In the beginning, there was...

The infinite regress crops up more than one might think. Consider the following fairly common theological argument:

A: Where did you come from?
B: My parents.
A: And where did they come?
B: My grandparents?
A: And where did they come?
B: Great grandparents.
A: But you can go back and back and back and back, and eventually you will have a problem, no? So there must be a Creator.

This is, in essence, the 'Cosmological Proof' of Thomas Aquinas. A short version is the following:
1. Every being is either a dependent or a self-existent being.
2. Not every being can be a dependent being.
3. Therefore there must be a self-existent being.

Of course, this does not tell us anything about the nature of this self-existent being. Indeed, a deist can turn around and say "that may be true, but why should this self-existent being care about us at all? If I walk along the beach, I leave footprints in the sand. I don't deny that these footprints cannot be uncaused, and that I am the cause, but it doesn't mean that I care about them after the fact." And indeed, an atheist can go further and say "why not just claim that the universe itself is a self-existent being?" (This would include the 'oscillating universe' cosmological theory.

So although the infinite regress may be a weapon for an argument, one must be careful that it is not turned against oneself!

Another area in which the infinite regress poses problems is with respect to the notion of 'a priori' knowledge. That is, knowledge prior to experience. Descartes, a rationalist, required an a priori justification for existence in his famous 'cogito ergo sum' argument. The clashes between the ideas of contemporaries Leibniz (the same Leibniz whose name arises in mathematics) and Locke with regard to whether or not a priori knowledge was possible is, in some ways, a definitive characterization of the difference between rationalism and empiricism.

Let us consider another major problem that the infinite regress points to: that of determinism. If everything must have a cause, then how is liberty/free will possible? This is a very important question, since its being posed by Hume in the Enquiry Concerning Human Understanding was what 'woke Kant from his dogmatic slumber'. Hume had concluded

"Whatever definition we may give to liberty, we should be careful to observe two requisite circumstances; first, that it be consistent with plain matter of fact; secondly, that it be consistent with itself. If we observe these circumstances, and render our definition intelligible, I am persuaded that all mankind will be found of one opinion with regard to it[:] … liberty, when opposed to necessity, not to constraint, is the same thing with chance; which is universally allowed to have no existence."

In other words, we can be 'free' with respect to constraint (e.g. not in prison), but our actions are necessitated by something else, i.e. according to Hume free will is impossible. One can conceive of it in the following way: consider every second or millisecond or ample 'division of time' as a 'frame' of existence. Then every 'frame' is somehow dependent on the previous 'frame'. If I suddenly 'choose' to go for a walk, it is only because there was something in the previous 'frame' that prompted me to do so, whatever that may have been.

Kant took this problem very seriously, and eventually attempted to argue that sponte (that is, uncaused events) can arise in the realm of thought. This prompted the German idealists after him: Fichte, Schelling, Hegel, and Schopenhauer to name a few, to come up with a way to 'iron out' the problems with regard to Kant's notions of freedom, i.e. the 'uncaused cause', though Schopenhauer broke from this trend and, in his essay 'On the Freedom of the Will', sides with Hume and explains that there cannot be such a thing as free will. Kant is one of the most important philosophers in the history of modern philosophy. His ideas led the way to Hegel who led the way to Marx, et al, and to Schopenhauer who led the way to Nietzsche, et al. Schelling's is often considered to be the first person to coin the term 'unconscious' and his ideas are a major contribution to modern psychology.

So, we have a lot that we owe to the infinite regress, unless, of course, ignorance is, indeed, bliss. For one cannot even begin to ponder a world without Kant.

Where would we be now if Kant had remained asleep?

Let's see... where can I begin...?

It may be seen as the bane of philosophy, and the boon of scepticism. We have all had the experience, especially with young children: an inquiring mind asks for an explanation, and upon giving the explanation, you are again asked a justification for this explanation, and on and on and on, until you have to say something to the effect of 'I don't know' or 'it just is', or you have to give a response akin to 'I don't have time for this'. It is the infinite regress. And it stems from the apparent absurdity of the 'causa incausata', the uncaused cause. In other words, it comes down to the question, how can something result from nothing (and/or itself)?

