Another Coursera course completed: Introduction to Mathematical Philosophy

I finished my second free online Coursera course last week: Introduction to Mathematical Philosophy.

It was a pretty intense and esoteric 8 weeks. Taught by two professors from Ludwig-Maximilians-Universität München it was not about the philosophy of mathematics. Instead it showed how some areas of philosophy can be made more precise by using mathematical language and techniques.

It’s hard to give simple examples but we identified axioms that indicate whether people are being consistent and logical in their judgment of probabilities, wrote formulae for indicative and subjunctive statements, expressed Bayes theorem and confirmation theory, defined sample metalanguages, used set theory to define possible worlds, and used different voting methods to determine group preferences.

lmu

I found it interesting and fun. Brain challenges are enjoyable. And the two professors obviously love the topic in an adorably nerdish way.

I passed, with a 79% grade on my first attempt at the final exam (worked up to 95% in later attempts; we had five). But the course creators admitted the exam is a bit of a formality; the course was to get people interested in the topic.

Just Thinking about Science Triggers Moral Behavior

I have never seen the conflict that some people maintain exists between an atheistic worldview and the presence of human morality. This Scientific American article, on a recently-published PLOS One paper, suggests that humans are actually inspired to be moral by science:

Researchers at the University of California Santa Barbara…hypothesized that there is a deep-seated perception of science as a moral pursuit — its emphasis on truth-seeking, impartiality and rationality privileges collective well-being above all else.

Across…different measures, the researchers found consistent results. Simply being primed with science-related thoughts increased a) adherence to moral norms, b) real-life future altruistic intentions, and c) altruistic behavior towards an anonymous other.

just-thinking-about-science-triggers-moral-behavior_1

Had my phil

I attended my last class in my Science & Religion course tonight. That’s it for my philosophy courses at Birkbeck then, I think. It’s been a lot of fun.

I got a decent mark on my quantum mechanics paper after all: 67% (Merit), only 1 per cent less than I got on my Epistemology paper. It was the highest grade I saw among the handful of other papers I was able to spy. Yay, I’m not the worst! I can live with that.

I think that Philosophy of Religion was my favourite course, followed byEpistemology, then History of Western Philosophy, with Science & Religion my least fave. I also took a short course in Consumer Psychology along the way, which was mildly interesting.

Philosophy paper

I’m not as pleased with this paper as I have been with previous ones. I procrastinated and rushed this one at the last minute. And it’s the same problem as before: these are big, big topics, and it’s hard for me to compress them down without making leaps and assumptions or feeling like I’m leaving important stuff out. So long as I get a pass, I’m not too bothered.

Could Quantum Mechanics Have Any Metaphysical Implications?

by

Tim Dickinson

Coursework submitted in accordance with the requirements for

Science and Religion

at

Birkbeck, University of London

on

22 March 2007

Metaphysical questions have always been a part of philosophical and theological inquiry. This is not surprising since these studies involve thinking about the world, and are not traditionally grounded in the testable, scientific physical realm that we experience. We are capable of wondering and of extrapolation, and these capabilities have always led us to ask big questions: What is the nature of the universe? How did it begin? Why does it exist at all? Is our experience of the world a real one?

Natural philosophy has been categorised as “science” from the 19th century. Since that time, metaphysics has – consistently, albeit at variable rates – diverged from scientific enquiry and focused on the big questions. In the last hundred years, however, we have encountered a realm of science that not only seems exceedingly strange in light of our experience and our common sense, but also forces scientists to look at the big questions again: that of quantum mechanics.

The predictions and phenomena of quantum mechanics seem to be at odds with much of what we previously regarded as laws about how the universe works. As I will show, quantum mechanics implies that our thoughts affect states of affairs in the physical world. It may support the idea that the world is non-deterministic, and this has implications for free will. It creates the possibility that parallel universes exist. Questions that we would previously have encountered only as philosophical ponderings are suddenly popping up in the laboratory. It seems as if our ability to be analytic, scientific enquirers has caught up with our ability to speculate about some of the grand questions that have only relatively recently been separated out as metaphysics.

In this paper, I will outline – to avoid the considerable mathematical rigour required to demonstrate the physical phenomena – why I believe quantum mechanics not only adds new perspective on some metaphysical questions, but also stands poised to answer them and thereby push back the boundaries of metaphysics.

