January 9, 2014
The elements of arguments
Atomic statementsMolecular statements and their logical
Necessary vs. sufficient conditions
So far we've seen the basics of what arguments are. Let's look a bit
more closely at what their elements are.
The elements of arguments are statementspremises and
conclusions. Statements, as we've seen, are sentences that are
either true or false.
Understanding the sort of argument you're dealing with on any
given occasion requires understanding the sorts of statements
premises and conclusionsit involves.
There are two basic sorts of statements it's important to
distinguish: atomic and molecular.
Atomic statement: a statement that does not contain other statements as elements or constituents.
Ex. “It is raining.”
Molecular statement: a statement that contains other statements
Ex. Either Harry loves Jim, or Chris does.
Here are some examples of atomic statements. Notice that the
constituents of these statements (some of which I've underlined)
are not themselves statements.
The sun is shining.
My shirt is black.
Harry loves Jim.
Xian is going to the movies.
Elizabeth II is Canada's head of state.
And here are some examples of molecular statements. Notice that
they all contain constituents (underlined) that are themselves
The sun is shining and my shirt is black.
Either Harry loves Jim or Chris does.
If Xian is going to the movies, then I am too.
Elizabeth II is not the US's head of state. (What makes this
molecular is that the part that makes Elizabeth II NOT the US
H.O.S. is part of the molecule).
What makes atomic statements true, or false? There are different philosophical theories of that, e.g.:
Correspondence with factsCoherence with other statements we
believe Practical usefulness of believing them
Correspondence – the statement corresponds with something in
Coherence – the way in which any atomic statement fits, or
coheres with, another atomic statement.
Pragmatic/pragmatist – if believing a certain statement allows us
to accomplish certain goals, then that's what makes it true.
Indirectly, you might say that whatever makes atomic statements
true or false isalso what makes molecular statements true or false.
But, directly, the truthvalues of their contained constituent
statements make molecular statements true or false.
How the truthvalues of their contained statements make molecular
statements true or false is indicated by what we call logical
Logical operator: a word/phrase in a molecular statement that
indicates how the truthvalues of the statement(s) it contains lead
to the overall truthvalue of the molecular statement.
Consider again our examples of molecular statements. What are
the logical operators in them?
The sun is shining and my shirt is black. Either Harry loves Jim or
Chris does.If Xian is going to the movies, then I am too. E