Introductory Remarks

§3 In this chapter we present the subject of the book, our approach to the problems presented, and discuss the implications of the work.

The Work

The subject, scope, and composition of the book.

§4

Explaining Experience In Nature

The content of the book and its objectives.

§5 The present inquiry explores a constructive explanation of consciousness in nature determined by natural laws and developed from first principles. Our goal is to illustrate1 how consciousness comes into existence, the role that it plays in nature, and the mechanics of the broad range of behaviors that are its products.

§24 The foundation of this new construction is a novel account of experience in nature.

§27 By the term “experience” we refer to the basis of consciousness. It is that which is most familiar. It is common to all senses. It is the first thing and the last thing for each of us. Though strictly, according to the model we will present, the first and the last thing for each of us is a sense, the primitive we will propose characterized by biophysical structure.

§28 From the beginning we take the existential status of experience seriously. It is something that exists in the world.

§32 All the world derives from primitive nature. Primitive nature is (currently) inaccessible² . However, three aspects of primitive nature are apprehensible and universally covariant^[1]: these are mass/energy, gravitation, and a primitive aspect of the world that is the basis of experience. Each aspect is necessary to provide a constructive explanation of the world and together they are sufficient. The current work explores the introduction of this last aspect of primitive nature, a primitive of experience, as a necessary distinction for an explanation that includes biophysics and consciousness.

§53 In our model this universal primitive is an aspect of the world that affects physical assembly simply by its presence. Although it is inert, in the same way that gravitation is inert, it is the root of all complexity.

§57 The new mechanics we propose characterizes the products of a natural assembly against3 this previously unconsidered primitive. The constructed mechanism is the basis of sensory differentiation and biophysical response.

§60 This newly proposed aspect of primitive nature has the same existential status as gravitation and mass/energy. It is a universal a priori aspect of nature just as gravitation⁴ is considered universal in General Relativity; and it is inert as gravitation is inert. Most important of all for us here, like gravitation it has a characterizable effect upon the formation of physical structure⁵ .

§72 As we proceed we will examine the behaviors associated with consciousness as described by a new mechanics. These behaviors are the emergent products of the unfolding world naturally engineered by this mechanics and the evolutionary principle of natural selection. They include the obvious products of experience: the variety of sense, the behavior of organisms, and the forms of intelligence that underlie them.

§81 On our journey we will develop foundations for the mathematical characterization of the range of behaviors that we consider. In that effort we develop a calculus for this new mechanics, inclusive of biophysics. The objective of this calculus is to enable us to reason rigorously about the formation of sensory and motile structures, and their operation. With this understanding of individual organisms we are then able to suggest a model for reasoning about their behavior in groups.

§85 We must navigate significant challenges before we can formalize our model. We will defend a claim that the established foundations of logic and geometry contain assumptions that, if left unchallenged, limit our formal inquiry. This is because the intuitions upon which they are based relate directly to our subject, they are assumptions concerning the nature of apprehension.

§86 These claims will lead us inevitably to review assumptions in the foundations of mathematical physics. And these challenges are difficult because they reject cherished beliefs.

§87 For example, we will argue that the “orthogonality” pervasive in our mathematics⁶ is false and has the effect of misdirecting problem solving behavior in physics. And so we challenge the conventional allowance of unlimited dimensions in contemporary mathematical physics.

§92 We argue that the Turing implementation of logical computation is false and constrained by limits that are fundamental to the world. To support this argument we show that the Turing implementation of logical machines is unlike the biophysical implementation and unable to compete with the efficiency found there. To this end we offer a conjecture concerning the Church-Turing thesis. This conjecture illustrates how and why systems built with Turing Machines will produce behaviors, our measure of results, that differ from the behaviors produced by our mechanics.

§93 We will have made progress on our journey if we can demonstrate that the new calculus can predict biophysical sensory and motile function. We will have proof of these theories in practice if we can use the mechanics described to implement new sensory and motile technologies, machines that experience.

The Field Of Endeavor

A summary of our field of inquiry.

§94 When consideration of logic goes beyond the effective techniques of syntax and semantic rules in symbolic systems to include the essential basis of apprehension and operation of the mind it is more rightly called “semeiotic theory,” the study of “signs.”

§111 Semeiotic theory, the subject of logical positivism and pragmaticism is a field of inquiry that develops general theories of signs and we develop such a theory here. The theory is built constructively upon the natural mechanics of sense and motility that we propose.

§123 There is some diversity and ambiguity in the literature concerning the exact definition of a sign. We adopt the simplest and least ambiguous definition: a sign is simply a differentiated experience.

§124 In his essay concerning human understanding the English philosopher John Locke divides the objects of our understanding into three distinct areas of intellectual consideration: Physics, Ethics, and Semeiotic7 .

§130 He puts it this way ^[2]:

§132 Locke saw these as three distinct areas of study.

§134 We will show, however, that these three are not distinct. An intellectual understanding of one is intrinsically dependent upon an intellectual understanding of the others. Put another way, we will show that there exists a continuum from elementary physics through biology, covariant with the embodiment of signs, and the inevitable and volitional behaviors that arise.

§135 We will show that the behaviors of all organisms are the natural product of the genetic disposition of physiology in its environment, mitigated by the embodied epistemic state, the embodiment of signs derived from apprehension and defining commitments made by the organism.

§136 Thus, for us, semeiotic theory is naturally first among sciences. It is through semeiotic theory that we infer the physical basis of nature as well as the operation of individuals and behavior of those individuals in groups.

§137 It is semeiotic theory that leads us to a sense that captures an understanding of the world. The product of this semeiosis, the semeiotic process embodied by an individual, are the marks, the subjects of signs, that represent our expression and analysis of that sense.

Against Prevailing Views

Our model and approach challenges prevailing views.

§145 The present work challenges a number of prevailing views. In particular, we make the following observations:

1. §146 The failure of a logical reduction cannot lead to supernatural conclusions. By necessity such failures lead us to reconsider, and ultimately revise, the basis of the logical construction in which the reduction failed.

2. §147 The mechanism of logical differentiation in biophysical structure produces results that differ from those produced by the mechanism of logical integration (the mechanism of contemporary computing machines).

   §148 This difference is most obvious in implementation at scale and is due to the distinct mechanisms of logical differentiation and integration.

   §149 In essence the primitive we propose enables a fundamentally different computational mechanics: a manifold, with no storage required, of parallel computation against which nonlocal differentiated results form in a physical structure closely bound to associated action potentials in a system of recognition. When a manifold conforms to an action state the cascade of biological events necessary for directed action occur.

   §150 The classical logic of integration is limited and unable to compete with this simple efficiency.

   §151 This is a controversial claim and, if it holds, it is a negative result for computer science.

3. §152 This same mechanism also produces results that differ from those of conventional “computational complexity” in explanations of physical behavior involving sentience.

   §153 Conventional “computational complexity,” the product of uniform classical mechanics, has no differentiating physics or logical constraint. Without such constraint the behavior arising is different than that predicted in our new computational model.

   §154 This too is a controversial claim and will be a negative result for computer science.

