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A Landscape of Knowledge

Escher21_1Epistemology is a branch of philosophy concerned with the study of knowledge. The epistemological continuum, therefore, is a term for the domain of knowledge – a vast landscape of ideas which hold true to varying different degrees, and have very different qualities in terms of their capacity to predict or produce tangible effects. The purpose of this post is to explore this landscape by placing a few arbitrary flags in the sand, from the hard sciences at one end, to the unknowable (what some would call God) at the other.

Largely, epistemologists tie themselves up in knots trying to find adequate definitions of knowledge. For some reason, the field does not seem to have quite caught up with the train of thought in philosophy of science where Popper and Kuhn have largely debunked the idea that knowledge represents absolute truths. This is the shadow of Plato all over again; people just can’t give up their belief in big-T Truth. It seems abandoning the concept of God is easier than abandoning the concept of Truth for most people, even though both depend upon belief for their veracity.

In epistemological thinking, belief and knowledge are generally taken as being distinct. This leads to all sorts of attempts to make logical definitions of knowledge, as epitomised by Gettier’s claim that a person knows something is true only if: (a) it is True (b) the person believes it is true and (c) the person is justified in believing it is true. I don’t really accept this point of view as useful. For a start, if one of our criteria for something qualifying as knowledge is that it is True, then we can never know what is knowledge and what is not, because we never get unequivocal access to big-T Truth – there is no epistemological tricorder which can tell True from False, because the veil of perception (to use John Locke’s term) is never lifted: we have no access to a “God’s eye view”.

Consider this example. Newtonian physics were considered true a hundred years ago, until Einstein took the physics of gravity up a notch. Does this mean Newtonian physics are no longer true? No longer knowledge? I contend that Newtonian physics are still knowledge. They have predictive value. They have descriptive value. What has happened is that we have added to our understanding of the limitations of Newtonian physics and also created new knowledge – General Relativity (the science of curved space). Our confidence about the domain of application for this particular knowledge has improved.

My contention is that confidence – degrees of belief – is a more practical approach for considering knowledge. However, exploration of this idea is slightly beyond the scope of this piece. Instead, I want to begin at the point in the epistemological continuum closest to “Truth” and work away from there.

The terms that follow are like flags in the sand – they exist solely to mark out the space they describe. Another person could use different flags and define a different pattern inside the same space. It is the shape of the space which is the essence of what I am trying to express, not the specifics of the language.


Two key philosophers, Spinoza and Leibniz, thought that in principle, all knowledge could be gained through the use of reason alone. However, they both accepted that in practice this wasn't possible for humans except in specific areas such as mathematics and logic. These two fields – which we will consider as just mathematics, since logic is a subset of this field – are the most often suggested as having an a priori status – which is to say that they can be derived by reason without need to refer to experiences.

That said, empiricists have traditionally denied that even mathematics could be a priori knowledge, with arguments such as John Stuart Mill’s claim that this sort of knowledge can only be derived from experience, and David Hume’s argument that mathematics does not constitute “real” knowledge. Personally, I don’t mind whether you put the line of a priori knowledge before or after mathematics, there is at least no argument that this line is somewhere near mathematics.

Empirical Science

Close to mathematics, but clearly in the domain of a posteriori knowledge, are the empirical sciences. By empirical, the notion is that these sciences are based on observation and inductive reasoning, not deductive logic, intuition or faith.

(I am using the term here in a slightly narrower context than is usual. For instance, the social sciences are often considered to be empirical sciences, and not without just cause. However, I consider them below as part of the statistical sciences.)

In essence, the space I am considering to be the empirical sciences is where those sciences about which there is a high degree of agreement live. Most of physics, chemistry and biology rests comfortably in this domain, at least, those aspects of these sciences which are not in significant dispute.

Empirical sciences generally produce technology. This in part is the key to the high degree of confidence we ascribe to them.

Statistical Science

Next to the empirical sciences are those sciences which are based upon observations, but which are dependent on statistics for their predictive value. In this domain, knowledge of the general cannot be applied to the specific. If I know that most wombles collect litter, this does not allow me to presume that a womble I meet collects litter – that womble might have ethical objections to collecting litter, or could be in a coma, or could be a mimic disguised as a womble.

I feel that psychology belongs somewhere close to this domain. Most of the field’s firm findings are at the statistical levels, but there is also the capacity for individuals to relate patterns derived from observation to individuals. At this stage, however, we have introduced a great degree of potential for human error.

Theoretical Science

What I am choosing to term theoretical science defines those theories which have some predictive value, but about which much remains unknown. Most of sociology, evolutionary theory and Gaia Theory lie in this part of the continuum (at least to my sensibilities).

Parts of evolutionary theory may well reach into statistical science, but nothing stretches as far as the largely undisputed territory of empirical science. The trouble with knowledge about evolution is that it essentially describes events in the distant past, often solely in terms of whichever biological artefacts have survived to the present day. As Gould observes, we have no way of knowing what has survived as a result of being a selective advantage, and what has survived purely as a random artefact.

