Three cheers for religious toleration

This was written for Scientia Salon, and partially repeats some of my previous posts.

In the all-time lists of Good Ideas the principle of religious freedom ranks high, preventing much strife and war and thus being responsible for saving more lives than penicillin and vaccination combined. [1]

“The legitimate powers of government extend to such acts only as are injurious to others. But it does me no injury for my neighbour to say there are twenty gods, or no god. It neither picks my pocket nor breaks my leg”, wrote Thomas Jefferson, who rated his Virginia Statute on Religious Freedom as his finest accomplishment. [2]

Yet, despite the fact that the principle of religious freedom is now universally accepted in the civilised world, [3] there is much less agreement on how to interpret it. Indeed, my thesis here is that the principle is widely misunderstood.

The unity of maths and physics revisited

A major part of scientism is the idea that maths and logic are not distinct from science, but rather that they arise from the same fundamental root — they are all attempts to find descriptions of the world around us. The axioms of maths and logic are thus equivalent to the laws of physics, being statements of deep regularities of how the world behaves that enable us to describe and model the world.

My article advocating that mathematics is a part of science was recently posted on Scientia Salon. This was followed by an article by Massimo Pigliucci which took the opposite line and criticised the return of “radical empiricism”.

In response I wrote about the roots of empiricism, defending the radical empiricism that Pigliucci rejects. That post was getting rather long, so I have hived off parts into this post where I return to the distinction between mathematics and science. This is essentially a third part to my above two posts, countering various criticisms made on Scientia Salon.

To summarise the above arguments in two sentences, my critics were saying: “Well no, mathematics is anything but studying physical objects. It is the study of abstract concepts”, whereas I was saying, “Yes, mathematics is the study of abstract concepts, abstract concepts that are about the behaviour of the physical world”.

I have argued that maths and logic and science are all part of the same ensemble, being ideas adopted to model the world. We do that modelling by looking for regularities in the way the world works, and we abstract those into concepts that we call “laws of physics” or “axioms of maths” or of logic. Thus axioms of maths and logic are just as much empirical statements about the behaviour of the world as laws of physics. In part one I discussed other possible origins of mathematical axioms, while in part two I discussed the fundamental basis of empirical enquiry.

That leaves several possible differences between maths and science, which I address here:

Musings on Gettier and the definition of knowledge

This article first appeared on Scientia Salon

Philosophers have traditionally defined “knowledge” as a belief that is both true and justified, a definition that sufficed until, 50 years ago, Edmund Gettier pointed out that the conditions could be fulfilled by accident, in ways that didn’t amount to what we would intuitively regard as “knowledge”.

Gettier pointed to scenarios such as:

“Smith has applied for a job, but, it is claimed, has a justified belief that “Jones will get the job”. He also has a justified belief that “Jones has 10 coins in his pocket”. Smith therefore (justifiably) concludes that “the man who will get the job has 10 coins in his pocket”. In fact, Jones does not get the job. Instead, Smith does. However, as it happens, Smith (unknowingly and by sheer chance) also had 10 coins in his pocket. So his belief that “the man who will get the job has 10 coins in his pocket” was justified and true. But it does not appear to be knowledge.”

Since Gettier’s paper many attempts have been made to patch up the “justified true belief” definition, often by adding extra conditions aimed at ruling out being right accidentally, though none of the proposed solutions has gained general acceptance and most have been shown not to work. [1]

A scientific response to the Brain in a Vat

Scientia Salon is an enjoyable webzine discussing philosophical matters, which recently addressed an old conundrum: how do we know we are not a brain in a vat? As I see it, this question is straightforwardly answered by the usual scientific method, so here I’ll summarise the argument that I advanced in the Scientia Salon discussion.

The Matrix-style scenario, which dates back to the skepticism of Descartes, supposes that we are a brain kept alive in a vat, being fed with a stream of inputs generated by an Evil Genius. Everything that we experience as sense data is not real, but is artificially simulated and fed to us. Since, ex hypothesi, our stream of experiences is identical to that in the “real world” explanation, we cannot know for sure whether or not we are such a brain in a vat.

How to respond? First, the whole point of science is to make sense of our “stream of experiences”. We do that by looking for regularities and patterns in those experiences, and we develop those into descriptions and explanations of the world (I’ll use the term “world” here for the sum of those experiences, regardless of whether they derive from our contact with a real world, or from a simulated world being fed to us).