What is metaphysics?

The word metaphysics is sometimes used in a very broad sense to mean all philosophical enquiries. It has also recently been used (quite incorrectly, I feel) to mean ideas which are clearly supernatural and outside any current scientific explanation. I will use the definition that metaphysics is that branch of philosophy that inquires after the nature of reality – particularly its first principles, including the ontology and cosmology of the universe. In this sense, I do not take metaphysics to include the natural sciences. Moreover, in the case where a metaphysical question receives a generally-agreed answer, that answer becomes part of physical science and the question is removed from the realm of metaphysics.

What is quantum mechanics?

Quantum mechanics was born – quite accidentally – in the period between 1900 and 1905, when German physicist Max Planck developed a mathematical model that would marry earlier models of black-body radiation with experimental data of that phenomenon.[i] In 1911, Austrian physicist Paul Ehrenfest demonstrated that Planck’s model and statistical methods for developing it necessarily implied that electromagnetic energy came in discretely-sized packets, or quanta. This result troubled the vast majority of the scientific community,[ii]since physicists previously believed that energy was continuously variable. Apart from this majority, Albert Einstein accepted the idea of these quanta and went on to develop fundamental and famous mechanical and electromagnetic theories around them.[iii]

I will not describe the experimental and thought methods by which these theories were developed, nor will I describe them in mathematical terms. I will instead focus on the well-established consequences and behaviours of quantum mechanics, as developed by Einstein (who won a Nobel Prize[iv] for his work on the theory). In addition to the quantisation of some physical quantities, quantum mechanics has, generally, three other outcomes that seem at odds with our classical knowledge: wave-particle duality, the uncertainty principle, and entanglement. Combined, these phenomena provide significant challenges to previously held views of how the universe works.

Even Einstein had problems accepting these outcomes, despite his being instrumental in their discovery. Prior to quantum mechanics, physicists believed that the motions of bodies could be described deterministically by Newton’s Laws. The uncertainty principle, however, showed that there is an intrinsic imprecision in measuring exactly any particle’s momentum and position. The motions of bodies therefore became a probabilistic process:

The uncertainty principle signalled an end to…a model of the universe that would be completely deterministic…quantum mechanics does not predict a single definite result for an observation. Instead, it predicts a number of different outcomes and tells us how likely each one of these is.[v]

Suddenly, we found that we were never able to predict exactly how things will move, and Newton’s “laws” of motion are clearly only approximations. How then does this probabilistic multiple-outcome process actually work? There are several views, but the most popular is the Copenhagen interpretation;[vi] some of its consequences are discussed in the next section.

Wave-particle duality implies that some physical quantities seem to display characteristics of both particles and waves, sometimes at the same time. The famous photon-slit experiments demonstrate this.[vii] This behaviour challenged the notion that we could draw clear lines of distinction between particles of matter and waves of non-material energy.

Entanglement is a very difficult concept, given our classical understanding of the universe. Entanglement implies that some properties of particles that are created from splitting a single larger particle seem to retain some relationship with each other. Changes to one particle’s properties can effect changes in its entangled partner, even though we do not understand any mechanism by which such entanglement could happen (so-called “spooky action at a distance”). Moreover, that entanglement happens instantly over any distance, which seems to contravene the understanding we have from the theory of relativity (that no signal could be travelling between the particles faster than the speed of light). Entanglement, in conjunction with the uncertainty principle, also means that we – as conscious observers – seem to become part of the systems we are measuring, and outcomes in quantum mechanics appear to be influenced by whether we are observing or not.

Metaphysics and the weirdness of quantum mechanics

The Copenhagen interpretation of quantum mechanics says that we have superimposed states of probability when we actually measure any state of affairs. For example, if we have a system that could be in one of two states with equal likelihood (say, red or green) then the system simultaneously exists in a superposition of both states (i.e., is both red and green) until such time as we actually measure it (at which stage it will be either red or green). This interpretation implies that we will have an infinite regress of states unless we can identify a mechanism that somehow “collapses” the set of superimposed states to the one that we detect when we do measure it.[viii]

