Ontology in science

2.1 Different conceptions of logic

On the one hand, logic is the study of certain mathematical properties of artificial, formal languages. It is concerned with such languages as the first or second order predicate calculus, modal logics, the lambda calculus, categorial grammars, and so forth. The mathematical properties of these languages are studied in such subdisciplines of logic as proof theory or model theory. Much of the work done in this area these days is mathematically difficult, and it might not be immediately obvious why this is considered a part of philosophy. However, logic in this sense arose from within philosophy and the foundations of mathematics, and it is often seen as being of philosophical relevance, in particular in the philosophy of mathematics, and in its application to natural languages.  $\int fdx$

A second discipline, also called ‘logic’, deals with certain valid inferences and good reasoning connected to them. The idea here is that there are certain patterns of valid inferences which are both an object of study in itself as well as connected to certain patterns of good reasoning. How this connection between inference and reasoning is to be understood more precisely and to what extent it obtains is controversial, and beyond the scope of this survey. However, see Christensen 2005 for more. In any case, logic does not capture good reasoning as a whole. That is the job of the theory of rationality. Rather it deals with inferences whose validity can be traced back to the formal features of the representations that are involved in that inference, be they linguistic, mental, or other representations. Some patterns of inference can be seen as valid by merely looking at the form of the representations that are involved in this inference. Such a conception of logic thus distinguishes validity from formal validity. An inference is valid just in case the truth of the premises guarantees the truth of the conclusion, or alternatively if the premises are true then the conclusion has to be true as well, or again alternatively, if it can’t be that the premises are true but the conclusion is false.