transcendental difference.

Well, this now is an astonishing parallel to the central pillar of a very different (!) sort of doing philosophy: that of Gilles Deleuze. In the interview series “ABCDaire” Deleuze [9] called the “school” of Wittgensteinian philosophy a “catastrophe” and denied to comment any further. Deleuze said

Non, je ne veux pas parler de ça. Pour moi, c’est une catastrophe philosophique, c’est le type même d’une école, c’est une réduction de toute la philosophie, une régression massive de la philosophie. C’est très triste […]

Notably, Deleuze did not refer directly to Wittgenstein himself. We all know that Wittgenstein is embarrassingly often taken as representative of “analytic” or “positivist” philosophy, which surely is a deep and violent misunderstanding [10]. (As we just saw,  even according to the Tractatus, Wittgenstein denies the possibility of a primacy of logical analysis before performance, which is a typical pragmatist attitude, and to label any “thinking” or dissecting as analytic, well…) Maybe, however, there is also a trace of sort of some higher form of rivalry in Deleuze’s comments. Everything in Deleuze’s approach is arranged around transcendental difference, and the differential. Despite the fact that both performed a very different style, I think that both share a certain disgust regarding the “analytic,” and certainly both favor the approach to look closely to their subject of investigation. “Broad strokes” (a term coined by Quine) do not belong to the tool-set of any of the two. We take this concord about the transcendental status of difference between those two great philosophers—maybe the two greatest philosophers of the 20th century—as a confirmation for the feasibility of our approach.

As a consequence of the transcendental difference of objects in logic, any logic that contains countable relations is already affected by semantic choices and empirical determinations. We follow Wittgenstein in his (implicit) proposal to discern “pure,” hence transcendental logics, in short “T-logic,” from practical quasi-logics, or in short “Q-logic”. Quasi-logic is best conceived as a heuristic instantiation of  “pure” T-logic, comprising almost any “amount” of semantics. From this follows, that there not only is an infinite number of different Q-logics, but also that many of them are incommensurable. Precisely this is what we can observe.

It is more than obvious that this has tremendous consequences for any possible (attempt to establish) machine-based epistemology. The core is about the idea that to “characterise truth functionality” is the first step. Putting down such a characterization is not the business of logic. The structure of the world precipitates in that characterization. The structure of the world that is before language and and before logic (which are co-genetic) is nothing else than the body of faculties, mainly, however, the faculty of association.

Before Space and Within It

So, based on the results available so far, we could put the issue at hand—about relation between logic and world—in different words:

How can we proceed from the realm of the indeterminate to the fields of the propositional?

Before approaching the path towards a possible solution more closely we should be clear about the characteristics of the two sides, and possible approximations, or, if you like, operationalizations. Upfront, we may expect that we will meet neither pure construction (of abstract scaffolds to stock perceptions) nor sort of a distillation (of such scaffolds from “empiric data”).

Generally spoken, the task is to describe a rather particular (class of) transform- ation(s). This transformation is not only settled completely in the structural domain, we even have to state that left-hand we have no identifiable entity at all. Using some symbols and denoting that transformation for instance as

A → B

is not applicable, since the “A” and the “B” are very different, so to speak, they are differentially different. A and B have a different status; it is not possible to think of a possible transformation between them, as it is for instance conceptualized in category theory. The transformation we are looking at is nothing else than an actualization of the indetermined into the propositional. Yet, this indetermined should not be equated with potential here, albeit the potential and the virtual are important aspects of it. Symbolizing it we could write

. → B

In order to make some substantial progress we want to draw an analogy to number theory here. Real numbers are not numbers in the “classical” sense, since there is nothing that could be enumerated. What real numbers share with more simple numbers like integers is the just order relation that is valid for all its members. Nevertheless, there is no such thing like a “particular” real number. They are more a space for the more simple numbers like natural or rational numbers. Dedekind formulated that real numbers (and irrational numbers as well) are not members of countable sets of (rational) numbers that approach each other (see Dedekind cut, or Cauchy sequences). Roughly spoken, real and irrational numbers fill the gap of any thinkable or selected number. Hence there are relations to the so-called “axiom of choice” of Zermelo-Fraenkel. Of course, the technique that Dedekind applied to the relation between countable and non-countable numbers, where the countable ones build the basis, can be applied to the real number itself. This way Conway “discovered”, or invented, the surreal numbers [11]. Those form a space which “contains” the real “numbers” as a possibility, just as the real number contain the natural numbers as a possibility.