How do we decide at what point of the process this collapse happens? Von Neumann was the first to propose that the collapse of the wave function happens when the signal reaches the brain.[ix] The question then becomes: at what stage does the signal reach the brain? More precisely: at what point does consciousness of sense data from the outside world occur? How do we separate the consciousness – presumably in or at least resulting from the brain matter – from the signal that is received in the eye or transmitted through the optic nerve? In his Discourse on Method, Descartes said that the thinking “substance” of his mind was separate from the unthinking “machinery” of his body, and that this mind-body duality was made possible by interactions in the pineal gland.[x] Modern science tends to think less of this duality, and more of “mind” as the complex conglomerate of all the machinery of the brain. Quantum mechanics re-opens the debate of the philosophy of mind, because consciousness appears to impinge on physical reality external to the body.

There are other interpretations of how quantum states of being translate into the universe we perceive. Some maintain that the brain exists in a superimposed state as part of the measurement system, and that we somehow arrive at a result not by a collapse to one of the possible outcomes, but by some sort of statistical evaluation of the most likely outcome.[xi]This is a consequence of the difficulty in demarking where the signal of light to the eye, through the optic nerve, and into the brain becomes consciousness, and thus where the system under examination ends and the mind begins. Even if that line were clear, it is still unclear how this evaluation of an outcome might happen. No matter where we draw the line for what constitutes our measuring system, quantum mechanics seems to require we understand the distinction between the world and our own minds.

The displacement of the Newtonian view (which, as previously stated, is at best an approximation and which we could now claim to be essentially reductionist) does influence two other longstanding metaphysical questions: that of a cosmological first cause and that of human free will. Since there is no clear causality line in a world of quantum mechanics, the view that the universe required a single first cause for its being appears to be made weaker.[xii] Also, the lack of determinism in the way that the world works – that nothing, including human beings, is a clockwork mechanism that must produce predictable results given certain conditions, and that outcomes are in some way contingent on our involvement – suggests that there may be an opportunity for at least some level of free will.[xiii]

Most scientists believe – as Einstein did – that our understanding of quantum mechanics is still incomplete. Many are working to introduce determinism to the theory.[xiv] One result of this is the “many-worlds” interpretation:[xv] that every act of measurement splits the entire universe into a number of different, non-interacting branches. There is no collapse or evaluation of probabilities, and the end result is a complex product of vector states of each possible quantum outcome and the observer. This interpretation then becomes deterministic. However, it also means that every possible outcome actually occurs, and we are left with the somewhat difficult notion of a branching universe, where new – but presumably isolated – realities are created at every point of measurement or interaction. If this has been happening since the Big Bang (say 15 billion years ago) then it has been estimated that 10100 universes might now exist.[xvi] A development of this idea is of parallel universes: that quantum options happen in pre-existing (but still non-contacting) universes, and they are not created by branching at each new measurement point.[xvii] Again, these interpretations are describing phenomena that are, in some sense, real enough that quantum computing (complex computing that uses quantum states of 0, 1 or a superimposed state of both) is a serious area of scientific enquiry.[xviii]

The ontology of physical objects is yet another concept that is affected by quantum mechanics. Einstein’s theories of general relativity show us that space and time are inextricably linked, and that time is a dimension not very different from the three spatial ones we perceive (i.e., space-time). Objects may therefore properly be thought of as four-dimensional hunks of matter.[xix] That is, we should conceive of matter as taking up four-dimensional space-time, not just three-dimensional space with time somehow happening separately. Defining separate objects therefore means defining them as objects that do not occupy the same 4-D space. As I have described, however, the uncertainty principle of quantum mechanics says that we may not specify objects precisely in this way, and our ability to be precise about what occupies what space-time – and what is therefore an “object” – is, like Newtonian motion, limited to approximation.

In the last 60 years, scientific enquiry has tried to focus on distinguishing what we can scientifically measure and what we should relegate to mysticism. The logical positivism of the Vienna Circle (and, to a lesser degree, Karl Popper) was the most significant attempt to remove everything non-analytical – mind, being, metaphysics, God, et cetera – from philosophy and place them with the arts and religion.[xx] Whether or not one agrees that positivism ever truly removed metaphysical questions from science, the discussion above shows that quantum physics would certainly have brought at least some of those questions back.

