not be connected with reality, it will not be a science, but only a possible, frame for one.
This is perfectly true, and it is clear that by introducing symbols for structures instead of the original variables, we have not given a definite meaning to the symbols but have postponed the decision about the meaning. It would be absurd to suppose that we can give a signification to our system by the introduction of new and more complicated signs, especially as everybody knows perfectly well the way in which an interpretation of a formal system is actually given by the scientist: it is done by observation.
In the case of the physicist, observation always takes the strict form which is called measurement. The relationships between what is actually observed or measured and the quantities which finally appear in the equations expressing the laws of nature are extremely complicated, but we do not have to concern ourselves with them. It is sufficient to remark that the whole process leads to the establishment of a one — one — relation between a particular value of a certain physical quantity and a particular fact of observation. In other words: it is stipulated — lastly by arbitrary agreement — that the proposition "Under such and such circumstances (here the apparatus and the whole procedure have to be exactly described) such and such a fact is observed" shall be equivalent to the proposition: "The quantity so-and-so has the value so-and-so". This is simply the definition of the quantity: it is the way in which the sign denoting the quantity is connected with reality.
Observation involves content ("data of consciousness" in the ordinary questionable way of speaking), and just because it does this can it link our symbols to the (real) world — or I should rather say: the two phrases "involving content" and "linking to reality" are equivalent in their use.
Now, at last, we are prepared to see with perfect clarity the part which is played by content when we seek to determine the meaning of our symbols and propositions and, as we knew beforehand, this part proves to be such that content is left entirely outside of our language and expressions.
For let us consider what happens in an "observation". We suppose it to be done visually, for instance by looking through a telescope and watching a blue spectral line coincide with a black mark in the field of
