 A second discipline, also called ‘logic’, deals with certain valid inferences and good reasoning based on them. It does not, however, cover 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. Validity so understood is simply a modal notion, a notion about what has to be the case. Others might think of validity as involving a more fine grained hyperintensional notion, but in any case, validity so understood is not what logic is concerned with. Logic is concerned with formal validity, which can be understood as follows. In a system of representations, for example a language, it can be that some inferences are always valid as long as the representational or semantic features of certain parts of the representations are kept fixed, even if we abstract from or ignore the representational features of the other parts of the representations. So, for example, as long as we stick to English, and we keep the meanings of certain words like “some” and “all” fixed, certain patterns of inference, like some of Aristotle’s syllogisms, are valid no matter what the meaning of the other words in the  syllogism.[1]  To call an inference formally valid is to assume that certain words have their meaning fixed, that we are within a fixed set of representations, and that we can ignore the meaning of the other words. The words that are kept fixed are the logical vocabulary, or logical constants, the others are the non-logical vocabulary. And when an inference is formally valid then the conclusion logically follows from the premises. This could be generalized for representations that are not linguistic, like graphic representations, though it would require a bit more work to do so. Logic is the study of such inferences, and certain related concepts and topics, like formal invalidity, proof, consistency, and so on. The central notion of logic in this sense is the notion of logical consequence. How this notion should be understood more precisely is presently widely debated, and a survey of these debates can be found in the entry on  logical consequence.