Fringe ideas

The degree to which quantum mechanics has re-opened questions of metaphysics is made clear by the degree to which pseudoscientific proponents have attached themselves to the theory. This tendency has sometimes been called quantum mysticism.[xxi]As an example, in a paper called Quantum Metaphysics, Stenger says:

In some sense, the wave function of the universe is an etheric cosmic mind spread throughout the universe that acts to collapse itself in some unknown way. The human mind (spirit, soul) is, of course, holistically linked to the cosmic mind and so exists in all space and time. Once again we have and example of what Paul Kurtz calls the “transcendental temptation.”[xxii]

These sorts of views are not useful from either scientific or philosophical points of view. They exist because quantum mechanics is scientific, but its phenomena look similar to those predicted by certain pre-existing unorthodox views. Concepts of entanglement, action at a distance, and outcomes influenced by our conscious states are irresistible to many of those who seek validation of New Age ideas of cosmic unity or powers of mind over matter. We should take care to exclude these views from serious inquiry into how quantum mechanics affects our metaphysical ideas.

The methods of positivism and the future of quantum mechanics

The behaviour of quantum mechanics seems to be in opposition to realism, the view that there exists a reality independent of us as conscious observers. If it truly is the case that a non-deterministic collapse of probabilities only occurs when observed, then what does it mean to talk about a reality independent of any observers? Similarly, if the many-worlds interpretation is true and there are many universes, either created or pre-existing, what does it mean to be a realist?

Even if we subscribe to realism, however, we should not discount current interpretations of quantum mechanics simply because we have not found a view that squares with it. Quantum mechanics is one of the most successfully predictive theories ever developed, and is obviously correct in some very significant way.[xxiii] It is part of the progressive mathematisation of the physical sciences that began with Galileo and continues today, using the methods – if not the entire philosophy – of the positivists:

Most Western scientists actually learn to use themethods of the positivists during their formal education…They learn to adopt a pragmatic, sceptical approach to science in which philosophy – and particularly metaphysics – appears to play no part.

However, for many scientists the stuff of their theories – atoms, electrons, photons, etc. – are quite ‘real’. Many assume these objects to have an existence independent of the instruments used to produce the effects their theories are supposed to explain…A modern scientist might typically adopt the methods of the positivist but the outlook of the realist.[xxiv]

There are also consequences of quantum mechanics that – while being at odds with previous theories – seem to make our universe more understandable, at least in some limited respects. For example, the relativistic space-time model of the universe leaves cosmologists with a gravitational singularity at the instant of the Big Bang: that is, a point where the mathematics of how we know space and time to work break down into meaninglessness. However, some scientists maintain that when quantum effects are included in the model this singularity disappears, and we get a definable and more consistent model of the universe that includes the moment of the Big Bang[xxv].

It may be that quantum mechanics – or whatever follows it – holds many more surprises for us. Albert speculates about future humans who might have artificial means of objectively analysing their own brain states (either through other observers, or cybernetic devices in their brains).[xxvi] He extends these capabilities to hypothesize – with some very complicated vector mathematics – that these future humans might be able to bypass the uncertainty principle, or have knowledge of what occurs in parallel universes, or even in the future. In the end, we might find that there is a deterministic interpretation of quantum mechanics – like that of parallel universes – after all, but that interpretation would almost certainly contain phenomena we find exceedingly strange.

It is clear that whatever our interpretation of it, our understanding of quantum mechanics is incomplete. There is no reason to assume, however, that we will not improve our level of understanding. Some philosophers of science have speculated that our current comprehension of the theory is roughly equivalent to the understanding of the atomic-molecular model in the mid-19th century.[xxvii] If this is true, we are certainly extrapolating some distance beyond our current abilities to accurately understand how quantum mechanics works, and this has the consequence of results which appear quite unrealistic.

Conclusion

Quantum mechanics seems certain to do as much damage to our ideas of the nature of the universe as did the Copernican revolution. I have shown that investigations into quantum mechanics are forcing us to ask questions about the nature of free will and determinism; about cause-and-effect; about where reality stops and our consciousness starts; and about whether our reality is the only one that exists. The fact that quantum theory has caused us to revisit areas of metaphysics is an indicator that we are grasping for straws to explain physical behaviour that is currently at odds with much of our previous experience. When we find explanations for these questions, some of these metaphysical questions will certainly be answered, and answered quite concretely. As we come to understand more about quantum mechanics, analytical knowledge will come forward to claim the ground that metaphysics has abandoned.