   §155 Later we discuss the implications of these two claims to the Church-Turing Thesis.

4. §156 There remains the question as to whether heuristic machines in efficient switching materials are more or less efficient for certain end results than the mechanisms referred to above.

   §157 Despite this, and despite the manifest success of chess playing machines, we conjecture that conventional machines implementing heuristics cannot ultimately solve problems involving recognition for reasons that are fundamental to the world. By this we refer to the basic ability of organisms, that is indifferent to their size and complexity, to consistently recollect similarity in their environment and act appropriately.

5. §158 Certain basic notions in the language of mathematics, derived from received authority, are false intuitions. One such notion is the geometric notion of perpendicular “orthogonality” that leads to unconstrained dimensions in analytic algebra.

   §159 We will not present it in these introductory remarks but later we present an experimental geometry as the basis of our calculus that does not use the conventional notion of orthogonality. Instead of an unlimited dimensional geometry that starts with “point,” “line,” “plane” we begin with “length” and derive “plane” and “point” as necessary distinctions . This geometry was considered in part earlier by Ernst Mach as a geometry in which length is the fundamental metric^[3]. The geometry is unrestricted by perpendicular orthogonality yet it still provides solids, planes, and unique points. It provides a new coordinate system well suited to our task.

6. §160 A resulting bias in the foundations of mathematics, the acceptance of an unlimited “dimensionality” in analytic algebra, leads to the misdirection of problem solving behavior in mathematical physics.

7. §161 As a consequence we argue, consistent with Einstein, and Godel^[4], that the notion of “time” is merely a way of speaking about the world. It follows then, consistent with Mach^[5] and Einstein, that the notion of “space” is also. For us “spacetime” is simply a way of speaking about mass/energy.

   §162 We will explore a model of mass/energy as a natural “tension” in the geometry of the world in which there exists no universal metric. We pursue this goal in expectation that it leads to a characterization of sense and motility.

8. §163 Finally, and perhaps most controversial, we claim a necessary extension of physics8 , a universal basis of experience whose role in nature is the production of physical complexity.

§166 In the following sections we address each of these observations in sufficient detail to justify their further investigation.

Rescuing Reductionism

§168 The present work advocates the return of certain scientific principles^[6] and the rejection of metaphysics, in the pursuit of a systematic and rigorous logical construction of the world. We pursue the development of such a construction.

§169 Logical constructions of this kind approximate the way things are with increasing degrees of completeness; in a continuous refinement that eliminates contradiction and defers to the evidence.

§170 Reductions within such frameworks must lead to verifiable predictions about the behavior of the world. The failure of such reductions by evidence or contradiction cannot lead us to supernatural conclusions. By necessity such failures lead us to reconsider and ultimately revise the basis of the construction in which the reduction failed.

§171 This view, surprisingly perhaps, is contrary to prevailing views in contemporary science proposed by several leading emergence theorists and some physicists.

§172 Advocates of these views include mathematicians Stephen Wolfram^[7] and Gregory Chaitin^[8], biologist and complexity theorist Stuart Kauffman^[9], and cognitive theorist Douglas Hofstadter^[10]all of whom have written recent books on the subject. However, the argument itself is not new^[11].

§178 According to these accounts the basis of experience is not universally primitive but is solely a product of the evolved parts assembled. Typically, it is manifest in these arguments as an identity with some observable phenomenon. And it is important to note immediately that experience in these theories has no role in the world.

§179 To be clear, we do not challenge arguments that support the increasing of what is logically possible based upon what has gone before. We accept as an epistemic argument, for example, Stuart Kaufmann's notion of unpredictable novelty in possibilities that are adjacent. We simply challenge the notion that experience can be among them. Only what can happen may happen.

§180 Emergence theories of experience echo the philosophy of mind known as identity theory attributed to Herbert Feigl(1950s)^[12]^[13] and others. Feigl is a member of “the Vienna Circle.”9 We will hear much about the Vienna Circle in our historical narrative.

§183 These theories argue that there is not only a one-to-one correspondence between conscious events and physical events but that the physical events are in fact the conscious events. In these models there is no mystery to the physical events involved they are simply the product of conventional mechanics.

§184 An older and frequent alternative argument made by some philosophers is that experience is an epiphenomenon^[14], a phenomenon that arises as the extra product of known mechanics and evolutionary theory.

§185 Here we will treat theories of identity and epiphenomena in the same way. We do so because the two theories are logically indistinguishable. Whether experience is the incidental product of evolved mass/energy or the events of mass/energy themselves simply cannot be detected. What is more, if one or the other is in fact the case then the matter here can never be resolved.

§186 In both models no aspect of experience is existent prior to the physical assembly that embodies it and experience plays no role in the mechanics of observable events. Experience is simply along for the ride. As long as these theories provide no role for experience in nature they amount to a form of dualism and no real progress on the matter has been made.

§187 The unspoken premise of these models is materialism. We take the view of materialism to imply a belief that our physical models are complete in all important respects. According to this view contemporary physical theory captures all the essential things of the world.

§188 Materialism is justified in a version of emergence theory by taking the position that levels of constructive complexity introduce new phenomena into the world and, to quote Chaitin^[15]:

§191 In correspondence with the author Chaitin says (quoted with permission):

§193 This correspondence illustrates two issues that we will address here. The first is the acceptance of the supernatural, metaphysics. This is due to a failed reduction and a failure to recognize the necessity to review the basis of the construction that leads to it. The second is a semeiotic issue that relates to how assumptions of received authority in our mathematical formalism, in this case in the notion of unlimited orthogonality, has misdirected problem solving behavior in mathematical physics.

§194 The idea of parallel universes or unlimited dimensions is based upon a false intuition, it is a clear and unsupportable fantasy. And while the idea of multiple universes in Inflationary Theory is intriguing (where expansion of the world leads to units separating at faster than the speed of light) there is little justification for any claim that the laws within these “universes” are not precisely the same.

§195 New properties of nature obviously do emerge and there is an equally obvious correspondence, an identity, between the physical assembly that manifests the property and the property itself. However, from the constructive point of view that we will follow in this work nothing new is brought into the world except a new assembly of its essential parts.

Laws and Principles

The uniformity of natural law.

§196 A central premise for us is that the natural laws are uniform, that they are everywhere the same. We argue that this uniformity is profound, the cause of perceived universals. And our model relies upon it.

§197 The world then, in our model, is a natural construction according to the laws of primitive nature (a priori determinants) and the principles (posterior determinants) that arise in the combination of these laws.

§200 In accord with the laws of conservation and equilibrium in thermodynamics these emergent properties transform, their structures change, and these new forms play a continuing role in the physical systems in which they appear.

§201 Yet in the argument we have heard from contemporary emergence theory experience has none of these features. It translates to no other form and it plays no continuing role.

§202 The emergence theory expounded by Chaitin and others is the product of a failed reduction. It is the inevitable logical consequence of a strict adherence to a materialist construction, a construction that forbids discovery in the foundations of the world.

