Introduction to Logical Argument
Every man is, by birth, a philosopher and an ethicist. You know what truth and falsehood are, you know what right and wrong are. In the 20th and 21st centuries, modern and postmodern philosophers and other academics have mounted a herculean project to convince us that nobody can really know what is right or wrong, or what is true and false. And I think one reason that many of us are reluctant to dive into the intentional study of logic and ethics is the feeling that it's all just a bunch of useless argument over how many angels can dance on the head of a pin. That is, anyone who can assert, in all seriousness, that they do not know what is real or true is practically insane, and if this is the fruit of studying philosophy, then philosophy is clearly a waste of time.
But the enemy has set a trap here. Philosophy is extremely powerful, in fact, it can be argued that all the notable achievements of humanity have been built on philosophy. I would argue that, apart from God, philosophy is not a sufficient foundation. However, it is a necessary foundation and if the enemy can persuade you not to study philosophy, he can weaken you and leave you vulnerable to all kinds of attacks that would not otherwise be possible for him. You're right to be suspicious of the agenda of many modern academics, but don't be suspicious of learning itself. Learning is the gateway to self-determination, and self-determination is an essential ingredient of liberty. A public that lacks the capacity for self-determination can never be free, no matter what legal rights it supposedly has under its system of government.
Before jumping into what logical argument is and some of the methods you can employ when making logical arguments, let me first distinguish between logical argument and other forms of persuasion. In the opening scene of
The Godfather, Michael Corleone tells Katy the following story:
MICHAEL
Well, when Johnny was first starting out, he was signed to this personal service contract; with a big band leader. And as his career got better and better, he wanted to get out of it. Now, Johnny is my father's godson. And my father went to see this band leader, and he offered him $10,000 to let Johnny go. But the band leader said no. So the next day, my father went to see him; only this time with Luca Brasi. And within an hour, he signed a release, for a certified check for $1,000.
KAY
How'd he do that?
MICHAEL
My father made him an offer he couldn't refuse.
KAY
What was that?
MICHAEL
Luca Brasi held a gun to his head, and my father assured him that either his brains or his signature would be on the contract.
Obviously, he's making a word play on the idiom "an offer you can't refuse" meaning, an offer too good to be refused. But in this case, it's an offer too violent to be refused. The story vividly illustrates the difference between persuasion and logical argument. A logical argument is an argument that any reasonable person ought to find persuasive. But because people are self-interested, they will often refuse to acknowledge the conclusion of a perfectly valid argument based on true premises. Or, they can be forced to accept an argument that does not follow logically as happened to the poor band-leader when he was faced with the choice to either sign or get shot. The band-leader was in the right, but Corleone was a big man so he could get his way by force.
Whenever persuasion involves some element of carrot or stick, it is often a form of
non-logical argument. This is not always true -- "You should eat more green vegetables because it has health benefits and you will feel better." Reason and personal biases can align; morality and self-interest can align. But in general, the good philosopher is always suspicious of personal biases, popular opinions and self-interest, whatever form these may take.
Because we want to believe certain kinds of things (for example, "I am attractive" or "I am funny"), we should raise the bar for the kinds of arguments that we will accept as valid for those things in particular.
And since it is human nature to desire applause, we should be automatically suspicious of popular beliefs and opinions... affirming what people generally believe is something we naturally want to do because that is one way to get applause. That doesn't mean that society is always wrong about everything. It is often right about many things. But when society goes off the rails, it frequently goes
way off the rails because of the broad desire of people generally to have each other's applause.
Whenever something is in our interest, or against the interests of those we oppose, we should raise the bar for belief in those things even further because our lower mind instinctively wants to be persuaded by them. I may want to believe that you wouldn't care if I don't mention the $100 bill that just dropped from your pocket but how likely is that to really be true? Of course, we know that it's not very likely at all to be true; since it is in my interests to believe it, I should raise the bar for believing that much higher.
We even acknowledge this in our social conventions. When someone who is not a relative or close friend gives you a valuable gift, it is considered polite to refuse the gift at least once. Why? Because the assumption is that the individual may have felt some kind of social pressure to give such a generous gift. So it ought to be refused once and, only if they persist, accepted.
