User:Phlsph7/Formal and informal logic

Formal and informal logic

When understood in the widest sense, logic encompasses both formal and informal logic. Formal logic is the traditionally dominant form of logic. Various problems in applying the insights of formal logic to actual everyday arguments have prompted modern developments of informal logic. They often stress the significance of informal logic for various practical purposes which formal logic on its own is unable to address. Both have in common that they aim to provide criteria for assessing the correctness of arguments and distinguishing them from fallacies. Various suggestions have been made concerning how to draw the distinction between the two but there is no universally accepted answer. These difficulties often coincide with the disagreements about how informal logic is to be defined.

The most literal approach sees the terms "formal" and "informal" as applying to the language used to express the arguments. On this view, formal logic studies arguments expressed in formal languages while informal logic studies studies arguments expressed in informal languages. Formal languages are characterized by their precision and simplicity. They usually contain a very limited vocabulary and exact rules how its symbols can be used to construct sentences, usually referred to as well-formed formulas. This simplicity and exactness in turn makes it possible for formal logic to formulate precise rules of inference that determine whether a given argument is valid. This approach brings with it the need to translate natural language arguments into the formal language before their validity can be assessed, a procedure that comes with various problems of its own. Informal logic avoids some of these problems by analyzing natural language arguments in their original form without the need to translate them into a formal language. But it faces related problems of its own associated with the ambiguity, vagueness and context-dependence of natural language expressions.

A closely related approach applies the terms "formal" and "informal" not just to the language used, but more generally to the standards, criteria, and procedures of the argumentation.

Another approach draws the distinction according to the different types of inferences analyzed. This perspective understands formal logic as the science of deductive inferences in contrast to informal logic as the science of non-deductive inferences, like inductive or abductive inferences. The characteristic of deductive inferences is that the truth of their premises ensures the truth of their conclusion. This means that if all the premises are true, it is impossible for the conclusion to be false. For this reason, deductive inferences are in a sense trivial or uninteresting since they do not provide the thinker with any new information not already found in the premises. Non-deductive inferences, on the other hand, are ampliative: they help the thinker learn something above and beyond what is already stated in the premises. They achieve this at the cost of certainty: even if all premises are true, the conclusion of an ampliative argument may still be false.

One more approach tries to link their differences to the distinction between formal and informal fallacies. This distinction is often drawn in relation to the form, content, and context of arguments. The error in formal fallacies is found on the level of the argument's form, whereas for informal fallacies, the content and context of the argument are responsible. This can be connected to the idea that formal logic abstracts away from the argument's content and is only interested its form, specifically whether it follows a valid rule of inference. This also includes the idea that it's not important for the validity of a formal argument whether its premises are true or false. Informal logic, on the other hand, also takes the content and context of an argument into consideration. In this sense, it sees arguments like the false dilemma and straw-man arguments as fallacies because of their false premise or their error on the level of content respectively, even if they are deductively valid otherwise.

Examples for possible inclusion

• Informal logic would talk about the inference from the English sentences "Al lit a cigarette" and "Bill stormed out of the room" to the sentence "Al lit a cigarette and Bill stormed out of the room", formal logic would address the inference from the formulas "$P$" and "$Q$" to the conclusion "$P\&Q$".

• Then go on to talk about generality (though I'm not sure how that's handled in informal approaches).

• To illustrate context-dependence of natural language, then you could mention that order of conjuncts alters meaning in natural language (e.g. Al smoking caused Bill to get mad vs Bill getting mad caused Al to need a smoke) but that order doesn't matter in (classical) logic.