§203 To escape this inevitable conclusion, since it is clearly inadequate, we are required to expand our physical theory, to change the basis of our logical construction of the world as the philosopher of science Rudolf Carnap (as we will hear shortly), and contemporary physicist Roger Penrose^[16]^[17], have anticipated:

§205 We agree with Penrose that our physical models are incomplete. Our goal here, however, is to identify new mathematics that accommodates “conscious mentality” from which we can derive the world.

Changing The Operational Basis Of Logic And Apprehension

The mechanisms of sensory differentiation in biophysics necessarily produce results that differ from those produced by the mechanisms of logical integration in traditional theories of computation.

§206 We propose a revision to the operational basis at the foundations of logic. The proposal is not novel. It is, in fact, the dominant view of logicians prior to the current era.

§207 We will present an historical narrative that illustrates this divide in logic, placing the strong locality of conventional computational logic against the nonlocality manifest in our sensory experience. At the center of this narrative, representing each side of the debate, is the work of Alan Turing and Rudolf Carnap.

§208 This divide is mechanistic and fundamental to the implementation of logic. Critically, we claim that the results produced by these two views differ.

§209 There are two aspects of conventional logical machines to consider: integrative logic and computational complexity.

§217 Integrative logic is the logic of computer systems. The results it produces are aggregations of strongly localized truth values. A result is a “truth” value.

§218 The conventional study of “computational complexity” looks at behaviors produced by these systems in the highly parallel case, where there are, at least conceptually, many such logical machines working concurrently and uniformly applying simple rules. Examples are fractals and algorithms such as Conway's game of life^[18]. The result is some characteristic behavior.

§219 The different results produced by differentiation arise at scale because the primitive we propose enables a manifold of parallel “computation” formed against our primitive in a physical structure of sense and associated action potentials. It is unified and storage free implementing cognition and motile behavior. Because it relies on these essential features of our physics it cannot be simulated by conventional machines.

§220 Conventional computational complexity is not constrained in this way. It has no physics of nonlocal differentiation and no logical constraint. There is no point at which the system produces a nonlocal differentiation of the kind seen in sensory architectures.

§221 The converse is the case for logical integration. Logical integration is constrained by the rules of logic and forced to a localized reduction, a final aggregation of the logical parts, a single truth value. In this case logic is forced to take steps too far and is unable reduce across a manifold of the kind we propose.

§222 This difference then derives from the nature of locality in these logical mechanisms and the effect introduced by the primitive we propose. This is aided by the fact that storage, required in the Turing model, is not required in our model because there is a direct covariance between the structure of the physical manifold and cognition/recognition enabled by the primitive.

§223 Since the action of a given manifold will always produce the same sense we also have the basis of memory. And we get the recollection of similarity for free, structures partially reformed will produce a partial sense ; providing a foundation for analogy. In such an architecture there is no need for storage.

§224 Action potentials are covariant with the recollection of similarity. Action behaviors occur either at the point of recognition or when physical circumstances require the organism to modify behavior, a forced collapse to a decision point at which the organism senses what it anticipates and acts accordingly.

§225 Does an organism make a “choice” and, if it does, are such choices “freely” or “randomly” made?

§226 Immediate choices in our model are inevitable, the outcome of action potentials in the established structure of these covariant manifolds. These action points are points of cognition that are refined by the processing of signs ( semeiosis ). We say “refined” because even if the inputs have not been encountered before there exists an a priori manifold born of genetic structure.

§227 In terms of behavior in our species this model tells us that immediate choices are determined: simply put, things happen, we apprehend them, and then we perceive them as our choice. Our volition, if there is any, exists in how we define ourselves, how the manifolds of sense have been refined by semeiosis in our development.

§228 Mechanistically: responses are not exactly “random” or “free.” The responses are constrained by the manifolds involved. If a point of recognition is reached then that determined behavior will follow10 . If a decision is forced by either external or systemic constraint before this point then the response associated with the most similar recognition will occur. If there are multiple of these then one of them will occur or the organism will exhibit a confused state¹¹ .

§231 We judge the difference we are exploring not by some perceived result from conventional symbolic logic but by resulting behavior. Specifically, it is not that the perceived truth values of logical statements differ in the two mechanics but rather that the truth values are concurrent, nonlocal coexisting differentiations distributed across a physical structure, and at scale classical Turing computations cannot deal with this concurrency and nonlocal decision making.

§232 The power of conventional computational complexity is often cited as a sufficient explanation for complex behaviors. We certainly accept the fluid and solid behaviors that arise this way from the uniformity of natural law in classical mechanics. But conventional computational complexity provides no account for the manifest nonlocality in sense, it provides no account of experience in nature. And this should be the most compelling reason to reject current notions of computational complexity as the explanation of nonlocal behavior in sensory architectures.

§233 Emergent behavior by the application of simple uniform laws is a necessary part of our explanation but it is logically insufficient if those laws are constrained to those of conventional computation or classical mechanics. The limits of computational complexity as currently conceived are, in fact, that it is not limited by the natural differentiating constraints that we propose.

§234 It is certainly not necessary in biology to integrate all the results before action is taken in our model, the distributed logic in our mechanics is bound to a manifold of distributed action potential and constrained by the physical structure. In terms of efficiency Turing computation is unable to benefit from the unified nonlocal differentiations freely available in biophysical structure according to our model.

§235 In other words, the concurrency we suggest is not merely the functional composition of localized computations that synchronize before proceeding or common events executed by all but is, rather, an intrinsic concurrency associated with logical differentiation upon these manifolds.

§236 To avoid confusion we steer clear of suggesting that this mechanism be called “entanglement,” a term used in Quantum Mechanics to refer to an observer based phenomenon.

§237 We can uncover a deeper understanding if we analyse the concurrency of these manifolds with the classic process algebra^[19][20] of Communicating Sequential Processes (CSP). If, for simplicity, we use just two processes $P$ and $Q$ to represent two distinct points on our manifold then concurrency of the following type is suggested:

§238 $P\parallel Q$.

§239 Processes $P$ and $Q$ are concurrent and share events in the set of events they may perform (in the “alphabet” of possible events) and these events they must perform together. For example, as the idealized synchronized sequence of the form:

§240 $\mathrm{SENSE}\to \mathrm{ACT}\parallel \mathrm{SENSE}\to \mathrm{ACT}$.

§241 The process points on the manifold are unified in some sensory behavior and then together perform some action.

§242 This is not the case in our proposal. In our model there is no delineation between sense and act, they continuously covary. In addition, the action at each point is dissimilar, the cooperative concurrent action is not uniform. The form of the biophysical manifold changes and the sense changes. At some point in this covariance they produce the “desired effect.” What is it, we may ask, that leads this physical system from gentle cogitation to deliberate act?

§243 The nature of these events cannot be synchronized as identical local events as is generally conceived in the process algebra of CSP. In other words the concurrent process is not a collection of “Communicating Sequential Processes” but rather a single coherent concurrent event. These events are differentiations upon a manifold that is intrinsic and intrinsically binds the manifold. The process $\mathrm{SENSE}$ is a distributed structural entity, it is a manifold of some “shape,” and it is the prior conformance of this entity that is bound to particular subsequent unified actions that are also unique “actions together.” The processes do not make local choices before proceeding, they join together in a grand unified inevitable action.