Yet, here we are not interested in the number theory as such. What strikes us is the structural similarity to our question here, showing a well-defined possibility for a transition from a space of the indeterminate that contains any determinable space into a space of identifiable entities. From this (more philosophical than mathematical) perspective the problem is not how to proceed from natural (or other countable) numbers to real numbers, i.e. from the countable, representable and identifiable to the indeterminate, but just the other way round. We could write it as

ℝ → ℕ

To be honest, it is not a problem, it is simply a choice; it is even consistent with the position of assuming a transcendental status for the “difference.” Starting with ℝ, we can select any kind of countable, i.e. discrete space 𝒩 by means of an “inverted” Dedekind cut.

ℝ → 𝒩

Now let us return to our problematics of the transit from the indeterminate to the logical. Any applicable logic (Q-logic) we know of so far is based on identifiable relations. Gödel’s proof of incompleteness of formal systems [12] is strongly based on the discreteness of those relations: he created the so-called Gödel numbering for it (cf. Hofstadter [13]). Gödel numbering is a function that assigns a unique natural number to each symbol and well-formed formula of some formal language. Yet, we arrive at such an enumerable structural system only by “selecting” it from a space that contains any enumerable structure. The nature of the “selection” process is important and we will have to clarify it.

That “any”-space is our space of indeterminacy. Yet, this space is not without structure, much like the real numbers are not without structure (e.g. as a topological entity), despite that they are not enumerable. One of the structures is what we call “randolation.” Randolations are open categories from which certain families of relations can be derived, similar to the derivation of natural numbers from real numbers, if we invert the Dedekind cut. The randolation is the manifold of a particular logical form, the relation.

We think that one may conceive of randolations not only in the space of the indeterminate. We may operationalize them into probabilistic distributions of relations. And exactly this happens in modeling, especially if we volatilize naive concepts of similarity into a similarity functional: collecting and grouping items and their relations into extensional sets.

The Practice of Transit

We have seen that proceeding from the space of the indeterminate to the logical implies a selection. This selection happens in modeling. The configuration of this selection is implicitly determined by the structure of practiced explication, which has been called “world” by Wittgenstein.

This structure of practiced explication is mainly given by the structure of the (quasi-) materiality that serves as a carrier for modeling. For instance, in a world of apples and trees (Newton), or arrows, swords and lances it is quite clear that the proposition of the excluded middle has been regarded as something rather absolute. Where the sword is, no body can be. This world is often characterized by the concept of classical causality. In a world of virtual networks we find a completely different kind of materiality. Here, the excluded middle has barely any relevance any more. To put it in simple terms: the materiality of information is quite different from that of apples, a fact that went unnoticed to authors like Pearl [14] of Salmon [15].

Yet, we shall not treat it unjustly. It is precisely this link from logic to  irreversibility of causality that allows to forget about doubts. If a glass broke irreversibly, there can’t be any doubt that it broke. Being broken implies for the glass that there had to be an identifiable act upon the glass, a transfer of energy, no doubt. The relation between the cause and the effect may be crisp, no doubt. Hence, it had to be an enumerable structure. But there is no necessity, still. There is still a lot of interpretation about it, on the structural level, and a lot of arbitrary choices. Obviously, if there already was a crack in the glass we could not claim that the energy transfer has been the cause, that is, the unique cause. For this particular glass we even can’t know if the energy transferred to the glass would have broke it, even if it had a crack before. We never can know perfectly, if the referent of this “knowing” is about the world. As Quine noted, any other claim is a dogma, and he found two dogmas in empiricism [16]. But we do not think, indeed, that conceptual truth is possible (see also, for a discussion of Öberg [17]). Concepts are entities (later we will say: choreostemic poles) that are not only outside of the world of possible effects, they are also outside of any available Q-logic, and of course, outside of T-logic. There is a long way to take from a concept to an effect, and from potentially perceived fluctuations to concepts as well.