[i] Baggott, J. (1992), The Meaning of Quantum Theory, 6.

[ii] Baggott, 9.

[iii] Hawking, S.W. (1988), A Brief History of Time: From the Big Bang to Black Holes, 56.

[iv] Hawking, 56.

[v] Hawking, 55.

[vi] Baggott, 81-83.

[vii] Hawking, 56-60.

[viii] Baggott, 186.

[ix] Baggott, 186.

[x] Baggott, 189.

[xi] Baggott, 191.

[xii] Baggott, 204-206.

[xiii] Baggott, 192-194.

[xiv] Baggott, 159.

[xv] Baggott, 194.

[xvi] Baggott, 199.

[xvii] Baggott, 200-201.

[xviii] Internet: http://en.wikipedia.org/wiki/Quantum_computing

[xix] Heller, M. (2001), “Temporal Parts of Four-Dimensional Objects” from Metaphysics: Contemporary Readings (M. J. Loux, ed.), 333.

[xx] Hamlyn, D.W. (1987), The Penguin History of Western Philosophy, 306-310.

[xxi] Internet: http://en.wikipedia.org/wiki/Quantum_metaphysics

[xxii] Stenger, V.J. (1995), paper presented at the Conference on New Spiritualities,Westminster College, Oxford, England, March. Published in Modern Spiritualities, Laurence Brown, Bernard C. Farr, and R, Joseph Hoffmann (eds.), 1997. Also published in The Scientific Review of Alternative Medicine 1(1), 26-30, 1997. Viewable on the internet at:http://www.colorado.edu/philosophy/vstenger/Quantum/qmeta.html

[xxiii] Norris, C. (2000), “Quantum theory and the logic of anti-realism” from Quantum Theory and the Flight from Realism, 66.

[xxiv] Baggott, 79-80.

[xxv] Hawking, 133-141.

[xxvi] Albert, David Z. (1992), Quantum Mechanics and Experience, 180-189.

[xxvii] Norris, C. (2000), “Is it possible to be a realist about quantum mechanics?” fromQuantum Theory and the Flight from Realism, 35.

Philosophy

In Science and Religion class the other night, we quickly looked at the question about whether faith can be good for you. We skipped pretty quickly over the idea that for a given individual, a life of faith and religion certainly can provide a framework of ethics and happy existence; it would be hard to argue that no one has ever benefited from that. Likewise, a system of blind faith can sometimes lead people down the wrong path.

We didn’t get into whether faith has, on the whole, been a positive or negative thing for humanity. We only have one 2-hour class on this.

We did examine in a bit of detail the Gaia hypothesis. This isn’t the hippy-dippy “we’re all one” New Age idea, but the unproven and controversial idea that the earth’s ecosystem is in fact regulated by the living things within it. One consequence of this theory is that it’s not just right to be environmentally responsible, but that it migth be essential for the survival of the entire earth ecosystem to do so. We did this, I guess, as an example of how faith – even of a non-religious type – might result in a system of ethical behaviour that is beneficial for you.

I’m not sure I buy that, but it was an interesting class.

Knowing your place

In philosophy class last night we discussed the Copernican revolution. As you’ll recall, his 16th-century theory that the Earth was not, in fact, the centre of the universe was the source of much controversy. It was the source of even more controversy (and condemnation) later, when it was supported by observations and models from Galileo and Kepler. In the end, of course, this was the first big defeat of an area of religious knowledge by a scientific one.

We had a fun exercise last night. We had to break up into small groups and come up with ten reasons why one might believe in a geocentric model for the universe; then ten reasons why one might believe in a heliocentric model for the universe; then come up with other models that the evidence might support. The first task saw most teams come up with similar ideas: it feels right that the Earth should be the centre of the universe because it feels biggest, because the other heavenly bodies appear to move around us, because we don’t feel like we’re moving, because we’re the reason God created everything, etc. The reasons for abandoning this model and adopting a heliocentric view produced a little more variety: the phases of the moon, lunar eclipses, the changing seasons, other planets and how the number of moons they have appears to change, etc. We didn’t come up with too many other models of the universe, but my favourite was that perhaps the earth is stationary and a new Sun, Moon, and set of stars are created fresh for us to observe each day.