§244 The synchronization mechanism that we propose here is an uncommon event and the result of physical structure formed against an inert primitive absent in other models. The deformations of this structure characterize sense and construct against it an associated action potential. It is the shaping of this manifold that leads to synchronized behavior in its continuous deformations.

§245 There is then an intrinsic unity across the behavior of the representative processes $P$ and $Q$ born of their physical structure against the primitive we propose. This “action potential,” a complex event of the manifold, leads to a collective unified response.

§246 By analogy this is precisely the same kind of covariant behavior that constrains conventional computational complexity in the gravitational field.

§247 The difference in result then would be illustrated by, for example, the direction an organism takes as the result of a given environmental input. We suggest, essentially, that organisms implemented with Turing machines will fail where organisms implemented with our new mechanics will survive.

§248 Our model suggests a new way to view the structure and architecture of neurons. It suggests that the complex and dynamic manifold constructed by the neuron's cell structure along with the manifolds formed by collections of neurons and other cells is the method of memory and refining thought, a particular manifold configuration corresponding to a differentiated recollection of similarity and motile response. Hence no storage is required in conventional terms.

§249 This suggests that electrical behavior in neurons should not be viewed as signaling activity but should be looked at for its effect upon neuron structure. In our model it is the conformational dynamics of neurons and the membranes in which they reside that produces covariant sense and motile action.

§250 First we observe a manifest nonlocality in sense that is explicitly unaccounted for in the work of Alan Turing^[21]. This nonlocality is most readily observed in any visual scene of the least complexity. The scene does not reduce to a point. In addition, while observing the scene other senses are present. We can hear the music of Beethoven and taste the sweet honey while observing the sunset. This unified differentiation is not a feature of the Turing model of computation or conventional computational complexity.

§251 Next we observe that sense and motility are covariant. This is not the same as saying that there is an identity but only that the two phenomena are mutually effective in precisely the same sense that the gravitational field and mass/energy exhibit general covariance.

§252 The manifest effect of gravitation characterized by the curvature of Einstein's “spacetime” is that observed by Newton, any two bodies appear to have a mutual attraction that varies, roughly, as the inverse square of the distance between them.

§253 It's important to note here the nonlocal nature of gravitation and our new primitive. The gravitational effect is a covariant differentiation and this is similar to the effect that we propose.

§254 The manifest effect of our proposed primitive, however, is more subtle. Clearly mass/energy is again an equal player in the game. It's structure and behavior in this case is exactly that which characterizes the form of sense just as its structure characterizes the form of the gravitational field.

§255 The manifest effect of our proposed primitive, the role that it plays in nature, is the formation of motile structures constructing, by natural selection, an ever richer characterization of sense.

§256 In other words, natural selection does the rest because richer motile sensory systems provide a survival advantage. If our model holds, an organism will always turn toward the richer characterization of sense, whatever behavior this may imply in the context of the organism in its environment.

§257 The basic elements of these structures are the cellular forms familiar to us in biophysics and an even richer characterization comes from manifolds of these cells when assembled together into membrane structures that develop individuated senses and other motile structures in an organism.

§258 This individuated structure of sense, a physical differentiation against our primitive evolved in the cause of an organism's structure, is dependent upon the structural form of a collection of cells but is independent of the individual cells that form the manifold. Cells can be replaced by equivalent cells and the sensory manifold remains intact.

§259 This individuation is critical and explains why it is that you do not feel what I do despite the universal nature of the primitive12 . The focus of the sensory structures is directed toward a particular characterization and this effectively isolates that sense to the individual organism. Similarly, in the formation of complex organisms such characterizations can be isolated to subsystems of the structure.

§264 To state the proposal more directly in the familiar case: a flexible sphere in some medium forms a simple manifold of sense, a physical structure in which the primitive we propose can demonstrate its role. A simple deformation of the surface of this sphere, in conjunction with the sense produced by such a deformation, that is beneficial to the survival of the structure in its environment is enough to begin the process of natural selection in that environment that leads to more complex organisms.

§265 The flexible sphere in some medium is the simplest example of our mechanics. Such a sphere is an uncharacterized manifold of sense. A distortion on the surface of the sphere produces the covariant motility and initiates the characterization of a manifold of sense.

§266 This is the earliest processing of signs ( “semeiosis” ) and the simplest form of “cognition.” “Recognition” is simply a return to form, a structural conformance. When placed in the environment in which natural selection has enough options this mechanics constructs sense and motility suited to survival. And there you have it, a richer characterization of sense and motile action is achieved by continuous evolution of these deformations.

§268 The effect, we predict, will be independent of material or scale. As long as the structural properties prevail the mechanics will apply.

§269 On their own these simple manifolds can evolve into single cell microorganisms. Such microorganisms eventually evolve complex receptors, motor skills, and genetic architectures in the support of the various characterizations of sense in deformations of their structures. This mechanism explains, for example, how and why bacteria migrate along a glucose gradient. Bacteria possess a simple sensory mechanism characterized by the response to glucose and tied to the motile actions required to stimulate the sense further.

§270 The primitive extends this architecture of sense across many cells so that similar cells can be an element of a larger manifold, a biophysical membrane in which the sense is characterized and the corresponding behaviors supporting motile action exist.

§271 Thus the biophysical implementation of logic by this model is intrinsically bound to the form and behavior of physical structure and cannot be localized into interpretations of bits and bytes.

§272 This is true even though we are able to invent such interpretations as the produce of reason, as ways of speaking about the world. Such symbolic systems, based upon a conception of truth that reduces to a cognitive point representing a decision or proof, are unable to perform the direct connection between highly distributed unified sense and action that comes for free in natural implementations in the manifolds that we describe. In other words, something essential is lost in such an interpretations.

§273 There remains the question of whether heuristic machines in fast switching materials perform with more or less efficiency than the mechanics described above. We conjecture that they cannot. Specifically, we claim that despite the success of chess playing machines; heuristic machines cannot ultimately solve the problems of recognition for the reasons, fundamental to the world, described above.

§274 This intuition is based upon the obvious benefits of sensory differentiation that is bound to motile action and requires no storage architecture, against the disadvantage of the need to scatter and gather results in concurrent systems that implement classical logic. We consider the nature of a formal proof of this claim.

Identifying Bias In The Foundations Of Mathematics

Certain basic notions, such as conventional “orthogonality,” in the language of mathematics, derived from received authority, are false.

§275 To enable a new mechanics that provides the characterization of the model we have just outlined we must first address issues in the foundations of mathematics that relate to apprehension. Certain notions in the language of mathematics, derived from received authority, contain assumptions about our apprehension of the world that our model can inform. If left in place these false intuitions will compromise our calculus.

§276 The first and perhaps most significant of these notions is that of perpendicular “orthogonality.”

§277 We will define “orthogonality” here broadly as the logical relation of one concept to another that asserts that the concepts do not intersect anywhere in their development, though they have a common conceptual “starting” point. The example analogy is the notion of intersecting lines.