Nevertheless, this may serve as a guide in our transit. In order to arrive at an arrangement of enumerable structures we have to imply a certain kind of materiality. We may call this step also a “decoherence“. We have to introduce incommensurabilities between subsets of structures that derive from their randolated “counterparts” as its operationalization, notably simply by choosing one.

This choice is not completely arbitrary. It remains bound to the requirement of providing the possibility for sufficient predictive power. It is very important to understand here that there is probably an infinite number of possible structures that could serve this purpose and from which we could choose. Quite naturally we will develop habits, often based on our body and its enumerable structures, we will draw on experiences how to organize that transit. But it remains arbitrary within the constraints of an infimum utility, there is no “causal” relationship between that choice and predictive success.

Note that there is no possible “logical” justification for this choice, or selection. This choice, which can be conceived as the inverse of the Dedekind cut, is just the result of a performance that in turn is constrained (“conditionalized”) by the embedding material and immaterial structures (“givens”) of the Lebenswelt.

We now can conclude the first part by providing an answer to the first part of the problematics about the relation between world and logics.

First, it is not adequate to talk about a relation between those two “phenomena.” Logic (and its enumerable structures) is created from the indeterminate (and its matrix of non-enumerable randolations) by a selection as a performance. Logic simply “appears” through associative modeling and its implied materiality, sometime aka as “body,” more generally labeled as “quasi-body,” as, for instance, in the case of symbols. Wittgenstein called it the structure of the world. The fact that we meet selection here, opens a passage to evolutionary processes and the structure of comparison. It is interesting that it is precisely this evolution that reverted the relation between the body as materiality and associativity. The evolutionary story went from “implied associativity” (in amoebas) to “implied materiality” (in complex brains). As a domain, logic could only appear as a secondary effect, which is the reason that applicable logics is always a Q-logics. As a structure, it is transcendental and not applicable as a “pure” form (whatsoever this could mean…).

For the same reason, truth and truth functions can not be considered as being part of the world, “world” here referring to a world of effects, or in other words, a non-conceptual world. In this respect, however, we disagree with Putnam about the possibility of conceptual truth, albeit we would defend it if he would be right about concepts. The concept of concept is a non-trivial concept! Categories like concepts and models we will call a “choreostemic poles.” Concepts acquire meaning and sense only in social context, in a discourse, and in a very particular way, as Brandom [17] demonstrates. For sure, “concept” can’t be defined exhaustively and positively. Nevertheless, truth functions disappear from the world together with ontology.

Second, the composite made from material aspects, habits concerning structural selections and styles of modeling is undeniably quite important for the empirical parts of any particular Lebensform. This compound is both a (provisional) result and a (dynamic) scaffold for deriving (further) results. Of course, perception is neither a “flat” input-output-relation nor should it conceived as a passive process.

Third, the transit into the area of the propositional is also a transit from the indeterminate into the realm of the symbolic, which in turn open the path to the realm of reversibility.

This brings us to an almost paradoxical arrangement. On the one hand, we have seen that logic is the paradigmatic representative of causality, at least as far it does concern finite value logics.9 On the other hand, this representation takes place in the realm of the symbolic, which provides just the opposite of classic causality: reversibility. Here, we take this as a clear hint that logics should not be seen serving this representative role, at least not in an idealistic or absolute manner. We will return to the conditional embedding of logics into the world elsewhere. It will become clear that there is no paradox.

