The most significant idea of philosophy in the 20th century, by far, and the one that had incomparable revolutionary impact on the world is the idea of logical positivism. This consists of two parts:
- Logical: using a formal language to describe what you mean exactly and precisely, like when you program a computer.
- Positivism: making only statements about things that are subject to direct observation, or which can be reduced to these by a chain of definitions, so that you make sure you know what you are talking about.
The positivism is important, because it means that to give meaning to a question, you must reduce the terms to simpler definitions, until you reach either bedrock mathematical terms, like integers, or terms that can be defined by simple experience, like "I see a white circle".
The point of this exercise is that many superficially sensible questions are actually meaningless:
- If the universe had a beginning, doesn't it require a cause?
- If you will to move your arm, do your atoms determine the motion, or does your will?
- What is gravity made of?
These types of questions are too vague to be meaningful, and when formulated properly, are shown to be mostly meaningless, or else the answer becomes obvious. The revolutionary effects of positivism meant that essentially all the questions of classical philosophy were either answered or mooted. It also allowed Turing to identify mind with computation , an identification which resolved many of the philosophy of mind difficulties.
Aside from the computer revolution, which was mostly through events in mathematical logic which have some overlap with this--- Russell and Whitehead are significant for Godel--- the most radical world-altering consequences of this philosophy was in physics, where it was the central motivating idea behind at least four separate revolutionary ideas (with more examples if you go back further, and as many as you like if you go to less Earth shattering examples).
- Quantum Mechanics
- S-matrix theory (aka string theory)
- Holographic principle
There are more: here and here. Most of the questions non-physicists ask are very ignorant, because they do not have a training in positivism, so that they ask vague or meaningless questions.
Once you have a little training in positivism (it doesn't take long), the discourse of non-positivists, which includes nearly all contemporary philosophers, becomes worthless and pointless to read, since non-positivists do not know how to identify questions with one another, and so spend most of the time arguing about positivistically equivalent positions, or inconsequential meaningless things.
In the 19th century, people believed in a lumineferous ether, a medium of light. Einstein showed that you could not measure your speed with respect to the ether, and therefore it is superfluous. Using positivism, he concludes that the ether is an unobservable entity, and therefore is meaningless. The ether was disproved in this way, the major step was positivism.
Ernst Mach developed philosophical positivism, along with important work in physics (the Mach number is named after him, since he studied supersonic fluid flow). Einstein admired and respected Mach, and made bold use of positivism in the early years.
Quantum Mechanics (1920s)
In quantum mechanics, positivism is the most important ingredient. The act of defining a measuring device and a measurement as a separate aspect of the theory from the time evolution was due to the explicitly positivist outlook of Bohr and Heisenberg.
The major idea of making a matrix description of the electron came from renouncing the idea of a microscopic well defined orbit, in favor of quantities which determine the atomic transitions, which are all that we can observe. As Pauli and Heisenberg argued, if you can't determine where the electron is when it is in the ground state of Hydrogen, on the left of the nucleus or on the right, even in principle (at least not without knocking it out of the ground state), then this question is meaningless, and the location of the electron in its orbit in the ground state is meaningless.
The positivism is still central to the interpretation of the most common statement of the uncertainty principle. Because we cannot measure the position and momentum simultaneously, these quantities do not exist simultaneously. The modern formalism does not include position and momentum, but a wavefunction which gives probability amplitudes for either.
S-matrix theory (1950s-1960s)
In the 1960s, physicists made the most radical positivist proposal you can imagine. The idea here was to renounce everything except for incoming and outgoing states in a scattering experiment, so that a physicist cannot describe events in space and time inbetween.
To make this clear: the S-matrix practitioners were saying that space is a reconstructed illusion, time is a reconstructed illusion (inasmuch as these statements are meaningful positivistically or mathematically), the only thing that is full meaningful to talk about are free cold particles in the infinite past, free cold particles in the infinite future, and an S-matrix to connect them.
This idea is manifestly absurd! It is the extreme of positivism. The S-matrix theory is inducting a principle: it is hard to make local measurements at a point in quantum field theory, and it is easy to do scattering experiments, so the idea that scattering is fundamental, and not space-time points. But this idea is completely crazy--- it means that fundamentally you can't talk about your own feet, or your grocery store, only about a large number of cold particles that come in to form the Earth and the Sun and everything else in the infinite past, and free cold particles in the infinite future, and an S-matrix that connects them (in one step).
This idea is so absurd, I could not accept it when I was a kid. I rebelled and rebelled against it, and I struggled to understand how sane people could believe this. Sidney Coleman explained it to me as follows:
Imagine you have some experiment that is not an S-matrix experiment. Imagine a robot doing the experiment. Assemble such a robot and some Hydrogen bombs from cold asymptotic particles, let the robot do the experiment, beam the results out in a photon beam to infinity, the detonate the H-bombs, so that the whole thing is blown into cold asymptotic particles. The S-matrix for that process includes the result of the experiment.
This was persuasive to me that the S-matrix was philosophically enough, but I could not be persuaded it was mathematically enough--- how do you reconstruct space and time from S-matrix?
This idea is positivism to the point of nihilism--- all space and time are rejected. This was a bit too radical for Feynman, but Gell-Mann could accept it, and helped found it and nurture it. The developments in the 1960s led to Regge theory and string theory, and it was realized by 1974 that S-matrix theory, in its string theory culmination, could only be a theory of everything, when Schwarz and Scherk made string theory a theory of everything.
Within string theory, and quantum gravity in general, the problem of black hole interiors was solved by a positivistic rejection of the black hole interior as separate from the exterior, since no observer can see both. The development of this principle refounded string theory, giving it a new founding principle, and at the same time explained the S-matrix theory, since the holographic description of space time turns into the S-matrix for flat spacetime with distant boundaries.
The holographic reconstruction of the interior from the boundary is the sensible way to understand how an S-matrix still encodes local physics. The idea is central to modern physics, in that the only theory we have of quantum gravity, is positivist to the point of nihilist--- it reconstructs everything from boundary data.
Rejection of positivism
Physicists are not immune to philosophical fasion, and between the years of 1974 and 1984, string theory was rejected essentially for the same reasons logical positivism was dying in other fields--- marijuana and New-Age thinking, plus a desire to revive the nice classical questions of philosophy about an objective world.
This is ridiculous reactionary nonsense, but it led to a decade of obscurity for string theory. In 1984, physicists picked up the theory, but not the positivism, nor the S-matrix origins. In the 1990s, the holographic principle gave new motivation to the S-matrix program, and in the last decade, S-matrix methods have been revived again in supergravity perturbation theory, and in studies of the pomeron by Polchinski, Tan, and collaborators.
This is a welcome relief--- positivism had almost been dealt the same blow that heliocentrism was dealt in Greek times--- death by stupidity.