So far, we have touched on persuasion and logical arguments. Another kind of argument that frequently sits on the boundary between these two types of discussion is the
ethical argument. An ethical argument or moral argument (sometimes,
normative argument) is an argument about what people
should or
should not do. Obviously, ethical arguments involve questions of truth and they are frequently made in the context of persuasion. So ethical arguments often rely on the conclusions of logical arguments and, in real social discourse, are usually made in order to persuade people to alter their own moral outlook and behavior. But in this post, we will just be focusing on logical arguments as opposed to persuasion and ethical arguments.
In general, when making a logical argument, we're assuming that our opponent (if a debate) is rational and open to persuasion by logical argument. This isn't always true, but this is the unstated assumption that pertains to any logical argument. There is no point in stating a logical argument to a rock, a tree or a dog, for example. What we're attempting to do is move from some common ground -- things we both agree on -- to some conclusion that is is
logically entailed by the things we agree on, and which I want to persuade you to believe.
Note that most of the debate that an ordinary person will see in their life is political debate. While political debates frequently ape the form of logical argument, the fact is that valid logical arguments are rarely, if ever, used in political debate. For this reason, I think that most people have a wildly erroneous idea of what a logical or philosophical debate is. Ideally, a philosophical debate would have little or nothing to do with who "won the crowd" since crowds are easily moved by many non-rational factors. The lesson of modern propaganda in the 20th-century can be boiled down to this crucial insight: non-rational factors are generally far more effective in persuading crowds than rational factors are. This post is about logical argument, not politics and propaganda, so I will leave detailed treatment of those things to a future post. Suffice it to say that there is no reason to
despair of using logic and reason in the public square but it is important to align logic and reason with the many non-logical factors that can easily distract a crowd away from the substance of the argument at hand.
For the purposes of introducing the subject of logical argument, we categorize arguments into one of two varieties: deductive argument, or inductive argument. In practice, most arguments are not purely deductive or inductive, but rely on a combination of these elementary types of argument. But we study them separately in order to better understand their use.
A deductive argument starts from a set of assertions or claims (called premises) that we both agree are true, and then applies
deductive inference to derive a new assertion which must also be true. A particular form of deductive argument is called
the syllogism and is used in philosophy classroom to introduce students to some of the technical considerations in deductive arguments. I will skip those details in this post.
Inductive argument is the kind of argument we usually use when reasoning about the real world. Mathematical arguments tend to be purely deductive but we do not often have an occasion to use that kind of reasoning in our daily life or we use it in ways that are so mundane that explaining them quickly becomes tedious. For example, if there were three oranges on the table when you went to bed, and now there are two oranges on the table, then it follows that someone ate an orange while you were sleeping. That's a deductive inference, not an inductive inference, even though you are reasoning about something in the real world. Inductive inference typically involves a conclusion that starts from uncertain premises and derives an uncertain conclusion. For example, "I see thick, black smoke billowing from my neighbor's window. Therefore, I believe there is a fire in my neighbor's house." Clearly, there exist other possible explanations for why there is thick, black smoke billowing from my neighbor's house. But the most likely explanation is that there is a fire in their house that is causing that smoke to billow out the window. This is an example of inductive inference.
Deduction is frequently presented as operating only on certainties. However, deductive arguments can also operate on probabilistic beliefs, so long as we separate between the probabilities in the premises themselves, and the probability of the deduction itself. For example, consider the following argument:
There's a 50% chance that it's raining
Whenever it is raining, I will get wet if I go outside
---------------
There's a 50% chance I will get wet if I go outside
This is a perfectly valid deductive argument -- it is not an inductive argument even though one of its premises is probabilistic. In the mathematics of probability, for example, we frequently engage in this kind of hybrid logic, where we are using absolute deductive reasoning to manipulate probabilistic statements. There are a lot of ways to get this wrong and intuition is often a feeble guide in this kind of hybrid reasoning -- this is one of the reasons why statistics are so notorious for leading people astray into all kinds of false beliefs.
There are many technical details in the types and techniques of both deductive and inductive argument. However, my goal here is simply to give an elevator-pitch presentation to explain the various types of logical argument and to separate them from other kinds of persuasion, and ethical arguments. For more details, watch the following two videos from Crash Course Philosophy:
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