Inadvertent Transits: Creating Actions

The second part of our problematics—the transition from logic back into the world—is much simpler. Regardless, how much operations we performed in the space of reversibility, once we act, we change the frame. Quite likely, we also forget about most of the “reversible” operations. “Acting” is precisely the language game for this change from the space of reversibility to the space of irreversibility. Acting does not create unambiguousness and uniqueness. It does create, however, the need for new interpretation. Acting introduces the indeterminate. Only for this reason it can be irreversible. This transit happens inadvertently.

Interestingly enough, we provoke this transit by writing, or other means of externalization. Meanwhile, human culture developed even as an art of externalization, from symbols to language to printing to the media to the web. Yet, we should not forget that dealing with this externalization requires again modeling, including a transit of the first kind. It is precisely this dynamics that creates the particular status of a text, or, in a different way, that of any ordinary discourse. It was Robert Brandom [18], whom we cite frequently on this site, who was the first to shed some light on the mechanisms of discourse from the perspective of the primacy of interpretation.

The Role of Logics

Undeniably, logic takes a particular role. Marcus Russell naturally called it the technical tool of philosophy [19]. Besides the question whether there are possibly tools that are not technical, we actually have to be concerned about the question which role (Q-) logic is playing. Henceforth we always refer to Q-logic when saying “logic”.

One major goal of philosophy is clarity. The major property of logics, regardless the actual flavor, is the notion of uniqueness. Of course, already the premises need to be distinguishable (Gödel enumerable). This obligation (propensity?) towards uniqueness is paired with a particular focus on a structural linearity, or at least pre-linearity in the case of many-valued logic like the Gödel logic. Else, even in further abstraction like Malinowski’s t-entailment [20] there is a direction. Also, self- referentiality is excluded from any logics, unfortunately so, I think. From that it follows that any (pretended) application of logics directly establishes a temporal order. Again, note that this temporal order is strictly linear and of a stepwise structure that is imposed on a synchronous set of steps. Within a logical expression, or a predicate, there is absolute synchronicity and contemporaneity, pure present time, if you like. This describes the trivial fact that we should not forget about the premises before we ended up with the assignment of a truth value. Q-logics induces a split in temporal reference. All parts of a logical expression are, however, impermeable. Without resorting to logical atomism we nevertheless are allowed to say that the elements of a logical expression (in a finite-valued, classical logic) are like particles. It is this property that renders Q-logic into a kind of (a simple) materiality. Regarding the temporal structure we can observe that the instantiation of a Q-logic also implies a separation of temporal reference into at least two lattices.

The principle idea is that from true premises everything else follows. Marcus [21] cites de Morgan’s famous proverbial characterization as the motto of his book: “The question of logic is: Does the conclusion certainly follow if the premises be true?” In practice, of course, one can utilize this “everything” in a reverted manner. We project it (take it for granted) and search for the effect that necessarily follows. Obviously, the art then is in setting the premises.

Leaving that aside, we can now address the question about the role of logic in thinking. There are several aspects to it: how to link it to the world beyond the concept of relation, its status in the world, and which effects could be achieved by using it. The latter point refers to the issues of symbols and knowledge.

First of all, we take the distinction of “logic” into a T-logic and the realm of Q-logics as an alleviation from the burden of ontological truth. Truth and truth functions are not applicable to the world, at least not directly, as we will see shortly. Truth is as little in the world, or an object of the world as any other concept. Just as any other concept, “truth” is dependent on some basic conditions. Yet, this does not mean that we propose to accept radical relativism, of course. Just as any other concept “truth” makes sense and has meaning only in a discursive context, i.e. as a particular language game. The important convention is to use it as tool for the construction of “as-iffs,” that is to create scenarios and simulations.

