# Power of Logic [Logic](Logic.md) is about how truth flows between [Propositions](Proposition.md). Given a theory (that must have been creatively conjectured) we can use logic in order to provide *criticism*. How so? We can look at the consequences of our theory (suppose it predicts something) and then observe if that actually happens. Or we can look at the internal consequences of our theory and see if they are consistent. In both cases we are using logic in order to criticize our theory. > The power of logic lies in its ability to *reveal contradictions* and derive *testable consequences* for empirical theories, and to *explore* the relationships and problem-solving capacity of theories in general, whether empirical or philosophical. Notice that I used the word *explore* above. This was done very intentionally. What do I mean by explore? What exactly would be be exploring? This is the beauty of logic. Given a (conjectured) theory, proposition, description, or idea, logic instantly links it to all of it's *consequences*. This forms a *structure* that we can then *explore*. We may have conjectured the theory, but the consequences are often entirely out of our control—we will *discover* them. We are trying to generate *true* theories and ideas about the world. Logic is the *consistency enforcer* in that process. Are the consequences of your theory inconsistent with empirical observation? Your theory is false. Are the internals of your theory inconsistent with each other? Your theory is false. Logic allows us to derive consequences from a theory, show they are false (a form of criticism), and propagate that falsity back up to the original theory. This is how we make progress. ## Popper has thoughts on this Popper explicitly states that formal logic (deduction) is the "Organon of rational criticism—that is, of refutation". This is because deduction allows the re-transmission of falsity from a conclusion to its premises: > [!quote] > For deduction, I contend, is not valid because we choose or decide to adopt its rules as a standard, or decree that they shall be accepted; rather, it is valid because it adopts, and incorporates, the rules by which truth is transmitted from (logically stronger) premises to (logically weaker) conclusions, and by which falsity is re-transmitted from conclusions to premises. (This re-transmission of falsity makes formal logic the Organon of rational criticism--that is, of refutation.) [^1] The role of logical argument, specifically deductive logical reasoning, is described as "all-important for the critical approach" because it enables us to discover what our theories imply. Finding the "weak spots" in a theory typically requires examining the more remote logical consequences derived deductively: > [!quote] > Nevertheless, the role of logical argument, of deductive logical reasoning, remains all-important for the critical approach; not because it allows us to prove our theories, or to infer them from observation statements, but because only by purely deductive reasoning is it possible for us to discover what our theories imply, and thus to criticize them effectively. Criticism, I said, is an attempt to find the weak spots in a theory, and these, as a rule, can be found only in the more remote logical consequences which can be derived from it. It is here that purely logical reasoning plays an important part in science. **Refutation through Deduction** While theories cannot be logically derived from observations, they can clash with observations. This clash makes it possible to infer from observation statements that a theory is false, and this inference is a "purely deductive one". The possibility of refuting theories by observations is the "basis of all empirical tests". > [!quote] > In this way the freedom and boldness of our theoretical creations can be controlled and tempered by self-criticism, and by the severest tests we can design. It is here, through our critical methods of testing, that scientific rigour and logic enter into empirical science. > > We have seen that theories cannot be logically derived from observations. They can, however, clash with observations: they can contradict observations. This fact makes it possible to infer from observations that a theory is false. The possibility of refuting theories by observations is the basis of all empirical tests. For the test of a theory is, like every rigorous examination, always an attempt to show that the candidate is mistaken--that is, that the theory entails a false assertion. From a logical point of view, all empirical tests are therefore attempted refutations. --- Date: 20250602 Links to: Tags: References: * []() [^1]: [Conjectures and Refutations](Conjectures%20and%20Refutations.pdf)