Hypothetical Science

Further from the higher degrees of confidence lie the hypothetical sciences. Here is a territory where predictions either cannot be tested accurately, or have not yet been fully explored. This area is full of fringe sciences such as psi research, evolutionary psychology and formative causation. Some of these are future sciences which will travel towards empirical sciences (although few if any will actually make it this far). Many of them are speculative nonsense.

Nowhere is this clearer than in cosmology, where dozens of different competing hypotheses exist, many of which have no means to distinguish themselves from the alternatives. Similarly, one may pick from an incredibly diverse set of models for quantum theory, all based upon the same mathematics.

Alchemical Science

Now we have traveled beyond where most scientists are willing to frequent. This region is populated with a wide variety of strangeness. Some, like NLP or hypnosis (which are two forms of the same thing) work, but we don’t know why. Some like astrology have no obvious predictive value but still provide a common language. Two astrologers can engage in detailed conversations about individuals using their common language of astrology, even though the predictive value of their astrological knowledge is at best questionable. There is, therefore, some degree of knowledge locked up in astrology, even if its predictive value turns out to be empirically negligible.

Some things will eventually gain some hypothetical framework, and begin to move up towards the theoretical science, but most are resistant to empiricism. Nonetheless, although we are a long way from certainty, that does not mean that there is not interesting things going on our here in the hinterlands of knowledge.

Faith Effects

And right on the edge of the knowable, we find prayer, placebo and magic. To my eyes, these are three different words for the same thing – and it’s an incredible thing at that. Placebos can apparently cure any disease. The empirical sciences can offer nothing so powerful and mysterious. Faith effects are far from where we can consider knowledge to lie – they are not knowable, in part because they are often not fully replicable.

The Unknowable

Beyond the faith effects lies the vast wilderness of the unknowable. To those who believe, this is where God can be found. God is impossible for us to fully comprehend; it is the very essence of the unknowable. Those that reject all attempts to personify the unknowable attribute much of this domain to chance. Many people fall between these two extremes: how would we separate chance from God from what will become future knowledge? We cannot. We can only choose what we believe.


This then is my vision of the epistemological continuum, a journey from signal to noise, from the knowledge about which we have the highest degree of confidence, to the unknowable, where belief and faith must by definition hold dominion.

When I look at knowledge in this way, I find no conflict between science and religion. If one believes that God created the universe, then everything that can be known was created by God. Science in this perspective merely describes God’s work. Furthermore, science can never eliminate God, because the unknowable always lurks outside the domain of knowledge, in the infinite and incomprehensible static of the unknowable.


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Re: the use of Information and Entropy as a model for the epistemological continuum.
I like Penrose's description of Entropy as the cancelling of order, where order equates the production of energy, or stars. The universe is a big blank canvas of entropy with a few stars dotted around as the root element in the 'foodchain' of order, which acts to disperse the order by becoming more chaotic forms of energy.
This doesn't strike me as a good analogy for the epistemological continuum. The steady state of entropy offers no potential for energy use, but the end of the epistemological continuum still contains us, the thinkers, so there still exists a mechanism for producing more certainty. Its not a stable state.

Hmm. That was a little throw-away, but there it is.

I really hadn't thought of equating chance/noise with entropy... One can have chance effects - from the perspective of an observer - without it being related to entropy, which is a measure of the energy not available for use in work. But it is also used as a measure of the state of disorder in a system, so there are parallels.

Chance in the context of an observer seems to me to be the collection of all events for which causality is beyond comprehension; I would link it more closely with complexity and emergence than with entropy in this context.

I don't think the model above will withstand being couched in terms of thermodynamics. I completely agree with what you say above - with self-organising systems emerging from an energy system rooted with stars and branching into complex ecosystems. But this is a model based upon physical systems, and the model above is purely abstract, based on its central conceit of accepting differing degrees of collective belief as a measure of knowledge.

Still, it's an interesting way of tilting it slightly to see from a different perspective. :)

Ah...I had thought, based on "...a journey from signal to noise...", that you were utilising Information Theory as a direct analog to your epistemological model. Truly, arguing on the known and knowable is on another level of argument from the areas that are meant to be covered by Entropy and Information.
Indeed, I see it as the presence of the observer so centrally within epistemological questions that makes it more difficult to resolve or define anything in this area.

The signal to noise analogue was an afterthought. It occured to me that 'chance' in the unknowable was similar to 'noise'; in retrospect, it is a touch misleading.

And yes, the vital role of the observer is one of the main things that makes epistemology such a quagmire. :)

The Halting Problem, Godel's Incompleteness theorem, Hiesenberg's Uncertainty principle, all these essentail concepts in computer science, mathematics and physics entail an unavoidable margin of uncertainty. But it is this uncertainty that makes any complexity at all possible. Personally, I think you can find God and immortality in a proof of Reimann's hypothesis.

Certainly Riemann found immortality in the proof of his hypothesis, whether or not he proved it himself. The moral of the story - always name all Theorems, Proofs, Questions or Hypotheses after yourself!

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