Carnapian programs propose a particular linkage between the world and logics. The basic claim is that there is the possibility for an exhaustive language in which all statements about empirical “facts” are completely within an exhaustive logic. This is equivalent to the claim that there are truth values to be found in the world. We already refuted that. Yet, Carnapian programs are also equivalent to the claim that sentences of natural languages can be rewritten in expressions that belong to a logic, notably to a T-logic. Despite the fact that such attempts have been proofed to be untenable (indeed, many times so), one still can find such attempts even nowadays (e.g. [20]).

Sentences in natural languages are clearly not logical predicates or propositions, and for many reasons so. Probably the story goes just the other way round: Any particular Q-logic is the form of the unfolding organization of a discourse. This would Q-logic tie to a particular Lebensform without prescribing one by the other. We have seen that this linkage between logic and Lebensform also creates the distinction between T-logic and Q-logic. If this is correct, logic is just a consequence of discourse pragmatics.

Q-logic is essential to establish knowledge. Knowledge, however, is not about empirical facts, at least not directly, as we argue in more detail in another chapter, neither it is reducible to things like “justified beliefs”(see Gettier [6]). Besides the trivial cases where we indeed may reduce knowledge to the figure of “knowledge that p”, knowledge is mainly the capability to establish a social resonance about empirical facts. Without Q-logics we would not have the possibility to reduce representations down to uniqueness, i.e. we could not exclude misunderstanding, or in still other words, we could not secure it mutually to each other.10

Due to its role in excluding vagueness, at least in local contexts, logic plays an important role for modeling as well as for using models, yet a quite different one here. With respect to the practice of modeling logic is a co-genetic phenomenon, as far as we are concerned with associative modeling. Of course, we have to distinguish sharply the performance of modeling from formalizing it using symbols, like we did with respect to the generalized model. In our investigation about associativity we have seen that associativity implies the transition from the realm of the quasi-material into the realm of immaterial. It is very important to understand here that associativity itself implies this separation. We may consider it also a compartmentalization in the abstract. The property “quasi-material” is not restricted to matter, of course. If we run an associative structure like the Self-organizing Map we meet a purely immaterial network. Nevertheless, its associativity implies the mentioned separation. In other words, associativity generates relative matter, i.e. the quasi-material. In the very same context, logic appears, notably by virtue of the associativity as performance, which is, in turn, creating and bound to the quasi-material, or if we regard it as a compartment, to the quasi-body. In short, any particular Q-logic is a consequence of a certain bodilyness.

The role of logics is a different one if we proceed to the application of models. Here, logic is simply an apriori condition. Applying a model implies the preceding selection of a logic via the inheritance from the modeling performance. This also means, however, that a particular model prescribes which (class of) Q-logic one has to obey to.

A last point remains that we want to deal with before going practical. The uniqueness built into logic provides a bridge to other entities that share this property: names, indexes, and symbols.

A name is a primitive. If we compare it with indexes we see that it is even a pre-specific primitive.Vilém Flusser called it “throwing out a name.” Names are elements of a language, in contrast to indexes, which are elements of a formal system. A name does not need a preceding quasi-material referent, quite in contrast to an index. Both, of course, share the property of uniqueness. Names usually develop into compounds consisting from at least one index and the potential to serve as a symbol, while an index is never a symbol.

Elsewhere we have seen that the concept of “symbol” describes a particular process of referencing that is routed two-fold in quasi-materiality, regarding both the starting point and the end point of their usage, so to speak. This symbol-process transits through immateriality like a looping ligament. It provides the hook for logic and for signs. While symbols always refer to a quasi-materiality, signs do not. Symbols refer to material, signs refer to signs.

Let us recapitulate the two aspects that are most salient for us here:

  • – Any particular Q-logic is both a consequence of a certain bodilyness as well as a kind of quasi-materiality.
  • – The instantiation of a Q-logic implies a separation of temporal reference into at least two lattices

If we contrast this with the symbol-process, then logic appears as a way to describe a certain policy for chaining those processes. Logic always remains close to the quasi-materiality of symbols. Else, logics remains inevitably a performance. As an performance, logic is the means to describe the mechanism for chaining symbol-processes, for finding or creating stable grounds for the purely immaterial semiotic processes. In short we may describe logic also as the story-telling of quasi-bodies.11

Practical Considerations

Now we can turn to consequences for the machine-based epistemology. These consequences derive all from the performance aspect of logics and the related quasi-materiality.

