Definition as Physical Fact

In science and philosophy the distinction between synthetic and analytic statements is fundamental, according to Kant's Critique of Pure Reason.

An analytic statement is about language and its truth can be evaluated by checking the meaning of the words forming the statements. A definition is analytic as a specification of the meaning of a new word in terms of previously defined words, e.g. bachelor as unmarried man.

A synthetic statement is about some reality and can in principle be checked by observing the reality.

The statement "1 meter is equal to 100 centimeters", is analytic, while the statement "this stick is 1 meter long", is synthetic.

To subject an analytic statement to experimental observation would be ridiculous: To check by experiment if there are 100 centimeters on 1 meter would not give a Nobel Prize, just laughs.

So if an experiment is set up to test a statement, that is a sign that the statement is viewed as synthetic.

In modern physics the distinction between a definition (analytic statement) and synthetic statement is sometimes blurred into statements which are viewed to be both analytic (true by definition) and synthetic about some reality, or rather sometimes analytic and sometimes synthetic, sometimes definition sometimes fact.

Such a statement makes it possible to say something about reality which cannot be denied, and it is directly recognized as such. When you hear a physicist making a statement claiming that something cannot be denied, then the statement is such a double analytic-synthetic statement.

See my knol Is One Dollar = One Euro?

Here are some key examples:

1. The speed of light in vacuum is constant.
2. Heavy mass is equal to inertial mass.

The constancy of the speed of light is a definition since according to the 1983 standard length

unit of a meter is defined as a certain fraction of a lightsecond = the distance traveled by light in one second. The speed of light is thus by definition equal to 1 lightsecond per second, no more no less.

On the other hand, a physicist is convinced that the speed of light is constant as a physical fact. A physicist would say that because the speed of light is constant in reality, it can be used to define the length standard. So we have a definition which is a physical fact at the same time: Double analytical-synthetic.

Einstein was a master of this form of double-play: The basic assumption of special relativity is that the speed of light is constant, and Einstein uses this statement sometimes as analytic and sometimes as synthetic. Very clever and very confusing. But according to Kant it is not reasonable.

In general relativity Einstein uses the equality of heavy and inertial mass both as definition and physical fact. In this case experimental verification of equality could give a Nobel Prize.

In climate science the following statement is the very basis of climate alarmism:

• No-feedback climate sensitivity is equal to 1 C,

with climate sensitivity the global warming from doubled atmospheric CO2.

This is presented as an undeniable fact and as such is an example of a double analytic-synthetic statement. The 1 C comes from a direct application of Stefan-Boltzmann's radiation law Q = sigma T, in its differentiated form dQ ~ 4 dT with Q ~ 240 W/m2, T ~ 288 K and dQ = 4 W/m2 as "radiative forcing" from doubled CO2. Thus dT = 1 C as climate sensitivity.

This statement is analytic because the simple algebraic law Q = sigma T cannot tell anything

about the reaction of the complex Earth-atmosphere system upon a small perturbation.

So climate sensitivity = 1 C is a definition but it is used as statement of factual global warming of 1 C. It is a double analytic-synthetic statement, and it is recognized as an undeniable fact about reality.

It is so undeniable that even skeptics like Lindzen, Monckton and Spencer, are convinced that it is a true fact and not just a definition.

We just learned that a double analytic-synthetic statement can be extremely powerful, the very basis of climate alarmism, yet it is easy to discover as soon as one is aware of the double-play.

I hope the reader is stimulated to find other examples of double analytic-synthetic statements

used in the debate today. They are not difficult to find once the light is on. For example, what about the statement:

• Educated people are superior to no so well educated people!

Definition or fact, or both?