Science and Religion

I attended my second class in my current (and probably last) philosophy course the other night. It was good, better than the first class, where the prof talked too much. There was more interaction this time, and some work we did broken up into small groups. In this class we spoke about the bases on which science and religion each claim to provide knowledge, and how each have developed over the years.

I like the readings he gives us between classes, too. The first week, it was some text from Tolstoy, who maintained that the fundamentals of all religions (a creator, the subservience of personal passions to love, etc.) are what’s important, but that the trappings and teachings of modern religion instead drive us away from true religion. This week, it was the famous philosopher Bertrand Russell, and his description of how science has constantly pushed back the boundaries of religion throughout history (e.g., in the 17th century, anaesthetics were denied to women during childbirth because the pain was Biblically indicated to be a just punishment for Eve’s original sin).

This isn’t the philosophy you’re looking for

I took the tube downtown to the university tonight to find out what building and room my philosophy class was in – and found that it was cancelled. I’d received no notification, no refund.

I was very disappointed, but there was no one from the registrar’s office to yell at at that hour. I turned to come home. Then I realised that it would now take until the end of next December to complete my philosophy certificate. Maybe there’s another course I can take, I thought.

I looked at the rolling video display of course listings. There were two philosophy courses at the same time. One was History of Western Philosophy, which I’ve already taken. The other was Science and Religion.

Ah ha.

Science and Religion wasn’t on the course list when I made my selections last year. If it had been, I might’ve chosen it; it’s right up my alley. And I knew that it was being taught by the same lecturer who did my epistemology course last autumn.

I wandered to that building, and met the lecturer on his way in.

“I didn’t know you were taking this course,” he says.

“Neither did I,” I say.

He let me sit in. It was quite interesting, and it’ll be an acceptable class to round out my certificate requirement. Here’s the summary:

Science and Religion

Can religious claims be evaluated scientifically? Does science have religious implications? We will examine in a philosophical way the main theoretical issues in the interaction between religion and science. We will explore approaches to science demonstrated by a variety of religious traditions.

I’ll ring the registrar tomorrow and switch over to that course.

As it turns out, there were two other people from my epistemology course that are also taking this class. And – joy – one of them was Global Warming Guy. When the prof asked each of us what we want to get out of the course, he said – as always – that he wants to understand science and religion as they apply to global warming. Somehow.

 

Can scepticism be refuted by writing it ‘skepticism’?

This is a copy of the paper I’m handing in tonight for my epistemology course. This is the only work required for submission. There’s still two classes left (tonight and next week) but it’s been a pretty interesting first dip into epistemology.

Can Scepticism Be Refuted?

by

Tim Dickinson

It is clear that humans seek knowledge. We know this about ourselves and we see it in others, to some degree or other. At minimum, we want to know things because of evolutionary selection, since animals that seek reusable knowledge and reason inductively are more likely to survive than those that do not. There may be less utilitarian reasons for this seeking as well: a desire for self-growth, for example, or an intrinsic value on truth. In light of this apparent importance, the question of scepticism – whether we can in fact ever really know anything – is therefore due some consideration. Can scepticism be refuted?

In this paper I will describe how scepticism can be broadly separated into Agrippan and Cartesian forms, and how these forms cast doubt on our ability to acquire knowledge. I will show that sceptical doubt is powerful because it seems basic and intuitively grasped, and is not so esoteric as to appear dubious. I will then demonstrate how these forms of scepticism can be refuted with theories of coherence and contextualism that are equally intuitive.

Forms of Scepticism

There is a form of scepticism more properly identified as incredulity. This is what I mean when I describe the viewpoint of someone who tends to reject ideas which lack supporting evidence; this is the opposite of dogmatism. I will not consider this form of scepticism here, since it is not general. This casual scepticism does not exclude any knowledge for which I do have evidence (and is, in fact, generally regarded as a good and important part of any analytical viewpoint). What I will examine is philosophical scepticism: the claim that acquiring knowledge is inherently impossible.

I will discuss two forms of philosophical scepticism: Agrippan and Cartesian. I will not include fallibilism because it is not radical scepticism: it is simply the view that I may be mistaken about some things and can probably not be certain of much, not that it is impossible for me to know things to be true. In fact, if we know anything, it seems likely to me that the fallibilist view is the right one, and that we can be absolutely certain about very little (if anything at all).