On the one hand, logics is a consequence of the performative capacities of the quasi-body and its implied associativity. The relationship, however, is opaq. It is (not yet) known how to control the emergence of a particular Q-logic from a particular bodilyness. I guess that’s even a matter of evolutionary dynamics, transcending the potential of individual capabilities. Philosophically spoken, it is a matter of the Lebensform as a whole.

We may further guess that the possibility for an evolvability of this relation between quasi-materiality and logics implies a more abstract, or alternatively, a pre-specific notion of logics. There are, however, indications that such a step is not possible, as the so-called basic t-norm logic is considered to be an extra-logical move (cf. [20]).

On the other hand, we may implement different models of quasi-(Q-) logics, even in a parameterized way, starting with an algebraic representation of a Q-logics. Such an implementation can be regarded as the simulation of a particular materiality.

Of course, both aspects have to be coupled. Yet, the path from associative quasi-bodies to both, the performed and the applied logics is pretty clear. It is demonstrated by the path we already described as the series: patterns → classes → models → named models → (names → indexes → symbols) → applied logic → signs → concepts. Obviously, the middle part of this transitional series is rather volatile. Else, we just would like to recall two issues here: (1) This path can’t be hosted by an isolated (or otherwise) closed entity. (2) This path does not imply any kind of causality, of course.

Names

The starting point of this chain is relatively easy accessible. Modeling is explicitly available in many different forms, indexes or logics can be implemented using standard techniques using e.g. databases, or logical programming. On the other side of the chain the concepts reside. As choreostemic poles, concepts are not accessible at all, while semiotic signs, i.e. a semiosic process is difficult to implement, but it should be possible using a population of lattices of growing SOMs. The mystery that remains is the naming,12 which also is the interesting part of symbols. Both, the material and the referential aspects of symbols are nearly trivial.

Perhaps you know the film The Pillow Book by Peter Greenaway. The film is (as Prospero’s Books) about the relation between body and text. In a more general perspective, the relation between the symbolic and the body can be met in any of his films. Anyway, in the “Pillow Book” there is scene, where the father paints the name of his daughter as a calligraphy to her forehead as part of a initiation ceremony. He also explains that (Japanese) people believe that god created man by the means of the same ceremony. Naming is probably indeed the focal point about everything we are interested here.

Of course, the act of naming can’t be pre-programmed. It has to be a particular practice of the “machine” “itself,” and most likely it has to be a social practice. One could argue that perhaps not any model has to be named. Yet, based on our analysis, we would oppose that view, guessing that the naming of every model is inevitable in order to achieve the ability to deal with signs (in the Peircean sense as “sign-situation”).

So the big question is: How to enable for the act of naming? Our provisional answer (admittedly, a guess): By means of sensual cross-modality. Of course, we have to justify this further in the future. Yet, it would mean that the capability for “active” understanding will not be achievable for any arbitrary kind of entity unless the entity does not deal with different modalities, i.e. basically, waves, words and images. These principles are needed to describe the world and to act upon it, which in turn provides the anchor points for practices and their names.

Notes

1. see Frege’s hyper-platonism, idealism.

2. Of course, we also could have started with identify, putting existence to the second line.

3. note that an expression like a=b already would refer to an algebra, since in such an assignment there is already an empirical element in claiming a particular symmetry that justifies the equation. Yet, we do not agree on Frege’s chasmatic distinction of analytic (“a=a”) and synthetic (“a=b”) [23, p.56]. Outside of transcendental relationships (like a=a), everything is more or less synthetic. In fact, it is the transcendentality of “pure logics” that allows us to drop Frege’s distinction.

