What is an Argument?
In the logical sense, the sense with which we will be concerned, an argument is a group of propositions (statements with a truth value), some of which are given in support of another. The supporting propositions are called premises, and the proposition being supported is called the conclusion.
Note that in this logical sense, an argument is not a disagreement between two or more people. In fact, an argument can be developed and proposed by a single person and arouse no disagreement whatsoever. An argument can have any number of premises, but it must have only one conclusion.
Some arguments are good (which is to say that the conclusion is compelling, it seems forced upon us) and others are bad (which is to say that they allow some means by which to evade the force of the conclusion). We use some technical terms to refer to argument types and the results of evaluation.
Two Types of Arguments
Deductive: A deductive argument is one in which the truth of the premises guarantees the truth of the conclusion.
- Valid: It is impossible for all the premises to be true and the conclusion false in the same scenario. (Opposite is: “invalid”.)
- Sound: The argument is valid, and all the premises are true. (Opposite is: “unsound”.)
- For more about validity and soundness click here.
Inductive: An inductive argument is one in which the truth of the premises makes the truth of the conclusion likely.
- Strong: If all the premises are true, it is very likely that the conclusion is also. (Opposite is: “weak”.)
- Cogent: The argument is strong, and all the premises are true. (Opposite is: “not cogent”.)
An argument is never true or false; only its propositions can be true or false. An argument is evaluated using only the foregoing technical terms. Conversely, propositions can never be valid or invalid, strong or weak; only arguments are evaluated in these terms.
In order to more clearly display an argument, we place it in Standard Form. In this form, it is impossible to mistake which propositions are the premises and which is the conclusion. Here is an example.
- 1) All men are mortal.
- 2) Socrates is a man.
- 3) Socrates is mortal.
Note several things about this formal way of presenting an argument. First, each line is numbered, making it easy to clarify which proposition is being addressed in discussion. Second, the line separating the premises from the conclusion makes a clear delineation between which propositions are premises and which is the conclusion. Finally, the order of the propositions expresses the order of support; if we accept (1) and (2), we must accept (3).
Distinction Between Sentences and Propositions
We emphasize the difference between sentences and propositions, because some sentences contain propositions, but not all do. For example, there are three main forms of speech in which sentences occur, and only one of those forms explicitly conveys propositions:
Imperative (commands) — “Close the door.”
Interrogative (questions) — “Is the door closed?”
Informative (statements) — “The door is closed.”
Notice that of the three forms of speech, only the last issues statements that can have a truth value. It would be at least odd to evaluate the question, “Is the door closed?” by exclaiming: “False!” No, instead you would respond with “yes” or “no.”
Your “yes” or “no” response would itself be an informative statement that would be shorthand for, “The door is closed,” or, “The door is open.”
But notice that the imperative form of speech does not convey a truth value; it instead is asking for an informative response that will contain a truth value.
The same goes for the imperative form of speech. If somebody were to command you, “Close the door,” it would be odd indeed for you to respond: “False!” You might respond: “I will not,” which would itself be an informative statement. But you do not evaluate a command in truth-value terms!
So, of the three forms of speech, only the informative form conveys propositions that have a truth value.
Another difference between sentences and propositions is that sentences can vary in verbiage and language while conveying the same propositional content.
For example, if I were trying to convey the propositional content, “For lunch I had a grilled cheese sandwich,” I could convey that same proposition with all sorts of different verbiage. I might say, “During my mid-day meal, I had two slices of bread containing a slab of aged, solidified mammal milk between them, and that whole thing was cooked in a frying pan.” Notice that both the original proposition (that was itself a sentence) and the second sentence are conveying the same meaning. So, the sentences themselves can vary in verbiage and convey the same content.
Sentences can also vary in language. If I knew French (instead of just using Google Translate) I might actually say, “J’ai eu un sandwish au fromage grillé pour le déjeuner.” A French-speaking listener would hear this and get the exact same propositional content as would an English-speaking listener when hearing: “I had a grilled cheese sandwich for lunch.”
Notice that the translation process itself depends upon the fact that propositional content can remain the same across languages, and even across verbiage. So, the translation process itself presumes that sentences and propositions are different entities.
We can sum up the differences between propositions and sentences with these two rules:
All propositions have a truth value, while not all sentences do.
Sentences can vary in verbiage and language, while the proposition expressed remains the same.
Now we can see that to evaluate arguments we must first be very crisp and clear about the particulars of what the author of the argument is trying to achieve:
What type of argument does the author intend to be producing? It would be extremely uncharitable of us to evaluate an intended inductive argument as though it was a deductive argument, and vice-versa. So, we must be careful to determine what an argument’s author is trying to achieve with the argument. Is it designed to be a rigorous proof (deductive)? Or is it designed to be strongly indicative (inductive)? We must then assess the relation between the premises and conclusion appropriately.
What propositional content do the premises and conclusion actually contain? Because verbiage can vary significantly, we must be careful and charitable to understand the propositions the author is actually trying to convey. It is a straw-man fallacy to misunderstand the propositional content of an argument and then tear down the argument based upon the misunderstanding.
One of the huge upsides of the analytic philosophy approach is that it seeks to achieve as much propositional clarity as possible, while holding arguments to the rigorous standard of logic. We get very clear about what an argument is actually saying, and then examine if the inferences of the argument are actually legitimate. Thus, we analyze arguments for validity/invalidity and strength/weakness as we charitably try to assess the propositional content to help an author make his/her best case.
By this approach, we intentionally seek for intellectual honesty rather than to simply sustain our own cherished view or “win” debates.
Logical Parlor Tricks
One final thing I will say in the context of arguments and argument evaluation is that non-logicians are often suspicious of this sort of careful reasoning. It is unfortunately far too common for people to respond to a sound argument by saying, “Well, I just don’t agree. I don’t know what sort of ‘logic games’ you are playing, because I’m not a logician. But I know you are doing something wacky, because I just don’t accept that conclusion.”
Like mathematics, logic “just is.” You cannot think in propositional terms at all without employing logic! There literally is no propositional thinking without inferences, and those inferences necessary follow (or break) fixed rules. The rules are objective and not open to “interpretation.”
You cannot say, “Well, I know that there are 20 chairs in that room, so sometimes 18 + 1 does not equal 19; sometimes 18 + 1 equals 20. There!” No! Either you have miscounted, or somebody has changed the number of chairs. The mathematical rule of addition just is. And logic is the same way.
So, analytic philosophy proceeds “according to the rules,” and the inferences are able to be evaluated by anybody. There are no “tricks” or “parlor games” being played. If you don’t agree with any particular conclusions, you have two and only two options:
First, you can show that the conclusion does not follow from the premises via valid inference rules.
Second, you can demonstrate that at least one of the premises is false.
If you cannot do one or both of these, then you are forced by logic itself to accept the conclusion of a sound argument. There are no games nor wiggle-room here. We strive for intellectual honesty, and that honesty is at core fundamentally logical!