by Scott F. Aikin and Robert B. Talisse
For the most part, we argue and reason when thinking about things – tigers, taxis, and ties. Logic is an investigation into how we think about these things. So, as we argue in a language, we do logic in a language about that language; logic is a meta-language. Now, we have many other meta-langauges. There is the meta-language of grammar that captures our rules for well-formed sentences. There is the meta-langauge of artistic criticism that articulates rules or norms of the use of language for beauty. And so we may speak of crooks and hooks in our first order language, but it is the meta-languages that permit us to speak of nouns and rhymes. Logic, as a meta-language, then takes what comes natural to us – reasoning and argument – and provides a vocabulary with which we may talk about that reasoning, and hence scrutinize it. But in what way is it useful to have such a meta-language?
Consider the usefulness of the meta-language of grammar. With some basic grammatical concepts, we can identify the infelicity of the sentence My tie are blue or the ambiguity of I met a smart logician's husband. Without grammar, we may correct the first sentence with My tie is blue, or we may clarify the second with a well-placed question: Who was the smart one- the logician or the husband? But the explanation of what had gone wrong is inaccessible in the absence of a vocabulary designed to talk about the language. When developing the skill of making this ascent from first-order talk to the meta-language, we come to possess our thoughts and statements in a more complete fashion. We don't just know how to use the language, we also know why.
Similarly, logic supplies the tools with which to explain why (and not just see that) the reasoning in the following inference is good:
If Penelope is a cat, Penelope is a mammal
Penelope is a cat. So, Penelope is a mammal
Moreover, with logic, we can explain what goes wrong with fallacious reasoning, too:
If Violet is a cat, Violet is a mammal.
Violet is a mammal. So, Violet is a cat.
Logic provides names for good forms of reasoning (the first example above is an instantiation of what's called modus ponens) and we have names for bad forms, too (the second example is an instantiation of the fallacy of asserting the consequent). This attention to the forms of reasoning allows us to distinguish two reasons we may give for taking issue with an argument.
On one hand, we may hold that the reasons given are not acceptable, not true. On the other hand, we may be fine with the reasons given, but they may not support the conclusion. So, consider two arguments that are unacceptable, but for these two different reasons:
All Americans are reptiles.
Some Americans are koalas.
So: Some reptiles are kolas.
And
All dogs are mammals.
Some mammals are pets.
So: Some dogs are pets.
The first argument is unacceptable, because the premises are false. But notice that its form is fine – were those premises true, they would indeed guarantee the truth of the conclusion. By contrast, the second argument is unacceptable because the premises – even though true – don't support the conclusion. This failing can be seen easily by simply replacing ‘pets' with ‘cats'. And so:
All dogs are mammals
Some mammals are cats
So: Some dogs are cats
These two unacceptable arguments show that in reasoning, it's not just what we reason about that matters; the form the reasoning takes is important as well. So even if our premises are true and we draw from them a conclusion that is also true, we can nevertheless fail at good reasoning. Sometimes, we just get lucky.
Logic is the means by which we manage reasoning's vulnerability to luck. Once we see that the form of a piece of reasoning is evaluable independently of the content of its premises, we make a large swath of our reasoning invulnerable to luck. This invulnerability is a focal objective of deductive logic – the aim is to show how, in the case of certain forms of reasoning, the truth of our premises absolutely guarantees the truth of our conclusions. This is a high calling, indeed.
The trouble, though, is that not all our reasoning aspires to be deductive. In real-world thinking, we often must make our inferences on the basis of incomplete evidence, small samples, and heavily generalized assumptions; we seek not guarantees of the truth of our conclusions, but justification in accepting them, and assurance that they are (at least) probable. Accordingly, in addition to deductions, there are inductions, inferences to the best explanation, and various forms of probabilistic and plausible inference. And there are ways in which our reasoning can be woefully inadequate, even when it meets deduction's already high standards. A simple example is that the widely recognized fallacy form of circular reasoning, wherein the conclusion does double-duty also as a premise, is a deductively valid form. Of course the premises will guarantee the truth of the conclusion if the conclusion is one of the premises! A more robust yet less formal notion of good reasoning is necessary, too, one that runs alongside and supplements our demanding formal criteria. This is the project of informal logic, and we will articulate its broad outline in our next post.
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Scott F. Aikin and Robert Talisse are professors of philosophy at Vanderbilt University and authors of the new book Why We Argue (And How We Should): A Guide to Political Disagreement (Routledge 2013).