Tag Archives: equality

Knowledge is power

Pitt Rivers Museum, Oxford

“The list of things that I believe is, if not infinite, virtually endless. And I am finite.  Though I can readily imagine what I would have to do to obtain evidence that would support anyone of my beliefs, I cannot imagine being able to do this for all of my beliefs.  I believe too much, there is too much relevant evidence (much of it available only after extensive, specialized training); intellect is too small and life is too short.”

These words are a direct quote from the opening paragraph of an article by John Hardwig published in the Journal of Philosophy in 1985. He goes on to argue that we can have good reasons for believing something if we have good reasons for believing that others have good reasons to believe it.  So, it is reasonable for a layperson to believe something that an expert also believes and that it is even rational to refuse to think for ourselves in these circumstances.  Because life is too short and there are too many other things to think about.

This implies a high level of trust in the expert as well as a concept of knowledge that is known by the community.  Someone somewhere has the evidence to support the knowledge.  For instance, as a professor, I am trusted by my students to provide them with knowledge for which I have the supporting evidence or I believe someone else has the evidence.  This trust is reinforced to a very small extent by replicating the evidence in practical classes.

More than 30 years ago, John Hardwig concluded his article by worrying about the extent to which wisdom is based on trust and the threat to “individual autonomy and responsibility, equality and democracy” posed by our dependence on others for knowledge.  Today, the internet has given us access to, if not infinite, virtually endless information.  Unfortunately, much of the information available is inaccurate, incomplete and biased, sometimes due to self-interest.  Our problem is sifting the facts from the fabrications; and identifying who are experts and can be trusted as sources of knowledge.  This appears to be leading to a crisis of trust in both experts and what constitutes the body of knowledge known by the community, which is threatening our democracies and undermining equality.


Hardwig J, Epistemic dependence, J. Philosophy, 82(7):335-349, 1985.

Ramblings on equality

By David Samuel, User:Hellodavey1902 – Own work, CC BY-SA 3.0,

I had some time to spare in Oxford last week and visited the Treasury in the Weston Library again (see my post entitled ‘The Red Crane‘ on July 26th, 2017).  I was amazed to be confronted by an eight-hundred year-old copy of the Magna Carta.  No fuss, no fanfare, just sitting there behind a glass screen as close as you are to your screen as you read this blog.  But the Bodleian Library has four copies of the Magna Carta; so, maybe it’s nothing special to them!  This one is slightly dogged-eared, or to be more precise, rodent-nibbled – there were a couple of small holes where an animal had gnawed it while it was folded up and stored at Osney Abbey from its issue following King John’s death in 1217 until the Abbey’s dissolution in 1539.  The equivalent documents in the USA, the declaration of independence, the constitution and the bill of rights, are housed in the grandiose building on the National Mall, shown in the picture.

After the Weston Library Treasury, I went to the bookshop next door and could not resist buying a couple of books: ‘Signs Preceding the End of the World‘ by Yuri Herrara and ‘The Wandering Falcon‘ by Jamil Ahmad.  Hopefully, I will not succumb to tsundoku (see my post on ‘Tsundoku‘ on May 24th, 2017) and will eventually read these novels.  BTW – you can read the Magna Carta here.

It’s October and the start of university term, which also means that once again I am teaching thermodynamics to first-year undergraduate students. I have blogged on thermodynamics frequently; so, I am going to provide links to these posts during the next couple of months.  Primarily for those of my undergraduate students who find their way to this blog, but hopefully these links will also be of interest to regular readers. My opening lecture set thermodynamics in the context of the more familiar sciences as described in my post entitled ‘And then we discovered thermodynamics‘ on February 3rd, 2016.  Last week’s lecture started with the Zeroth Law of Thermodynamics, which I have discussed in two posts entitled ‘All things being equal‘ on December 3rd, 2014 and ‘Lincoln on equality‘ on February 6th, 2013 – now I’ve gone in a full circle, if somewhat shakily!

Undermining axioms at the speed of light

International Prototype of the Kilogram (IPK)

International Prototype of the Kilogram (IPK)

An axiom is a statement so evident or well-established that it is accepted without controversy or question.  However, in his review of Sokal’s Hoax, Steven Weinberg has suggested that ‘none of the laws of physics known today (with the possible exception of the general principles of quantum mechanics) are exactly and universally valid’.  This propels physics to the same status as biology (see my post entitled ‘Laws of biology?‘ on January 13th 2016) – in lack exactly and universally valid laws and it suggests that there are no scientific axioms. 

‘Things that are equal to the same things are equal to each other’ is Euclid’s first axiom and in thermodynamics leads to the Zeroth Law: ‘Two things each in thermal equilibrium with a third are also in thermal equilibrium with each other’ (see my posts entitled ‘All things being equal‘ on December 3rd, 2014 on ‘Lincoln on equality‘ on February 6th, 2013).   Thermal equilibrium means that there is no transfer of thermal energy or heat between the two things, this leads to the concept of temperature because when two things are in thermal equilibrium we say that they are at the same temperature.   Last week I explained these ideas in both my first year undergraduate class on thermodynamics and my on-going MOOC.  This week, I have challenged MOOC participants to try to identify other measurement systems, besides temperature, that are based on Euclid’s first axiom.

For instance, its application to mechanical equilibrium leads to Newton’s laws and from there to mass as a measure of a body’s inertia.  We use Euclid’s axiom to evaluate the mass of things through a chain of comparisons that leads ultimately to the international kilogram at the Bureau International des Poids et Mesures in France.  Similarly, we measure time by comparing our time-pieces to an international standard for a second, which is the duration of  9,192,631,770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. 

However, given Weinberg’s statement perhaps I can give you a harder challenge than MOOC participants: can you identify exceptions to Euclid’s first axiom?

I think I can identify one: if you calibrated two very accurate timepieces against a cesium 133 clock and then took one on a journey through space travelling at the speed of light while the other remained on Earth, when you brought the two together again on Earth they would not agree, based on Einstein’s theory of relativity, or what he called relativity of simultaneity.  Now see what you can come up with!


Steven Weinberg, ‘Sokal’s Hoax’, NY review of Books, 43(13):11-15, August 1996.

Oliver Byrne, First Six Books of the Elements of Euclid, London: William Pickering, 1847

Joseph Schwartz & Michael McGuinness, Einstein for Beginners, London: Writers and Readeres Publishing Cooperative, 1979 & Penguin Random House, 2013.

Albert Einstein, Relativity: The Special and the General Theory, (translated by Robert W. Lawson), London: Methuen & Co Ltd., 1979 & on-line at www.bartleby.com/173/