§278 This notion is a familiar foundation in geometry and algebra, generally pervasive in our mathematics, and intrinsic to Cartesian systems. It is a notion that derives from our earliest mathematical considerations. But the justification for this notion is an intuition nurtured solely by received authority.

§279 Here we will argue that this orthogonality, leading to unlimited geometric “dimensions,” is a false intuition and simply a way of speaking about the world.

§280 We will describe an experimental geometry that has a different orthogonality with naturally finite dimensions; equally capable of characterizing physical structure. It is a geometry predisposed to characterizing cellular forms and their structure as manifolds. From this same geometry we will introduce a number theory that eliminates infinities and provides an analytical algebra that we currently propose as the basis of our calculus. Instead of an unlimited dimensional geometry that starts with “point,” “line,” “plane” we begin with “length” and derive “plane” and “point” as necessary distinctions.

§281 For this mathematics to gain acceptance it must apply to all physical systems. However, we will not require that it be convenient to apply to human affairs. In addition to our new mechanics, therefore, it should be possible using the new geometry to re-characterize General Relativity but it is not necessary, for example, for the derived new formalism to be convenient to use in trade and commerce.

§282 We will also investigate the implication of our proposal to conventional logic. In particular, we look into the implication to formal logic of nonlocal differentiation distributed across unified manifolds. This may enlighten us, for example, concerning the nature and apprehension of formal completeness.

§283 We will find other issues in the foundations of mathematics but, for the most part, these have been explored by others. In particular, when dealing with what we will call “inevitable behavior,” the kind of determinism (unavoidable behaviors) produced by our mechanics, we will take a position that probability is epistemic. That is, we will adopt the view that probability theories are a way of speaking about the world.

Epistemic Primacy

The source of that which is most certain is the refinement of concepts as necessary distinctions and ways of speaking.

§284 In everything that we describe here, as there must be in all scientific work, there are base assumptions concerning the content of what we say, the way we speak about the world and the existential status of that referred to. So to be clear we briefly state our epistemic model here and we will explore it in more detail in the following section on our model of existence.

§285 We place epistemic primacy, the source of that which is most certain, with the refinement by the mechanics we propose of “necessary distinctions” and note that such a distinction must be drawn between necessary distinctions and “ways of speaking” about the world. A necessary distinction is itself a “necessary distinction” and way of speaking is itself “a way of speaking” and the distinction between the two is a necessary one.

§290 A necessary distinction is distinguished by its “force” upon us. A way of speaking is distinguished by its “force” upon the world. One is a distinction of the world acting upon our mechanics, the other is distinction of our mechanics acting upon the world. These are the elements of our epistemology.

§291 This is not to say that one is “true” and not the other. In fact both may correspond to the fact of the matter, to the way things are in the world.

§292 Ways of speaking do not possess the existential framework of necessary distinctions. And it should also be clear that all that we say is a way of speaking until the distinctions to which that speech refers, the necessary distinctions that are claimed by it, have impressed themselves upon us. And this must not be achieved merely by the force of what is said but by the evident truth. Thus necessary distinctions and ways of speaking are both products of our mechanics.

§293 Let us briefly draw here an example from the work that will follow. We will claim that mass/energy, gravitation, and the primitive that we propose are necessary distinctions, aspects of primitive nature; while we will claim that space and time, or spacetime, are simply ways of speaking about mass/energy.

§294 How are we to distinguish one from the other? In some cases it is easy enough, “house” is a necessary distinction while “home” is a way of speaking often about houses.

§295 A necessary distinction can always be distinguished from a way of speaking by the definition we have provided above in our mechanics.

§296 Informally, a necessary distinction is distinguished by its “force” upon us independent what people say.

§297 You may hesitate and say that the three primitive aspects of the world mentioned above do not themselves have a force upon us since nowhere can they be found in distinction. Nowhere can I find mass/energy alone or gravitation or even the primitive we propose. Surely they are not distinctions but are also ways of speaking about the world, the product of reason alone?

§298 The answer is that they are indeed necessary distinctions, for without them there are no other distinctions. Thus necessary distinctions are the elements and components of a logical construction with an existential status before ways of speaking.

§299 Ways of speaking about the world are a very useful means of making intellectual progress. They may indeed accurately describe the world. But if ways of speaking are not about necessary distinctions then they are vacuous.

§300 As a practical matter do not let this concern you too much. However, it is mentioned here because we will use this distinction between necessary distinctions and ways of speaking throughout and in a very particular way in our inquiry.

The Misdirection Of Problem Solving Behavior In Physics

This bias in the foundations of mathematics leads to the misdirection of problem solving behavior in mathematical physics.

§301 Combined, these observations suggest that problem solving behavior in mathematical physics has been misdirected by the formal language that it uses.

§302 In particular, the acceptance of unconstrained “dimensionality” as the basis of formal physical description is often given the existential status of a necessary distinction when this has no basis.

§303 Despite words of caution from many, including Einstein and Godel, there is wide acceptance that time is a necessary distinction and that the perpendicular “dimensions” of space are more than a simple pragmatic, a useful way of speaking about the world.

§304 The way we teach physics, General Relativity in particular, indoctrinates students and the general public with the notion. For most students and public “spacetime” is an existent phenomenon and not simply a convenient way of speaking about the world as Einstein had suggested in his original presentation of the subject^[22].

§305 The received authority of unlimited dimensionality has led to serious and intriguing mathematics, much of which has proven useful, but it has also led to physical proposals that would otherwise be rejected as simple nonsense.

§306 “Many-worlds” theories and some “parallel universe” theories, relying upon the authority of unlimited orthogonality, abound. These fantasies have entered into popular culture as plausible conceptions of the world and yet they have no obvious merit beyond their entertainment value.

§307 The force of received authority at these fundamental levels has led many physicists, and mathematicians such as Chaitin, into a Wonderland as rich in fancy as any faced by Alice^[23].

§308 The worst of it is Quantum Mechanics itself where we deal entirely with the past and the future and not at all with the present, failing to observe the necessity that consideration of the past and the future is physically vacuous.

§309 The results of Quantum Mechanics are, in our view, simply a matter of record. The distinctions are necessary and the ways of speaking are to a large degree true but these distinctions are empty. They simply concern matters of record, past and future, and none of it exists13 .

Existential Thinking

An existential model that includes experience as more than a spectator.

§311

Uniformity and Distinction

The uniformity of natural law and existential distinction in our model.

§312 If dualism^[24] then is to be rejected, and experience is not to be dismissed, there is a necessity that in our new construction an element of that which we liberally label consciousness is a primitive aspect of the world. This being the case our new primitive must play a role in the formation of physical structures.

§313 Like gravitation the effect of this aspect of primitive nature does not become manifest until later in the development of the unfolding universe. Since this effect appears much later in the evolving cosmology this primitive aspect must be considered a much “weaker” influence than the gravitational field.

§314 As discussed in the previous section, these effects can be characterized as a sensory and motile manifold.

§315 In the model of natural law that we will follow here the features of the world derive their existence, their existential status, from a strict functional dependence. Ultimately that dependence reduces to aspects of primitive nature.

