The Concepts of Boundary and Trace

The concepts of boundary and trace are intimately intertwined and are both fuzzy. Physical boundaries are often the measurable manifestations of the operation of boundary conditions. They, therefore, have to do with discernible change which, in turn, is inextricably linked to memory: a changed state or entity are always compared to some things (states or entities) that preceded them or that are coterminous and co-spatial with them but different to them. We deduce change by remembering what went before.   We must distinguish memory from trace, though. In nature, memory is reversible (metals with memories change back to erstwhile forms; people forget; information disappears as entropy increases). Since memory is reversible, we have to rely on traces to reconstruct the past. Traces are (thermodynamically) irreversible. Black holes preserve - in their event horizons - all the information (traces) regarding the characteristics (momentum, spin) of the stars that constituted them or that they have assimilated. Indeed, the holographic principle in string theory postulates that the entire information regarding a volume of space can be fully captured by specifying the data regarding its (lightlike) boundary (e.g., its gravitational horizon).   Thus, boundaries can be defined as the area that delimits one set of traces and separates them from another. The very essence of physical (including biological) bodies is the composite outcome of multiple, cumulative, intricately interacting traces of past processes and events. These interactions are at the core of entropy on both the physical and the informational levels. As Jacob Bekenstein wrote in 2003:

"Thermodynamic entropy and Shannon entropy are conceptually equivalent: the number of arrangements that are counted by Boltzmann entropy reflects the amount of Shannon information one would need to implement any particular arrangement (of matter and energy)."

  Yet, how does one apply these twin concepts - of trace and boundary - to less tangible and more complex situations? What is the meaning of psychological boundaries or political ones? These types of boundaries equally depend on boundary conditions, albeit man-made ones. Akin to their physical-biological brethren, boundaries that pertain to Humankind in its myriad manifestations are rule-based. Where the laws of Nature generate boundaries by retaining traces of physical and biological change, the laws of Man create boundaries by retaining traces (history) of personal, organizational, and political change. These traces are what we mistakenly and colloquially call "memory".   The concepts of "boundary" and "trace" are best discussed within the context of the concept of "context". 

I. The Meaning-Egg and the Context-chicken

Did the Laws of Nature precede Nature or were they created with it, in the Big Bang? In other words, did they provide Nature with the context in which it unfolded? Some, like Max Tegmark, an MIT cosmologist, go as far as to say that mathematics is not merely the language which we use to describe the Universe - it is the Universe itself. The world is an amalgam of mathematical structures, according to him. The context is the meaning is the context ad infinitum.

By now, it is a trite observation that meaning is context-dependent and, therefore, not invariant or immutable. Contextualists in aesthetics study a work of art's historical and cultural background in order to appreciate it. Philosophers of science have convincingly demonstrated that theoretical constructs (such as the electron or dark matter) derive their meaning from their place in complex deductive systems of empirically-testable theorems. Ethicists repeat that values are rendered instrumental and moral problems solvable by their relationships with a-priori moral principles. In all these cases, context precedes meaning and gives interactive birth to it.

However, the reverse is also true: context emerges from meaning and is preceded by it. This is evident in a surprising array of fields: from language to social norms, from semiotics to computer programming, and from logic to animal behavior.

In 1700, the English empiricist philosopher, John Locke, was the first to describe how meaning is derived from context in a chapter titled "Of the Association of Ideas" in the second edition of his seminal "Essay Concerning Human Understanding". Almost a century later, the philosopher James Mill and his son, John Stuart Mill, came up with a calculus of contexts: mental elements that are habitually proximate, either spatially or temporally, become associated (contiguity law) as do ideas that co-occur frequently (frequency law), or that are similar (similarity law).

But the Mills failed to realize that their laws relied heavily on and derived from two organizing principles: time and space. These meta principles lend meaning to ideas by rendering their associations comprehensible. Thus, the contiguity and frequency laws leverage meaningful spatial and temporal relations to form the context within which ideas associate. Context-effects and Gestalt  and other vision grouping laws, promulgated in the 20th century by the likes of Max Wertheimer, Irvin Rock, and Stephen Palmer, also rely on the pre-existence of space for their operation.

Contexts can have empirical or exegetic properties. In other words: they can act as webs or matrices and merely associate discrete elements; or they can provide an interpretation to these recurrent associations, they can render them meaningful. The principle of causation is an example of such interpretative faculties in action: A is invariably followed by B and a mechanism or process C can be demonstrated that links them both. Thereafter, it is safe to say that A causes B. Space-time provides the backdrop of meaning to the context (the recurrent association of A and B) which, in turn, gives rise to more meaning (causation).

