In the last posts, I discussed why it would make sense for the physical laws to be a priori.
However I think because I failed to clearly explain what I mean by a priori, the post might be not very clear, so I will add few notes here:
Let’s say we have a conditional in this form:
CF: If a concrete is U1, then it will necessarily also be U2.
We can have reason(s) (call it RP) to believe that CF holds, without knowing…
- if CF really holds
- if it holds, is there a fully determining reason (call it RA) why it holds
- if there is RA, what is it
RP we can call consequently determining reason or “a posteriori reason”, and the RA – antecedently determining reason or “a priori reason”. (Of course time relations doesn’t have anything to do with that, i.e. reasons don’t have to be causal reasons, they can be logical, mathematical, psychological etc..)
If we believe CF for a posteriori reason, we can call it a posteriori belief that CF holds. (In that case we can’t say if CF is true. We don’t know.)
If we figure-out that CF really holds by understanding RA, then we have a priori knowledge that CF holds, and also we can call CF – a priori true.
So, now I can explain more precisely what I talked about in the previous post:
Scientist beliefs scientific laws (say in the form of CF) for a posteriori reasons – PR.
But while believing on base of PR negates possibility of knowing 1., 2. and 3. previously mentioned (by definition), and while scientists can’t know if CF really holds, she can still believe that it might hold, i.e. it is possible that CF for which we have only a posteriori reasons to believe in, actually holds.
So the previous post was about those physical laws, which scientist might believe are true for a posteriori reasons, but which happens to actually hold in the world. So, I was arguing why it would make sense for those laws to have a priori reasons.
Anyway, to spice this post a little in hope to make it less boring, I will tell something else too – I did a search on the internet, trying to find something on the issue of a priority of the physical laws. One of the things I found is a short text called Nothing but Relativity on arxiv.org. It is an interesting read – it analyzes what kind of general space-time transformation laws can come out if one postulates just relativity (and don’t postulate the constant speed of light). Their answer is that the only two possible transformation equations are the Galilean and Einsteinian relativity. It is not really a priori development of special relativity, but seems as a step in that direction, and if you have time it is fun to check the many ways the principle of relativity is used in the text to limit the transformation equations.
Also, the titles of some of the referenced articles are interesting, and it seem that people have already argued that Lorentz transformations can be deduced from, as one of the titles says, “set of necessary assumptions”. I found this title particularly amusing:
A. Sen: How Galileo could have derived the special theory of relativity, Am. J. Phys. 62 (1994) 157-162.