§318 This strict dependence implies that the universal properties of the world are existentially distinct, the product of this uniformity alone.

§320 This uniformity of natural law is a base assumption of our model. We argue for this uniformity by observing the absence of observable discontinuity in the laws of nature. Nowhere is there an observable discontinuity in natural law and our model would be falsified by the discovery of one. For example, if we discover galaxies that function according to different laws then this would be an observable discontinuity and our model will be falsified by it.

§321 The uniformity of natural law is the sole reason that there are similar things in the world.

§322 Two diamonds, therefore, are existentially distinct. They form in nature independently and that they are at all similar is clear testimony to the uniformity of natural law. A diamond and a tree are existentially distinct in exactly the same way.

§323 In our model each “molecule” of water in a body of water is existentially distinct. A body of water is a reflection not of any relation between the molecular parts but simply of this great uniformity.

§324 Natural properties of this kind are the product of this uniformity, functionally dependent on a construction from primitive nature but the elements of that property are strictly independent; quantum phenomena not withstanding14 .

Relations And Epistemology

A relation is entirely the product of apprehension.

§326 In our model relations are solely the product of apprehension. They are present only as the result of the biophysical mechanics of sentience that we will present.

§329 Relations can be apprehended, they have epistemological status, but they do not exist in the world beyond apprehension in the mechanics we describe.

§330 The product of invention, a television for example, emerges from the assembly of its parts. There is clearly an identity between the apprehension of television-ness, that which defines a television, and the apprehension of the physical assembly of a television, what it is to be a television.

§331 Television-ness is an essential property of the apprehended assembly alone. It is not a property of the world as a whole. Television-ness has epistemological status but a television has no existential status beyond its apprehension. A television is not actually existent in the world. The physical assembly of a television corresponds merely to an apprehensible assembly of parts.

§332 Properties like television-ness and experience are in distinct categories. Television-ness, in particular, is a property dependent upon the existence of experience not only in that one has to possess experience for it to have any relevance in the world, but also in that it is the product of conscious intelligence. A television does not exist if there is no-one to apprehend it.

§333 Television-ness is also distinct from the properties of the world that emerge from the uniformity of natural law. What we call “fluid” and “solid” exist without our participation in the world. In our model they have existential status in deference to their construction from primitive nature alone. Any perceived relation is entirely the product of apprehension.

The Uniqueness of Experience

The distinct place of experience in the world.

§334 In our existential model fluids and solids arise in the world because of a great uniformity in natural law. They are features of the world that recur widely and this recurrence is testimony to that great uniformity.

§335 They are not constant. In their own state they transform under the laws of nature and they may transform under those laws from one to another, fluids become solids and vice versa.

§336 These are features that continue to play a role in the world.

§337 Emergence theorists^[25] have argued that experience may arise in nature in the same manner as fluids and solids15 .

§339 For this to be true in any model experience would have to be the consequence of the uniformity of natural law. It would have to transform to other forms and play a continuing role in the physics of the world. Yet experience in emergence models has no such role. It is merely present, a dualism. It is a logical construction that ends with the claim “and then magic happens here.”

§340 The position of emergence theory is logically inadequate and amounts to a direct appeal to magic. As Penrose suggested earlier there is nothing in our current physical models that leads us, logically and constructively, to experience as a property arising from some assembly.

§342 Unlike solids and fluids there is no transformation in emergence theory from experience to any other form. There is no logical reduction or constructive route to experience and no role given to it. Whereas, the appearance of fluids and solids, while picturesque, is clearly not magical and these forms continue to play a role in the physics of the world.

§343 Experience is a necessary distinction. And while we will argue here that the various forms of sense are in fact characterized by forms of mass/energy, we find a clear necessary distinction for the essence from which those senses arise and a role for it in the formation of physical structure.

§344 A failure to consider the revision of our physical models has led emergence theorists to suggest that “When you go to a higher level, the lower level may be irrelevant.” The suggestion is that, by this failure of reduction within the limited materialist construction, we abandon the rigorous systematization of nature by science and break the natural chain of functional dependence to produce a supernatural account.

The Rise of Complexity

Where does all the complexity of the things we call “living” come from?

§345 Consider a final example: an apple.

§346 Clearly an apple is not a product of intelligence, as all things in our model it derives in a construction from primitive nature according to natural law. But apple-ness is not at all like television-ness. Nor is its form readily explained by the brute force and uniformity in physics that produces the elements or fluid forms of them.

§347 The diversity of apples, of fruit and of all living forms, suggests that something else is going to disrupt the great uniformity in natural law as seen in the partial cosmology that includes fluids and solids.

§348 Where does all the complexity of “living” things manifest on this planet come from? What brings it about? How are we to describe the mechanics that enables nature to produce the variety of sense?

§349 Frustration over hard questions like these has led emergence theorists to consider the possibility of “and then magic happens here.” But, from our point of view, to consider such magic viable is to undermine the principles of good science. It is an act of desperation.

§350 Oh, we have some inductive expectation that apples are constructed in the same way that fundamental elements are, in a continuum of increasing complexity, but this expectation has weak foundations.

§351 We understand many of the mechanisms involved in the assembly of an apple and its function. We know that it is a product, at least in part, of the substantive essence, of energy/mass. We know that its form is, at least in part, the product of gravitation.

§352 However, the origin of an apple is not readily explained by our established ideas. There is something else going on, a different kind of mechanics, that is not evident in the formation of the elements and their solid or fluid forms. These are simply the product of nature's brute force and the uniformity of natural law. There is something more delicate and subtle going on.

The Business of Thinking

Experience and logical machines.

§353 All of science relies upon the nature of logic and apprehension. Indeed, human understanding of any kind, be it philosophic, religious, or scientific, relies upon our base assumptions concerning what is happening when we apprehend the world. It relies upon our assumptions about what is really going on when we sense the world.

§354 We make natural inferences, we anticipate, we predict. Those predictions are intimately bound to action, to our response. Conventions of all kinds shape the nature of this anticipation and action to form the foundation of our individual understanding and our behavior.

§355 The foundations of logic are built upon our understanding of apprehension and what is apprehensible. This understanding relies upon how we view the existence of experience and what we consider to be its place in the world. This foundation is fundamental to our navigation of and our survival in the world. It is the basis of any epistemology.

§356 Yet experience itself cannot logically be apprehended. Simply, we cannot experience experience. Experience cannot be the subject of experience. We simply experience.

§357 For all of this, contemporary logic, and most especially its manifestation in computer science, has no place and no role for experience. It has reduced to nominalism and the mechanics of symbolic integration16 . It has disregarded the original foundations of logic from George Boole to Rudolf Carnap, a reduction to experience, sense.

§362 At best, due primarily to the work of Gottlob Frege, logic has yielded explanation in exchange for subjectivism, a form of dualism in which experience is an unexplained end in itself but otherwise provides a conception of meaning that has no role in the world.