Agrippan scepticism is an ancient form that developed from earlier Greek scepticism[1]. It implies that beliefs always rely upon an unfounded assumption, circularity, or an infinite regress[2]. That is, every attempt I make at justifying why I have knowledge must end up at some fundamental assumption upon which I build the rest of my knowledge; or my reasoning ends up in a loop where my justifications all rely on one another; or my justification can always be met with another request for justification. These are simple, yet powerful, obstacles. Since, according to the Agrippan view, all attempts at justification must fall into one of these traps, no knowledge is possible. To refute Agrippan scepticism, I will thus have to demonstrate that justification does not always fall afoul of these traps.

Cartesian scepticism derives from the philosophy of Descrates[3], who questioned the possibility of asserting that we have reliable knowledge of the external world. Others have built upon this viewpoint, and what is now called Cartesian scepticism may be regarded as the claim that – given all the evidence I will ever have to make some claim about the world – an alternative explanation that makes my claim false is just as likely to be true. This form of scepticism implies that justified beliefs must be either direct knowledge or inferred (deductively or inductively) from direct knowledge. This is sometimes expressed as a problem of underdetermination (i.e., I have inadequate evidence necessary to decide that my belief counts as knowledge). To refute Cartesian scepticism, I will thus have to show that I may sometimes have sufficient justification for knowledge.

Refuting Agrippan Scepticism

As discussed above, to refute Agrippan scepticism I will have to show that unfounded assumptions, circularity, and infinite regress do not block all claims to knowledge. I will consider the first two problems by examining existing models of knowledge that claim to overcome them. I will then go on to propose that a model might exist that circumvents the third problem.

Foundationalism – the model that I have certain fundamental, directly knowable true beliefs, upon which others can be built – claims to refute to Agrippa’s problem of assumptions. Foundationalism would say that these basic beliefs are neither unfounded nor assumed: they, at least, are justified. I find foundationalism unconvincing. What special knowledge requires no justification? Some level of assumption seems difficult to avoid, at least for anything beyond self-awareness. Foundationalism does not appear to be a theory that defeats Agrippan scepticism.

Coherence – the model that our knowledge is a network of mutually supporting true beliefs – claims to refute the second Agrippan problem, that of circularity. A coherence view would imply that circularity of justification is not an obstacle to knowledge. A complex, non-contradictory network of knowledge implies a tested, reliable system of knowledge in much the same way that the subsets of knowledge we are more familiar with (e.g., physics) do. As such, a coherence system of knowledge gains force as it becomes more comprehensive and increases in accuracy. To maintain sceptical doubt in the face of such force requires an increasingly infallibilist position (that our justification and knowledge must be free of the chance of error). I note that Williams[4] claims that coherence requires me to make assumptions about the validity of my whole system of my knowledge, and is therefore simply another form of foundationalism. I disagree with this view. The modularity of my knowledge, or my inability to hold the entirety of it at all times in my mind, does not threaten my justification: only a poor standard of justification does. Coherence therefore appears to be a strong possibility for refuting the Agrippan assertion that circularity should make us sceptical about our knowledge.

A similar line of argument holds for theories of knowledge that are part of an infinite regress, Agrippa’s third sceptical challenge. I recognize that this position is not commonly given credit. In fact, Agrippa’s scepticism is usually described as a ‘twin-horned’ dilemma – comprised of assumption and circularity – upon which the non-sceptic impales himself whilst attempting to avoid the infinite regress of justification. However, I see nothing inherently impossible about an infinite chain of justification. Infinite series are commonly used in mathematics and are both understood and applied practically. I believe that our distaste for infinite regression lies in our perception of a direction of time. Few people have difficulty imagining an infinite progression into the future. Modern physics has shown that time is in fact a dimension more similar to the spatial ones that we had previously supposed[5]. I will not claim that this is strong evidence that an infinite regress refutes Agrippan scepticism in the same way that a coherence system does. I will here simply assert that a system of knowledge justified on an infinite regress cannot be rejected out of hand.