There are two main areas where this shows itself: in metaphysics, and in epistemology. In metaphysics, it arises because of the nature of time and its connection to causality: if something happens, there seemingly must be something that happened before it to cause it to be so; in epistemology (in which the problem is not so different) it follows the pattern of the above paragraph: if you want to argue for or establish a truth, you must provide a justification, but then this justification must also have a justification, and so on, ad infinitum.

The problem of the infinite regress is used mostly for a sceptical approach. One of the first (over 1500 years before Hume's Enquiry Concerning Human Understanding, and, arguably, the most illuminating summary of this idea is that of Sextus Empiricus (ca. 160-210 AD) in his Outlines of Scepticism. He describes the two situations thus:

I) [Epistemic] [179] They do not concede that anything can be apprehended by means of something else. If that by means of which something is apprehended will itself always need to be apprehended by means of something else, they throw you into the reciprocal or infinite mode; and if you should want to assume that that by means of which another thing is apprehended is itself apprehended by means of itself, then this is countered by the fact that, for the above reasons [which I have excluded], nothing is apprehended by means of itself.

II) [Metaphysical] [185] The [causal] explanation which is offered will either be in agreement with all the philosophical schools as well as with Scepticism and what is apparent or it will not. No doubt it cannot be in agreement; for both what is apparent and what is unclear are all subject to dispute. [186] But if it is subject to dispute, we shall ask for an explanation for this explanation as well; and if he gives an apparent explanation for an apparent explanation or an unclear of an unclear, he will be thrown back ad infinitum, whereas if he gives his explanation crosswise he will fall into the reciprocal mode. If he takes a stand somewhere, then either he will say that the explanation holds so far as what he has said goes, and will introduce something relative, rejecting what is by nature, or else he will assume something as a hypothesis and be led to suspend judgment.


One should note, however, that Sextus is not an absolute sceptic i.e. he is careful to limit this to 'belief', whereas "[Pyrrhonian] Sceptics assent to the feelings forced upon them by appearances—for example, they would not say, when heated or chilled, 'I think I am not heated (or: chilled)'. Rather, we say that they do not hold beliefs in the sense in which some say that belief is assent to some unclear object of investigation in the sciences."

So what is to be done? Must we, when asked for an explanation, however simple, heed the same warning that Dante put above the gates of Hell in The Inferno, namely "Abandon hope all ye who enter here"?

'Luki'

I felt there was only one topic for my first post. By request: Wittgenstein.

My interest in philosophy began when I returned to Canada after spending a bit of time off and on living in England. I had heard of this thing called ‘philosophy’ that had ‘all questions and no answers’ and, cocky as I was, I thought ‘how is this possible? Let me at it and I’ll put these issues to bed.” Not knowing where to start, and worrying that a turgid slog through a random philosophical treatise might put me off (books had not really appealed to me much since I had got out of school), I went to the local library and began collecting all of the possible books in the ‘Great Philosophers’ series that I could find. Basically, these were pocketbooks of between 50 and 70 pages giving a quick summary of their major philosophical points. Since I was new to philosophy at the time, I had only heard a few names here and there, and of books I found with names I knew: Plato, Aristotle, Rousseau, I found it a bit difficult to get a good picture of just what was going on. I had not really done much critical thinking or testing of my understanding of the world at the time; it simply was what it was. Two philosophers in the series changed everything for me and put me on the path to having a genuine interest in philosophy and all that it deals with. One of those was Wittgenstein (the other was Schopenhauer, but more on that some other time).

Many historians and ‘Wittgensteinians’ refer to ‘Wittgenstein I’ and ‘Wittgenstein II’. Wittgenstein I was the man who had claimed to have ‘solved all philosophical problems’ in the Tractatus Logico-Philosophicus in which the final and most important point is

‘Whereof one cannot speak, thereof one must remain silent.’