But are space and time "real", objective entities - or are they instruments of the mind, mere conventions, tools it uses to order the world? Surely the latter. It is possible to construct theories to describe the world and yield falsifiable predictions without using space or time or by using counterintuitive and even "counterfactual' variants of space and time.

Another Scottish philosopher, Alexander Bains, observed, in the 19th century, that ideas form close associations also with behaviors and actions. This insight is at the basis for most modern learning and conditioning (behaviorist) theories and for connectionism (the design of neural networks where knowledge items are represented by patterns of activated ensembles of units).

Similarly, memory has been proven to be state-dependent: information learnt in specific mental, physical, or emotional states is most easily recalled in similar states. Conversely, in a process known as redintegration, mental and emotional states are completely invoked and restored when only a single element is encountered and experienced (a smell, a taste, a sight).

It seems that the occult organizing mega-principle is the mind (or "self"). Ideas, concepts, behaviors, actions, memories, and patterns presuppose the existence of minds that render them meaningful. Again, meaning (the mind or the self) breeds context, not the other way around. This does not negate the views expounded by externalist theories: that thoughts and utterances depend on factors external to the mind of the thinker or speaker (factors such as the way language is used by experts or by society). Even avowed externalists, such as Kripke, Burge, and Davidson admit that the perception of objects and events (by an observing mind) is a prerequisite for thinking about or discussing them. Again, the mind takes precedence.

But what is meaning and why is it thought to be determined by or dependent on context?

II. Meaning and Language: it's all in the Mind

Many theories of meaning are contextualist and proffer rules that connect sentence type and context of use to referents of singular terms (such as egocentric particulars), truth-values of sentences and the force of utterances and other linguistic acts. Meaning, in other words, is regarded by most theorists as inextricably intertwined with language. Language is always context-determined: words depend on other words and on the world to which they refer and relate. Inevitably, meaning came to be described as context-dependent, too. The study of meaning was reduced to an exercise in semantics. Few noticed that the context in which words operate depends on the individual meanings of these words.

Gottlob Frege coined the term Bedeutung (reference) to describe the mapping of words, predicates, and sentences onto real-world objects, concepts (or functions, in the mathematical sense) and truth-values, respectively. The truthfulness or falsehood of a sentence are determined by the interactions and relationships between the references of the various components of the sentence. Meaning relies on the overall values of the references involved and on something that Frege called Sinn (sense): the way or "mode" an object or concept is referred to by an expression. The senses of the parts of the sentence combine to form the "thoughts" (senses of whole sentences).

Yet, this is an incomplete and mechanical picture that fails to capture the essence of human communication. It is meaning (the mind of the person composing the sentence) that breeds context and not the other way around. Even J. S. Mill postulated that a term's connotation (its meaning and attributes) determines its denotation (the objects or concepts it applies to, the term's universe of applicability).

As the Oxford Companion to Philosophy puts it (p. 411):

"A context of a form of words is intensional if its truth is dependent on the meaning, and not just the reference, of its component words, or on the meanings, and not just the truth-value, of any of its sub-clauses."

It is the thinker, or the speaker (the user of the expression) that does the referring, not the expression itself!

Moreover, as Kaplan and Kripke have noted, in many cases, Frege's contraption of "sense" is, well, senseless and utterly unnecessary: demonstratives, proper names, and natural-kind terms, for example, refer directly, through the agency of the speaker. Frege intentionally avoided the vexing question of why and how words refer to objects and concepts because he was weary of the intuitive answer, later alluded to by H. P. Grice, that users (minds) determine these linkages and their corresponding truth-values. Speakers use language to manipulate their listeners into believing in the manifest intentions behind their utterances. Cognitive, emotive, and descriptive meanings all emanate from speakers and their minds.

Initially, W. V. Quine put context before meaning: he not only linked meaning to experience, but also to empirically-vetted (non-introspective) world-theories. It is the context of the observed behaviors of speakers and listeners that determines what words mean, he said. Thus, Quine and others attacked Carnpa's meaning postulates (logical connections as postulates governing predicates) by demonstrating that they are not necessary unless one possesses a separate account of the status of logic (i.e., the context).

Yet, this context-driven approach led to so many problems that soon Quine abandoned it and relented: translation - he conceded in his seminal tome, "Word and Object" - is indeterminate and reference is inscrutable. There are no facts when it comes to what words and sentences mean. What subjects say has no single meaning or determinately correct interpretation (when the various interpretations on offer are not equivalent and do not share the same truth value).