§364 Our advances in the utilization of current symbolic computation and our stalled consideration of the foundations of logic have left behind an unfulfilled promise. That promise was best articulated at the birth of computer science by Charles Sanders Peirce. In 1887 he noted the opportunity that the invention of logical machines afforded.

§368 The machines that Peirce refers to here¹⁷ are the early machines, constructed mainly of wooden mechanisms, by William Stanley Jevons and Peirce's student Allan Marquand. They utilized the first physical representations of Boole's logic.

§370 Conventional computing machines have certainly thrown light upon the nature of reasoning processes and they have endowed us with productive mathematical and social tools. Yet the question of the identity of that part of thinking that must be left for the living mind is neglected, widely considered irrelevant or the subject of fantastic invention.

§371 The opportunity that Peirce foresaw is unfulfilled and the frustration it affords in best reflected in comments made some years later made by Rudolf Carnap and first published in 1928^[26].

§375 These comments reflect the frustration of our position as it continues today.

Our Story

A summary of the historical narrative.

§376 This brings us to the narrative that we will present. It concerns the distinction between two world views in mathematical logic, the distinction between logic as the integration of the parts and logic as a differentiation from the entirety of sense. The conflict in these world views is represented by the two most influential logicians of the twentieth century: Rudolf Carnap, and Alan Turing.

Rudolf Carnap

The rise of positivism.

§377 Before the 1950's the existence of experience was taken seriously by logicians and scientists. For the mathematicians interested in questions of apprehension in the foundations of geometry such as Henri Poincaré^[27], for pragmatists influenced by Charles Sanders Peirce^[28], for the logical positivists and empiricists of the renowned Vienna Circle and Berlin Schools, for physicists such as Ernst Mach and Albert Einstein, and for those later concerned with interpretations of quantum theory the existence of experience was a central and dominant concern.

§379 Both positivism and empiricism necessarily imply a reduction to experience, though the nature of that final reduction has never been clear.

§382 In particular, the advocacy of physicalism by logical positivists such as Rudolf Carnap rests upon a pragmatic and fundamental understanding. It is an understanding that appeals to the scientific method and that reduced to characterized experience, to sense. The physicalism advocated by Carnap sought a naturalistic basis and anticipated extensions to our physical models as we made new discoveries about perception. These discoveries he anticipated would allow an explanation of experience in nature.

§387 The physicalism of Rudolf Carnap is not materialism. As noted earlier, the materialism of modern conception assumes that we have identified all the essential things of the world.

§389 In our unqualified use of the term “physicalism” here we refer to the physicalism of Rudolf Carnap. This we qualify as liberal physicalism and not the type physicalism of identity theory advocated by Carnap's colleague Herbert Feigl.

§392 Carnap took the first thesis of physicalism to be simply that claims about the world can be confirmed by others. He rejected the idea that you can have private knowledge, gifts from God, that cannot ultimately be shared, rigorously systematized, and confirmed. He took the second thesis of physicalism to be that the laws of nature, including those for organisms and their behaviors, are logical consequences of natural physical laws.

§393 He clarified this by saying:

§396 This is a view that allows for new discovery.

§397 He goes on to affirm my own rejection of claims in emergence theory^[29]:

§399 It should be clear then that the physicalism expressed by Carnap reflects a monist view that there are no fundamental divisions and a positive view that all is open to a unified scientific explanation. Carnap takes experience seriously as existentially essential. He simply did not know how to proceed.

Alan Turing

Excitement over conventional computation and the rise of objectivism.

§400 In the 1950s a ruthless and supernatural objectivism began to take hold in which, despite the mandate of empiricism, the existential questions surrounding experience are marginalized and eliminated from the agenda of science.

§401 This happens primarily because logical techniques, that Carnap had made significant contributions to, provided immediate benefits that enabled the revolution in computing devices and the economic benefits they brought with them.

§402 The advantages of the effective techniques established in the work of Alan Turing^[30], Alfred Tarski^[31]^[32], and Claude Shannon^[33] seemed so powerful and so productive that they appeared to be able to solve quite literally everything18 .

§407 Alan Turing offered a useful notion of computation and took a first step toward reasoning about intelligence without recourse to sense or experience^[34]. Alfred Tarski offered a notion of truth, eliminating experience in his definitions^[35]. Claude Shannon developed a mathematical theory of communication that led to the foundation of information theory^[36]. None ever found, or in Shannon's case needed, a place for experience in their developments. And perhaps all of them are victims of subsequent over-simplification and a generalization that neglects the goals and boundaries of their original inquiry.

§408 Alan Turing's influence is the most profound. His broad consideration to the questions of consciousness is widely misrepresented^[37].

§409 Turing's objectives are practical and more modest than are widely reported. He was challenged by the presence of experience and recognized the limits of his proposals. He sought primarily to take clear and rigorous first steps toward understanding the problem of the mind. He took up Peirce's vision. Unfortunately, subsequent advocates have conveniently ignored Turing's own separation of issues and acknowledgment that questions remained unanswered.

§410 Turing felt that certain mysteries related to consciousness did not need to be explained before the question he sought to address could be answered. That question was whether a machine could be as intelligent as you or me:

§412 We will argue that this was, in fact, a fundamental mistake that is unmitigated by the practical success of his models. As a result, we will argue that there are fundamental limits to Turing's model of computation.

Reclaiming Experience

Reclaiming the existential necessity of experience.

§413 The central point of this narrative is that while the practical contributions of Turing and others had clear and immediate benefits a consideration that had been of principal concern in science, and more particularly in the foundations of logic, was subsequently neglected.

§414 That consideration had simply been put aside by Turing for purely practical reasons, in the interest of more immediate progress.

§415 Unfortunately, in the sixty year period since 1950 the field of logic has stagnated with questions at the foundations that remain neglected. The product of that neglect is systemic. Despite the flurry of interest around computer science, and perhaps because of it, logic is generally considered “a done deal” with little more to be said except in those uninteresting (sic) quiet and unfunded corners of the foundations of mathematics.

§416 In the past sixty years Logic has made no advance as profound as those in the previous one hundred years since Boole. Logic proper, following Frege^[38] and Lewis^[39] not Peirce or Carnap, has mostly (as far as I can tell) resolved to a subjectivist philosophy of intension. It is a philosophy in which Logic observes no difference in the world beyond a change to sense and there is no conception of how such a difference relates to action.

§418 By our definitions such Logic is meaningless and in stark contrast to the fact that its implementation in semiconductors has proven useful. In this role the syntax and semantics of Logic has found meaning as a rigorous language able to articulate the integration of machine inputs and order the switching in computing machinery. But in this role it is missing any differentiation or cognition and has no sense. Thus while it is the case that in its role as an engineering language Logic is rich with meaning it is disconnected in this role from Logic proper.

§419 Before 1950 science took the existential questions surrounding experience seriously. Led by people like Rudolf Carnap of the Vienna Circle and its advocacy of a logical positivism the sentences of science were viewed as marks describing structure and behavior that can be verified by an individual's experience of the world.

§420 This strict solipsism, the view that one's own sense is all that can ultimately be relied upon, was later rejected. It was not rejected because solipsism is fundamentally wrong but simply because logical inference is more powerful than at first considered.