Refuting Cartesian Scepticism

Cartesian scepticism is sometimes illustrated by Descartes’ ‘Evil Deceiver’ or ‘dreaming’ scenarios; or, more recently, by the ‘Brain in a Vat’ scenario. Putnam claims to refute this sceptical view by using semantic externalism to claim that if I am a brain in a vat, then the statement ‘I am a brain in a vat,’ is incoherent, and therefore false[6]. I reject this argument as unconvincing; Putnam simply points out that some things that may be possible areconceptually impossible.

Phenomenalists claim to refute Cartesian scepticism by stating that all I can ever know is my experience, my sense-data. This sense world, they claim, is the only one that can exist for me. They believe that they thus defuse the problem of scepticism because there is nothing for me to be deceived about. This view strikes me as an unsatisfactory cheat. Everything about my experience seems to imply an objective world where things take place without me, and so it seems right that I should give that world credit and attempt to know it.

Grayling[7] stages an elaborate refutation of scepticism. As discussed above, however, the problem of scepticism is significant not only because of its implications about the truth of our knowledge, but also because it is so intuitive (themes in popular culture support this). Grayling’s position requires transcendental arguments and a discussion of realism that, I feel, are not sufficiently intuitive to combat such fundamental doubts.

To refute Cartesian scepticism I will therefore need to show that the evidence I am able to collect does not always underdetermine my justification of my beliefs about the external world. My first problem is then how I am to decide what constitutes sufficient justification. I have previously rejected an infallibilist requirement for certain justification as needlessly prohibitive. What lesser level of justification will do?

My approach is rooted in my everyday experience. How do I typically decide what constitutes sound justification in my day-to-day life? I judge the circumstances. I assess what I know of the source of the information; I try to consider my own frame of mind; I take into account the urgency attending the knowing and the importance of the outcome. The type of justification I might require to know that I smell my dinner cooking is likely to be quite different than that I might require from someone who is explaining a mathematical proof to me.

This view is the contextualist theory. I believe that it offers the best way to refute the sceptical position. The contextualist position is broadly that the level of justification required to be epistemically responsible depends on the circumstances. I can recognise the contextualism of semantics (e.g., we all use the words ‘I’ or ‘my brother’ in the same way, but refer to different people when we do so). Similarly, I recognise that I apply different levels of justification in my everyday decisions about knowledge (as above, I adjust my justification requirements depending on what I’m being asked to believe, who’s doing the telling, etc.). Contextualism says that there is an appropriate epistemological standard of justification depending on the context of what it is that I am being confronted with. If I am consistent and intelligible with my application of these standards, then there seems little reason to believe that contextualism is failing as a system for justification (even if I sometimes make errors).

Williams claims that, in addition to being a reliable view of knowing the external world, the contextualist view attacks hidden premises of scepticism[8]. Cartesian scepticism, he claims, inherently imposes a priority of experiential knowledge over direct knowledge of the world[9]. For the contextualist, there is no reason to grant that this context-invariant assumption is true. Cartesian scepticism amounts, he says, to a form of foundationalism. This undermines the sceptical claims, since they now depend on more complex theoretical assumptions and are not as basic and intuitive as before. I find this argument convincing. There are many instances of successful thought experiments predicting nature, for instance, which implies that sense-data may not always automatically supersede other knowledge about the world. Contextualism therefore seems to not only provide a reasonable system of justification within the framework of coherence, it challenges scepticism at its root.

Conclusion

I believe that coherence theory has the best chance of avoiding Agrippan scepticism (and that a theory of knowledge based on infinite regress might also do), since it shows how a justified system of knowledge can exist, self-contained, without supposition to support it. With that basic structure in place, I believe that contextualism then provides a means for the justified acquisition of knowledge.

[1] Hamlyn, D.W. (1990), The Penguin History of Western Philosophy, 85-86.

[2] Williams, M. (2001), Problems of Knowledge: A Critical Introduction to Epistemology, 61-63.

[3] Hamlyn, 138.

[4] Williams, 137.

[5] Hawking, S.W. (1988), A Brief History of Time, 143-153.

[6] Putnam, H. (1992), ‘Brains in a Vat’, in K. DeRose and T.A. Warfield (eds.),Scepticism: a Contemporary Reader, 385-399.

[7] Grayling, A.C. (1985), The Refutation of Scepticism.

[8] Williams, 187.

[9] Williams, 189.

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