As the Oxford Dictionary of Philosophy summarily puts it (p. 194):

"Inscrutability (Quine later called it indeterminacy - SV) of reference (is) (t)he doctrine ... that no empirical evidence relevant to interpreting a speaker's utterances can decide among alternative and incompatible ways of assigning referents to the words used; hence there is no fact that the words have one reference or another" - even if all the interpretations are equivalent (have the same truth value).

Meaning comes before context and is not determined by it. Wittgenstein, in his later work, concurred.

Inevitably, such a solipsistic view of meaning led to an attempt to introduce a more rigorous calculus, based on concept of truth rather than on the more nebulous construct of "meaning". Both Donald Davidson and Alfred Tarski suggested that truth exists where sequences of objects satisfy parts of sentences. The meanings of sentences are their truth-conditions: the conditions under which they are true.

But, this reversion to a meaning (truth)-determined-by-context results in bizarre outcomes, bordering on tautologies: (1) every sentence has to be paired with another sentence (or even with itself!) which endows it with meaning and (2) every part of every sentence has to make a systematic semantic contribution to the sentences in which they occur.

Thus, to determine if a sentence is truthful (i.e., meaningful) one has to find another sentence that gives it meaning. Yet, how do we know that the sentence that gives it meaning is, in itself, truthful? This kind of ratiocination leads to infinite regression. And how to we measure the contribution of each part of the sentence to the sentence if we don't know the a-priori meaning of the sentence itself?! Finally, what is this "contribution" if not another name for .... meaning?!

Moreover, in generating a truth-theory based on the specific utterances of a particular speaker, one must assume that the speaker is telling the truth ("the principle of charity"). Thus, belief, language, and meaning appear to be the facets of a single phenomenon. One cannot have either of these three without the others. It, indeed, is all in the mind.

We are back to the minds of the interlocutors as the source of both context and meaning. The mind as a field of potential meanings gives rise to the various contexts in which sentences can and are proven true (i.e., meaningful). Again, meaning precedes context and, in turn, fosters it. Proponents of Epistemic or Attributor Contextualism link the propositions expressed even in knowledge sentences (X knows or doesn't know that Y) to the attributor's psychology (in this case, as the context that endows them with meaning and truth value).

III. The Meaning of Life: Mind or Environment?

On the one hand, to derive meaning in our lives, we frequently resort to social or cosmological contexts: to entities larger than ourselves and in which we can safely feel subsumed, such as God, the state, or our Earth. Religious people believe that God has a plan into which they fit and in which they are destined to play a role; nationalists believe in the permanence that nations and states afford their own transient projects and ideas (they equate permanence with worth, truth, and meaning); environmentalists implicitly regard survival as the fount of meaning that is explicitly dependent on the preservation of a diversified and functioning ecosystem (the context).

Robert Nozick posited that finite beings ("conditions") derive meaning from "larger" meaningful beings (conditions) and so ad infinitum. The buck stops with an infinite and all-encompassing being who is the source of all meaning (God).

On the other hand, Sidgwick and other philosophers pointed out that only conscious beings can appreciate life and its rewards and that, therefore, the mind (consciousness) is the ultimate fount of all values and meaning: minds make value judgments and then proceed to regard certain situations and achievements as desirable, valuable, and meaningful. Of course, this presupposes that happiness is somehow intimately connected with rendering one's life meaningful.

So, which is the ultimate contextual fount of meaning: the subject's mind or his/her (mainly social) environment?

This apparent dichotomy is false. As Richard Rorty and David Annis noted, one can't safely divorce epistemic processes, such as justification, from the social contexts in which they take place. As Sosa, Harman, and, later, John Pollock and Michael Williams remarked, social expectations determine not only the standards of what constitutes knowledge but also what is it that we know (the contents). The mind is a social construct as much as a neurological or psychological one.

To derive meaning from utterances, we need to have asymptotically perfect information about both the subject discussed and the knowledge attributor's psychology and social milieu. This is because the attributor's choice of language and ensuing justification are rooted in and responsive to both his psychology and his environment (including his personal history).

Thomas Nagel suggested that we perceive the world from a series of concentric expanding perspectives (which he divides into internal and external). The ultimate point of view is that of the Universe itself (as Sidgwick put it). Some people find it intimidating - others, exhilarating. Here, too, context, mediated by the mind, determines meaning.