§421 Intuitive inference arising from genetic disposition, inductive inference arising from what we have sensed before, and deductive inference arising from rigorous and systematic methods allow us to expand beyond a dependence on direct experience. Inference allows us to discover that which lies beyond our direct experience.

§422 We will show that there is nothing magical about prediction, inference in all its forms is a natural product of the mechanics we propose.

§423 The techniques of Shannon, Tarski, and Turing in logic and computation has proved useful. They have allowed us to apply effective techniques of thinking in mechanized symbolic systems. But we have become over excited by our success and this usefulness has distracted us from the fundamental issue. We appear to have forgotten that empiricism fundamentally relies upon the existence of experience and that existence warrants explanation.

§424 For a generation of logicians and physicists the existential challenge of experience has become an inconvenient and embarrassing fact. It is manifest to all of us. Yet it is difficult to deal with or to identify any role that it may play.

§425 Contemporary optimism, in the practice of Artificial Intelligence for example, is founded upon the premise that our physical models are complete. These expectations, based on the premises of emergence already discussed, cannot be met for reasons that are fundamental to the world.

§426 The technological “singularity” of Ray Kurzweil is merely a technologist's fantasy^[40]. There is no imminent artificial intelligence comparable to the capabilities of our species. And this is quite simply because this intelligence is not merely heuristics or self-reference. There is something fundamental to cognition and recognition that is unaccounted for in this work. Human-level intelligence requires that we first understand the basis of intelligence: the deeply connected mechanisms of sense and motility in biology.

§428 We appear to have missed the obvious and simple fact that an explanation of the existence of experience requires that we identify a role for experience in the formation of the world. There must be a role for the essence of experience in the formation of organisms in general and senses in particular. For if we cannot identify such a role then it is simply beyond scientific explanation and the matter here can never be resolved.

§429 This is a position we stubbornly refuse to accept.

♦

End Notes

Concepts

Necessary Distinctions

behavior: A difference in the world.

construction: Systematic assembly.

distinction: A distinction is a differentiation, it is a concept that carries a unique difference.

explanation: Identification of causes.

first: Before all others.

intension: Intension is the sense in the apprehension of a mark.

intention: Intention is a reference to the experience of the creator of a mark in the process of that creation.

intentional mark: Marks are the subjects of signs. An intentional mark is the product of semeiosis. It is something created by a sentient individual. For example, this text is an intentional mark.

law: An a priori determinant.

meaning: The behavior that is the direct consequence ( “product of” ) a sign.

motility: Motion that is spontaneous and self governing; the covariant product with sense of a characterization of the primitive of experience.

natural mark: Marks are the subjects of signs. A natural mark is not created by a sentient individual. For example, the morning star is a natural mark.

necessity: We use the term “necessity” in its logical sense first put forward by Hume. Necessity is the inevitable force of natural law.

principle: A posterior determinant.

principle: A posterior determinant.

semantic rule: A transformation of valid syntax from one form to another.

semeiosis: Semeiosis is the biophysical processing of signs.

sense: A physical characterization of the primitive we propose.

syntax: The intentional marks of language.

Ways of Speaking

"computational complexity" speaks about: computation: Computation is that which derives from mathematics.

"computational complexity" speaks about: complexity: Complexity is that which is not readily apprehended.

"consciousness" speaks about: sense: The variety of biophysical sensory architectures.

"consciousness" speaks about: cognition: Cognition is the act of apprehension. It is the product of semeiosis, the processing of signs, that has a potential to affect behavior.

Specifically, a cognition is a change in action potentials that results from semeiosis.

"existential status" speaks about: existence: Existence is that which derives constructively from primitive nature.

"integrative logic" speaks about: integration: The bringing together of parts.

"integrative logic" speaks about: logic: The mathematical language of effective methods.

According to Peirce “Logic is the science of the general necessary laws of Signs and especially of Symbols” [CP 2.93].

"language" speaks about: syntax:

"language" speaks about: semantics:

"logical positivism" speaks about: Logic: Logic is a rigorous and systematic system of inference founded upon some clearly defined epistemology.

"logical positivism" speaks about: Positivism: The philosophy, established by Auguste Compte, that advocates the supremacy of science as a means of apprehending the world.

"variety of sense" speaks about: sense: The structural conformance of the primitive of experience.

People

Alan Turing: (1912-1954) Alan Turing's contribution and influence upon computer science cannot be understated. He articulated the model that defines computational science today.

Alfred Tarski: (1901-1983) Alfred Tarski defined the notion of truth used by generations of logicians and mathematicians until today .

Charles Sanders Peirce: (1939-1914) Charles Sanders Peirce is perhaps the first semeiotician. He made foundational contributions to logic and computer science and gave detailed consideration to matters of apprehension in the context of mathematical logic.

Claude Shannon: (1916-2001) Claude Shannon founded information science by specifying a formal view of information in telecommunication.

Douglas Hofstadter: (1945-) Douglas Hofstadter is Professor of Cognitive Science and Computer Science at Indiana University. He also directs the Fluid Analogies Research Group at the Center for Research on Concepts and Cognition.

George Boole: (1815-1864) Nineteenth century logician, author of the Laws of Thought.

Gottlob Frege: (1848-1925) German mathematician, logician, and philosopher who worked at the University of Jena. Frege constructed a formal system of symbolic logic, the first predicate calculus, a calculus of prediction.

Gregory Chaitin: (1947-) Gregory Chatin is affiliated with IBM's Wolfram Research Center and has contributed important results to the theory of computation. He is a lifetime visiting Professor of Computer Science at the University of Auckland in New Zealand.

Henri Poincaré: (1854-1912) The great French mathematician, theoretical physicist, and philosopher of science. Poincaré wrote extensively on questions of apprehension.

Herbert Feigl: (1902-1988) A member of the Vienna Circle, a colleague of Carnap's and an articulate advocate of identity theory.

John Locke: (1632-1704) The English enlightenment philosopher. Locke gave first consideration to many of the issues that we look at here in his book “An Essay Concerning Human Understanding.”

Ray Kurzweil: (-) Popular author of “The Singularity is Near” in which he predicts a technological explosion that will rapidly out pace our capacity to manage it. In particular, he projects the arising of an artificial intelligence and poses the question: will it be friendly toward us?

Rudolf Carnap: (1891-1970) Perhaps the most important philosopher of the twentieth century. A principal member of the Vienna Circle and cofounder of Logical Positivism.

Stephen Wolfram: (1959-) Stephen Wolfram is the leader of Wolfram Research the produces of the Mathematica software package. He is author of the book “A New Kind of Science” and a past member of the Institute for Advanced Study.

Stuart Kauffman: (1939-) Stuart A. Kauffman is a member of the University of Calgary’s Faculty of Science. He is a professor to the departments of Biological Sciences and Physics and Astronomy. He is also the founder of the Institute for Biocomplexity and Informatics (IBI) there.

Originally a medical doctor, Kauffman is an emeritus professor of biochemistry at the University of Pennsylvania and a seminal member of the Santa Fe Institute.

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