The meaning of which was simply that for Wittgenstein (at that time), there was no such thing as a philosophical ‘problem’. What were actually being debated in philosophical circles were ‘puzzles’ that arose because our use of language and our attempts to understand each other’s meaning are imperfect. And so we disagree about things not because there are ‘realities’ to disagree about, but rather because we are not able to properly define terms and communicate ideas. It is only language and meaning that could properly be debated. After a hiatus that he spent teaching schoolchildren in the mountains somewhere in Scandinavia (if I remember correctly) Wittgenstein II then went back on this rather bold summary of philosophy, and wrote his ‘Philosophical Investigations’, which, in my opinion is both a brilliantly ‘playful’ and a brilliantly profound exploration of language (in contrast to the rigorous formality of the Tractatus). The Investigations is famous for, amongst other things, the ‘private language argument’ (he argued that one cannot have a ‘private’ language, that is, a language limited entirely to oneself).

If anyone reading this is interested, I recommend ‘Wittgenstein’s Poker’ for a brilliantly entertaining synopsis of Wittgenstein the man and Wittgenstein the philosopher based around a ‘legendary’ meeting (and the only one ever) between Wittgenstein and another very ‘self-assured’ (i.e. cocky) philosopher, Karl Popper.

At the time of reading this 60-odd-page intro to Wittgenstein, I knew none of this, and a lot of the finer details were lost on me. What struck me as so radical (and still does today) is that all of a sudden language went from a tool to communicate to a thing that can be analyzed in and of itself (and it is especially radical when it is presented in such a way as to lead one to believe it could possibly be a metaphysical basis of reality). I had never really had a reason to ponder over the fact that we call the white liquid that comes from cows ‘milk’ on no other pretense than that a bunch of people once upon a time agreed that it should be so (of course, etymology enters the picture, but one can apply the same argument to the etymological roots of any word). It is nothing more than custom that we use the term ‘milk’ as opposed to, say, ‘rabagooba’ to denote this item in English.

And this idea can be useful to try to make mathematics less intimidating. Of course, we usually take mathematics as the ‘everyday’ mathematics that is grounded in arithmetic and such, and this is entirely justified. We have utilized both language and mathematics for thousands of years, and it has only been within the past 150 years with Frege and Cantor that each of language and mathematics have been seen as an ‘item’ to be analyzed in and of itself. However, if one looks at mathematics itself, one sees that as opposed to all of the other ‘sciences’, which are based on understanding and interpreting reality to some extent, mathematics is a self-contained axiomatic system. Thus it is, in a sense, a ‘language’ as well (and therefore, from a certain point of view, it is entirely a ‘human invention’ not wholly grounded in reality), though one based on the rules of logic. Gödel’s Incompleteness Proof established that there is no such thing as a logical system that can prove itself. Basically, if one begins with different axioms, one can get an entirely different system of mathematics, so long as the axioms are not, in some way, self-contradictory. Hence, there is no ‘true’ mathematics, like one may say there is a ‘true’ chemistry, physics, or biology that accurately describes the secrets of Mother Nature, just like there is no objective reason why one should call milk ‘milk’ rather than ‘rabagooba’. The only difference is that the ‘rightness’ or ‘wrongness’ of mathematics is based on rules of logic in contrast to language, which is based on custom and the systematization of grammar. That is, in terms of mathematics as a ‘system’; the manner in which mathematics is actually applied and 'done' is based on custom. Once students understand that ‘x’ is simply a 'placeholder' and its use to designate an unknown is based entirely on custom (and ‘ease’, since mathematicians are lazy)—there is nothing to stop one designating said unknown by drawing a map of Indonesia, making a chicken noise, or dancing a jig—they stop making silly mistakes, like using x to designate different unknowns that are not equal. The main problem with the other three options is one’s ability to duplicate it when needed: dancing can get pretty tiring, and making a chicken noise? That's just stupid.

Gauss once called mathematics ‘the queen of the sciences’. I forget his justification for this statement, but I always think that maybe his intention was to say that mathematics is such that although it doesn’t rule, you cannot do anything without it. Maybe this is a somewhat sexist (and, along the same vein, overly ‘biological’) interpretation, but one must remember that it was said about 300 years ago, and the human race and its approach to gender equality and human rights has come a long way since. Supposedly.