On the social construction of electrons

One interesting fact about electrons is that they are all literally identical. And I really do mean completely and literally identical, in the sense of sharing all properties. Yes, even the spatial distribution of their wavefunctions.

To illustrate how this is possible, consider a simple scenario, where we have two electrons, one at point A, and the other at point B. At first it would seem that electron 1 has a different location from electron 2. But in fact, the universe is in a quantum superposition of two states–the first state has electron 1 at A and electron 2 at B, while the second state has electron 2 at A and electron 1 at B. So even though we observe electrons at two distinct locations, the two electrons involved are actually identical.

The fact that electrons are identical has really important consequences.  One consequence is the Pauli Exclusion Principle, which states that no single state can be occupied by two electrons simultaneously. So when we have a large atom, electrons will occupy many different orbitals of the atom, instead of having all electrons occupy the one orbital with lowest energy.

Of course, it’s not really practical to think of it this way all the time. Generally we prefer to think of each electron as being at a distinct location, and then we tack on additional rules like the Pauli Exclusion Principle.

The point is that the individuality of electrons is an idea that arises from practical necessity, and not from the fundamental physics. Practical necessities arise from social context. And in principle, a different social context could have different needs that are better fulfilled by some other way of thinking about it. Therefore, the concept of individual electrons is a social construct.

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Trump’s past light cone

When Trump was elected, and for many months following, people kept on talking about why he was elected. What caused it? This conversation irritates me deeply, because people lack a base-level understanding of what causation is. But I’ve waited to say anything because I thought it might be too crass to insert a philosophical discussion into a political one, at least while it was still hot.

Cause and effect is often thought to be a fundamental part of the way the world works, but I and other physicists understand that it is not. For a brief explanation, I recommend this video by Sean Carroll. It is better to think of causality as an emergent property, more in the realm of philosophy than physics.

What does physics have to say about the cause of Trump’s election? It’s everything in Trump’s past lightcone! It was the DNC, it was Clinton, it was Comey, it was Russia, it was neoliberalism, it was identity politics, it was ancient supernovae. This answer is rather naive, but what did you expect from us? Physics can’t provide all the answers.

When we talk about causes, we’re typically just selecting a few things from the past lightcone, and highlighting those things as important. In philosophy, this is known as causal selection. Sean Carroll talks a little bit about causal selection. He says that one way of thinking about it is that a cause is something that has great leverage over the future. But that’s just one way we might think about it.

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Scientism in the atheist movement

Larry Hamelin pointed me to a recent Existential Comic which criticizes Richard Dawkins and Sam Harris for scientism. The explanatory text below the comic goes on to criticize the New Atheist movement as a whole. It argues:

The real goal [of scientism] is often just to draw a border around what we should or shouldn’t question, because they don’t want any of the fundamental aspects of society to change.

Larry Hamelin has a couple good posts responding to the comic commentary, and looking back on the New Atheist movement as a whole. Partially following Larry, these are my critiques:

  • Harris and Dawkins don’t represent the atheist movement. Harris and Dawkins are widely criticized within the movement, and many (myself included) are positively disposed to philosophy.
  • To the extent that scientism is or was present in New Atheism, it was not motivated by an attempt to maintain status quo. I believe that scientism was primarily a reaction to the way people would hide behind the authority of philosophy, insisting that there exists a complex and subtle defense of religion or belief in God. Of course, the complex and subtle defense did not materialize, and failed to address religion or belief in God as they are popularly practiced.
  • Of all the strengths of philosophy, I do not think effecting social change is one. Certainly academic philosophy is not a force for change. And though my writing is often infused with philosophy, that just makes me a more effective thinker, not a more effective activist.

This might be a bad idea, but let’s read the comments on this comic to see what other people are saying.

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Clearer thinking about definitions

Do you believe that people waste too much time arguing over definitions?

I do too. But I also have a second problem: I’ve read some philosophy. And so, when I’m frustrated with pointless arguments over definitions, my frustration becomes compounded by the fact that nobody understands the thing that they’re arguing about, and the only way to solve the problem is by spending even more time arguing over useless stuff.

