Technical matters reloaded

Doc, I am only going to answer your Saturday 12:11 pm comment on the issues concerning science because only that will be necessary.

Logical Positivism was intended as a technical branch of philosophy. And its technical tool-set is formal (mathematical) Logic. Either LP succeeds in giving a formal logic account of science or it is nothing at all, by its own choice.

Your comment contains plenty of technical physics but I do not see any technical philosophy in it. You use terms like 'simplifying assumptions', 'reasonable approximation', 'large' or 'small' which seem perfectly valid to me. I know that physics works like that and that it could not do otherwise. But none of this is formal Logic.

Let us go back to the Galileo experiment and try to give it as formal a treatment as possible :

A. Definitions. Let there be the following statements :

1. E. A formal (precise and complete) description of the Tower of Pisa experiment.
2. P. The statement 'Both spheres reach the ground at exactly the same time'
3. P'. The statement 'The big sphere reaches the ground slightly before the small one'
4. T. Galileo's theory of free fall expressed in the suitable logical form so that it can apply to the statements above.

B. Demonstration

1. T - (E =>P). As per theory T, the statement (E => P) is true.
2. - (P' => ~P). As per general logical rules, the statement (P' => ~P) is true.
3. E /\ P'. The experiment has been conducted as described in E and we have observed P' so both are true statements (they are our premises).
4. E /\ (E=>P) - P. P is true in virtue (modus ponens) of 1. and 3.
5. P' /\ (P' => ~P) - ~P. ~P is true in virtue of 2. and 3.
6. ~P /\ P is a contradiction.

Given this, either one can find a technical (formal logic) mistake in the above demonstration or one must abandon the claim that Logic can be applied to physics (all of physics, not just theory) without meeting with contradictions.

Alternately, one can also abandon the claim that Galileo was doing physics but I think this is what no one wants to do.

One last caveat, Doc. If you want to try to find fault with the above argument, you cannot appeal to any theory that was not available at the time of Galileo. Physics is Physics at any point in time, provided it obeys certain rules. Thus the above argument is about Physics as it was when Galileo was practising it, not about Physics in an intemporal sense or Physics as it is now. No statement that involves elements not available at the time can count as a premise for or against it.