4. A must read here is certainly Hilary Putnam’s “Ethics without Ontology.” [3] We just want to note that quite some of his arguments would become much simpler if one would put Putnam’s ideas onto the foundation of generalized modeling and choreosteme.

5. selective interaction., pan-semioticism, yet not only in relationships to external entities.

6. You see, we don’t take neither reductionist nor nominalist (or even eliminatist) positions.

7. The concept of the “brain in a vat” has been invented by Putnam himself, in order to defeat skepticism.

8. B. McGuinness (ed.), Ludwig Wittgenstein and the Vienna circle. Blackwell, Oxford 1979.

9. The status of logics that incorporate infinite truth values is not clear yet. see the entry about many-valued logic in the Stanford encyclopedia for philosophy.

10. This perspective onto knowledge and its relation to logic is deeply influenced by the approaches first explored by Wilfrid Sellars [22] or Robert Brandom [18], and, so I think, also perfectly compatible with their views.

11. The relation between bodies and concepts also appears in another domain that seems, at least at first sight, completely different from what we are doing here: The art of performance and the pedagogy of art. This relation we explored in [24].

12. So far, there is no convincing concept about names in philosophy, see the entry about names in the Stanford encyclopedia for philosophy. Albeit we think that our approach as presented here is more appropriate than any other, we don’t feel that we are done yet.

  • [1] Ludwig Wittgenstein, Tractatus
  • [2] about Illusion of “Genes”
  • [3] Hilary Putnam, Ethics without Ontology.
  • [4] Carnap
  • [5] Wolfgang Stegmüller
  • [6] Edmund Gettier (1963), Is Justified True Belief Knowledge? Analysis 23: 121-123.
  • [7] I. Peschard
  • [8] Colin Johnston, Tractarian objects and logical categories. Synthese (2009) 167: 145-161. available here in an annotated version
  • [9] Pierre-André Boutang, Claire Parnet, L’Abécédaire de Gilles Deleuze. Arte TV 1988 [released 1996]. Wikipedia
  • [10] Wilhelm Vossenkuhl, Solipsismus und Sprachkritik: Beiträge zu Wittgenstein. Parerga, Berlin 2009.
  • [11] John H. Conway, On Numbers and Games. Academic Press, New York 1976.
  • [12] Gödel on his numbering
  • [13] D. Hofstadter, Goedel, Escher, Bach. 1978.
  • [14] Judea Pearl, Causality – Models, Reasoning and Inference. Cambridge University Press, Cambridge 2000.
  • [15] Wesley C. Salmon, Causality and Explanation. Oxford 1998.
  • [16] W.V. Quine, Two Dogmas of Empiricism.
  • [17] Anders Öberg, Hilary Putnam on Meaning and Necessity. Thesis, University of Uppsala 2011. available online (mirrored)
  • [18] Robert Brandom, Making it Explicit. 1994.
  • [19] Russell Marcus, Logics. Syllabus Announcement, Fall 2011. available online. (last accessed 5/1/2012)
  • [20] Siegfried Gottwald (2009), Many-Valued Logic. Stanford encyclopedia for philosophy.
  • [21] Russell Marcus, What Follows. book in prep, available online.
  • [22] Wilfrid Sellars, Does Empirical Knowledge have a Foundation? in: H. Feigl and M. Scriven (eds.), The Foundations of Science and the Concepts of Psychology and Psychoanalysis. Minnesota Studies in the Philosophy of Science, vol. I. University of Minnesota Press, Minneapolis 1956. pp. 293-300. available online.
  • [23] M. Black, P. Geach (eds.), Translations from the Philosophical Writings of Gottlob Frege.
    Blackwell Oxford 1952.
  • [24] Klaus Wassermann. The Body as Form – or: Desiring the Modeling Body. in: Vera Bühlmann, Martin Wiedmer (eds.), pre-specifics: Some comparatistic investigations on research in design and art. JRP Ringier, Zürich 2008. pp.351-360. available online.

۞

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