Case in point, in all the time you’ve ever spent arguing over definitions, have you ever once glanced at the relevant articles in either Wikipedia or the Stanford Encyclopedia of Philosophy? I’m guessing not, because I never thought to do such a thing myself for a long time.

So now that I’ve made everyone feel guilty, let’s talk about one of the things you’d learn from some basic research: intensional vs extensional definitions.

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Gödel’s Second Incompleteness Theorem Explained

This is a followup to an earlier post where I talked about Gödel’s First Incompleteness Theorem. Here, I discuss the Second Incompleteness Theorem, and further implications.

Could you remind me what the theorem was?

The theorem states that a consistent formal system cannot prove its own consistency.

As previously discussed, there are a couple qualifiers. The formal system must include some amount of arithmetic, and must have a computable set of axioms.

What does consistency mean?

A system is consistent if it cannot prove any contradictions. A system is inconsistent if it can prove a contradiction.

Contradictions sound bad. Are they bad?

Yes. The Explosion Principle states that if you can prove a direct contradiction, then you can prove absolutely any statement.

Here’s how the Explosion Principle works. Suppose A and not-A are both provable. Now consider statement B. “(A implies B) or (not-A implies B)” is a tautology. Since both A and not-A, that means we can prove B. Following the same procedure we can also prove not-B.

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Gödel’s First Incompleteness Theorem explained

Once upon a time, mathematicians thought they would be able to prove everything. The endeavor was known as Hilbert’s Program. They would find a complete and consistent set of axioms, and on this foundation build all of mathematics. (Although to be fair, much of mathematics was already built and was to be placed upon on those foundations retroactively.) And then, if everything went well, they would generate an algorithm that could prove every statement either true or false.

To some extent, Hilbert’s Program was successful. We now have Zermelo-Fraenkel set theory, which is a solid foundation for the vast majority of mathematics. But there are two problems. First, set theory isn’t complete. Second, we can’t prove it’s consistent. And Gödel showed that these problems have no solutions.

Gödel’s First Incompleteness Theorem: No consistent formal system is complete.
Gödel’s Second Incompleteness Theorem: No consistent formal system can prove its own consistency.
(Both of these theorems have additional qualifiers that I’ll get to later.)

Here I will explain the proof for the First Incompleteness Theorem, and a few of its implications. In a later post, I will talk about the Second Incompleteness Theorem.
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Plantinga’s private language

One of the great things about arguments for gods and the supernatural, is that you can always look back at them and find new problems. Alvin Plantinga’s arguments are especially lovely in this regard. Having been recently been thinking of Wittgenstein’s private language arguments, it occurred to me that somewhere in there is a rebuttal to Plantinga’s evolutionary argument against naturalism.

The evolutionary argument against naturalism argues that if both evolution and naturalism are true, then we cannot trust our own rational faculties, and therefore cannot trust our belief that evolution and naturalism are true.  The reasoning goes that naturalistic evolution does not specifically produce true beliefs, but rather produces adaptive beliefs. An adaptive belief does not need to be true, it just needs to produce adaptive behavior. For example, rather than believing that you should run away from a tiger because it will eat you, you might believe that you should run away from a tiger because that’s the best way to pet the tiger (Plantinga’s example). The number of false beliefs that produce adaptive behavior is much larger than the number of true beliefs that produce adaptive behavior. Therefore, most beliefs are probably false.

There are numerous issues with this argument, a few of which you might be shouting at the screen. From a scientist’s perspective, Plantinga appears to be ignorant of how evolution actually works. Evolution does not necessarily produce the most adaptive traits, certainly not immediately. If you have false but adaptive beliefs at one point in time, it is questionable whether those beliefs would continue to be adaptive when your descendants find themselves in slightly different environments. Also, Plantinga ignores that brain efficiency is an adaptive trait. I would imagine that a brain which produces true beliefs via reasoning is far more efficient than a brain that produces false but adaptive beliefs via some mysterious yet reliable process.
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