Everyday Abstract Conditional Reasoning: in Light of a 2,400 Year-Old Mistake in Logic

The interpretation of the ‘if P then Q’ conditional statement is a central element in most logical systems. It largely shapes how these logical systems function. It is well known that, although attempts have been made, logical systems are principally unable to encapsulate how people reason in everyday life. This is mainly due to the discrepancies between the logical abstractions of the conditional statement and its everyday interpretation. Among other things, this makes it difficult to design artificial intelligence based on the abstract rules of logic. However, the ancient logicians who first defined the traditional interpretation of the conditional erroneously took into account more propositions than were actually being denoted. They characterised the ‘if P (or R) then Q’ relationship in place of the ‘if P then Q’ relationship. In relation to this, they also committed the error of leaving the context undenoted, which led to an unnatural interpretation of logical truth and logical necessity. This mistaken interpretation is still predominant today and can also be found in several mathematical logics, such as in propositional logic, even though mathematical logics were allegedly created independently of the ancient Greco-Roman logic. Fixing these problems reveals that the correct interpretation of the conditional statement is the equivalence/biconditional. This equivalent interpretation is interpreted by logicians as one of the most common everyday fallacies. Yet looking back on how the conditional statement was actually abstracted in the antiquity, it is evident that people were right and logicians were mistaken. Although the almost 50-year-old experimental psychological literature on the conditional did not confirm this common everyday tendency towards the biconditional interpretation, these findings are merely the result of unsystematic research. Running some of the long missing experiments leads the main experimental tasks to reveal overall the basic biconditional inferences. The approach presented in this book also resolves such dilemmas as the Wason’s abstract selection task, the paradox of the conditional statement and the Raven paradox. It is also shown here that the probabilistic interpretation of the conditional statement is not in conflict with this basic equivalent/biconditional interpretation. The approach is described in this book as the simplest possible non-monotonic logic, and pragmatic inferences, context effects, counterfactuals, possible world semantics and psychologism are also discussed. Since the conditional statement is equivalent to the universal affirmative statement in syllogisms, it is plausible to observe that fixing this same error in syllogisms also makes them compatible with people's actual inferences. Even the normally ambiguous Euler circles become an excellent tool to depict how this updated logic functions. Finally, with this new approach, the root of learning processes is inherently embedded into the logical abstraction of the conditional/universal affirmative statement, and hence, into logic in general. Therefore, this simple logic, presented in a non-technical way, has the potential to bring both human reasoning and learning under the umbrella of the same abstract system. This might be beneficial both for formalising psychology and for creating artificial intelligence.