1.1 Logic is a tool, as it were, for deriving conclusions from accepted assumptions.
1.2 Here the first problem shows up: What’s an accepted assumption? Such assumptions can be ‘logical’ themselves, or they can be ‘non-logical.’
1.3 ‘Non-logical’ is not pejorative, as common speech sometimes suggests, but just means extra-logical.
1.4 ‘Extra-logical’ is everything beyond the formal machinery of logic. Physics, e.g., is extra-logical (non-logical) in this sense.
1.5 Physics uses logic. This, however, does not make its truths logical truths.
[A nice description of the relation Logic/Science gives W.v.O. Quine, Mathematical Logic, HUP 1981, 7]
1.6 Logical truth is only that which is derived by formal logical means, that is, by certain accepted ‘rules of inference.’
1.7 It is assumed (cf. 1.1) that these formal rules, to which we come later in detail, lead to logically true conclusions.
1.8 No logic, however, can derive from a sequence of completely false factual, e.g. physical, premises a formally true conclusion.
1.9 So for a true scientific conclusion we need both factually true premises and a consistent sequence of formal logical inferences.
1.10 Application: A critical test of any scientific theory is its accuracy in predicting phenomena before they are observed.
1.11 Any such prediction must involve the application of the formal rules of logical inference.