## Formal Logic

Formal Logic

In formal logic, often
thought of as a foundation for or a relative of Critical Thinking, we
distinguish deductive from non-deductive arguments. Deductive
arguments, we say, are those whose *reasons to think* a
conclusion *guarantee* the truth of that conclusion.
Non-deductive arguments are those whose *reasons to think* a
conclusion only make the conclusion *very likely* to be true. In
this, we appeal to structure, truth, and judgements about likelihood.

The pieces of
evidence we deal with in formal logic are called *premises.*
We infer *from* premises
*to *conclusions. In
this process we apply rules to help determine whether the move from
the premise to a conclusion is justifiable, as well as assess the
truth of the premises. We judge that the steps *follow*
one another, and that they *lead to *the
conclusion*.*

Generally, in formal
logic we separate the structure of an argument from its content. When
the premises of a deductive argument, *if* they were true,
ensure the truth of the conclusion, we call the argument “valid”.
When we evaluate that the premises of a valid argument are *actually*
true, and therefore that the conclusion is true, we call the argument
“sound”.

However, not all arguments are best rendered in the terms of formal logic. In Critical Thinking we approach these other sorts of arguments differently. Moreover, formal logic does not explicitly accommodate the fallibility of our judgements. Here we create a system to do just that. Here we create a system that allows for correction and revision of reasons and conclusions, which allows us to strengthen or weaken our arguments as we discover new facts and evidence.

In informal
settings, such as critical thinking, we concern ourselves not with
*truth* but with
*reasonableness *and
*best explanation*. When
the reasons given in an inference are good, it is “reasonable” to
accept an explanation as “best” or to accept a recommendation as
“reliable” (terms that we will continue to refine in the course
of this discussion).

This distinction between “reasonable” and “true” can make critical thinking seem a subjective version of formal logic. However, our judgements of informal arguments are not capricious. There are standards against which we can judge, and by and large, this process resembles judgements we make in our ordinary lives quite effortlessly.

For example, I might judge (conclude, assess, think, say, determine) “it is raining”. We might choose to represent my thought process as a deductive argument, perhaps something like this:

**A Valid Argument**

**Premise 1**: When students enter a lecture hall with wet umbrellas, it is raining.

**Premise 2**: Students are entering the lecture hall with wet umbrellas.

**Therefore**,

**Conclusion**: It is raining.

In formal logic, we
would investigate the structure of this argument to determine whether
it is valid. That is, we would consider, hypothetically, *if*
the premises were true, would the conclusion *follow* from those
premises. If so, the argument is valid.

Then, if it is valid, and this sample argument is, we would investigate the truth of the premises to determine whether it is “sound”. A valid argument with true premises is “sound”. If we found that the argument was not sound (and this argument is not sound, because Premise 1 is not “true”), then we could not for certain say that the conclusion is true. In formal logic, the exercise would end here; our assessment of the argument would be complete.

Consider this example, of an invalid argument with a true conclusion:

**An Invalid Argument with a True Conclusion**

**Premise 1**: All Presidents of the United States have been male.

**Premise 2**: Obama is male.

**Therefore**,

**Conclusion**:
Obama has been President of the United States.

When we assess this
argument, we see that the conclusion *does not *follow from the
premises (lots of males *are not *President). *This does not
mean the conclusion is false*. It simply means the proposed path
does not lead to the conclusion. End of story.

We might say that in
formal logic, the primary interest is in arguments and their
*structures*. In Inference to the Best Explanation, the primary
interest is in the conclusions themselves, and their relationships to
evidence and circumstances. This is to say that, here, our
investigation into *the reason *for wet umbrellas, for example,
continues.

As noted, in the
language of Formal Logic, Premise 1 in the umbrella example is false.
There are lots of reasons why people might carry wet umbrellas, so
there is something dissatisfying about simply determining the
argument un-sound; we still wonder “w*hat’s with all the wet
umbrellas*?” Since in the form above it is difficult to see how
to proceed, here we introduce a variation of how we might come to the
judgement “it is raining”. Informally we might write the argument
as follows.

**Example 1.1**

**It is raining”**

In short, a
comparison of the two expressions of a simple argument shows us how,
in formal logic, a conclusion might follow from a set of premises. We
can see that the premises and the conclusion are *related*
in the right sorts of ways that the relationships between the
premises, assuming the premises are true, licenses us to assert that
the conclusion is true.

On the other
hand, when we release ourselves from the burden of *truth*
we allow ourselves to assess nuances and alternatives. So, here our
task here is to come up with a systematic way of representing Best
Explanations that licenses us to assert that one-among-the-many
answers to an investigative question is *the best*.
Lurking behind both deductive and informal cases are acts of
judgement.