Craig Biddle at the Objective Standard Whiffs Explaining the "Is/Ought Problem"

A good friend posted the Craig Biddle video below to Facebook recently. I commented that unfortunately Craig does a very poor job representing what advocates of the is/ought dichotomy are really saying. When people talk about the is/ought dichotomy, what they’re really talking about is a point about the nature of deductive reason rooted in formal logic. Logic (that is deductive argumentation) has two components. There is the question of good evidence and that of good argument. Is there evidence the premises are true? And is the argument formally sound so that the conclusion necessarily follows from the premises? Both these components are required to sustain the conclusion of the argument

The is/ought dichotomy is an idea which arises from the second part – that concerning the form or structure of deducative reasoning rather than one of evidence as Biddle tries to maintain. Because it examines the form that valid arguments take, this second area is known as “formal logic”. It deals with the relationships between statements, determining which relations between statements allow us to make logical inferences and which do not.

Formal logic has identified many acceptable forms or “shapes” an argument may take and still convey logical inferences. Most of these acceptable “shapes” date back to antiquity, having been stated by even the earliest of recorded logicians. One of the simplest, for example, is known as Modus Ponens, or the way of affirming:

A implies B.
And A is true.
Thus B is proven.
A simple English example: If it is going to rain, you ought to take your umbrella. The clouds forebode a violent rainstorm. Thus, I say you must take your umbrella.

Another is known as Modus Tollens, proof by denying:

A implies B.
B is false.
Thus A is disproven.
E.g. If we have reached Boston, then we have entered Massachusetts already. But we have not yet crossed any state line. Thus, the city we are in cannot be Boston.

In addition there are multiple forms of argument based on dichotomies, for example:

Either A or B.
Not A.
Therefore B.

And also:

Either A or B.
If A then C.
If B then C.
Therefore C is proven.

But sometimes an argument includes a malformed inference. This may happen by accident or through intentional trickery. The structures that false logical inferences can take are nearly infinite. One example would be a false dichotomy:

Either A, B or C.
Not A.
Therefore C.
Either it is raining, or the sky is clear. It is not raining. Therefore the sky must be clear.
Obviously this is a false inference. Perhaps it is snowing or perhaps there are clouds which are producing no rain.

At this point it’s important to notice that for any argument we can show the form the argument takes by replacing its statements with letters such as the A’s, B’s and C’s above. This allows us to simplify, and to see clearly whether the structure of the argument itself is a valid one. If the structure follows valid forms of inference, then we know that the conclusion follows from the premises. If there is good evidence for the premises, then we accept the conclusion. But if the structure is bad, the conclusion does not follow from the premises, and the argument is not valid regardless of the evidence. The important thing for now is to recognize that every logical inference has a “form”. Bad, or illogical inferences also have a form we can represent with letters as above. But in the case of illogical inferences, we can see from their structure that they are unsound. We will come back to this idea later on, but for now note what is meant by the simplified “form” of any inference.

These simplified “forms” or methods of deduction can be seen in all arguments. And logicians have been using them for millennia. Many very simple and completely valid arguments take the form of only one of these named methods of inference. More sophisticated arguments consist of a long series of individual inferences one “form” of inference being used after another. Nonetheless, every valid argument has a structure that involves a series of one or more methods or “forms”of valid logical inference and we can map out its shape with letters as above..

Interestingly, some forms of inference take as their premises conditional statements and give as their conclusions statements that are not conditional. Modus Tollens is an example of that. Conditional premise, declarative conclusion. In this and many other ways, each method of logical inference modifies the information contained in the premises. But it does so in a way that is logically valid – the change does not harm or “destroy” the truth contained in the premises. In short, when valid logical inferences are used, the conclusion is a different piece of information than the premises but we can be certain it is also true so long as they are. This characteristic of reason or logic to change the information but preserve the truth is simple, but also a stunningly powerful tool.

In summary, for any valid argument we should be able to show two things: first that there is good evidence for our premises. Second, we should be able to show that each of the inferences we make upon the premises are all valid. That is to say, mapped out with A’s and B’s, we should be able to show the form that each inference in our argument takes, and that it is a valid inference and not a “malformed” one as described above. This idea concerning the importance of evidence as well as “form” in an argument is not novel. It is not controversial. And it is as ancient as the very earliest recorded thinkers. The study of this idea, as we have said, is known to logicians as “formal logic”.

Upon this very basic idea, the advocates of the ought/is dichotomy make a simple case of their own. Before stating that case, it may be important to clarify a point of English grammar. We must have the distinction between two grammatical terms. Grammarians refer to what are known as grammatical moods. In English there are more than two moods, but for the purposes of our discussion only two need to be defined. In English we have the “imperative mood” and also the “indicative mood.” The imperative communicates an obligation.

Here are simple examples:
“I command you to eat.”
“Shut the door.”
“You shall not pass!”
“You must pay.”
“Thou shalt honor thy mother and thy father.”
In the sentences above the verbs eat, go, shut, shall, must, and shalt are all in the imperative mood.

Indicative verbs are put differently, they are like these:
“I went.”
“John never shuts the door.”
“I pass whenever I want.”
“I pay nothing”
“You do honor your father and your mother.”
In these sentences the verbs went, shuts, pass, pay, and do are all indicative.

In English we use imperative statements to talk about obligations, instruction and commands. We use indicative statements to talk about observations, facts or falsehoods. One must easily recognize the difference between indicative and imperative grammatical statements in order to lay out the argument made by proponents of the is/ought dichotomy.

The first simple observation the argument is based upon is this: every form of known logical deduction can take a statement in the imperative mood as one of its premises. And every form of logical inference can take a statement in the indicative mood as one of its premises. Likewise, inferences can produce as their conclusions statements both indicative and imperative. But among all the methics of logical deduction, there is a remarkable pattern. No known form of valid inference gives a conclusion in the imperative without an imperative premise.

We might say for example, “You must stay dry. If you go out without an umbrella you will get wet. Therefore you must take an umbrella.” A simple Modus Ponens. The conclusion gives us an imperative, an “ought”. But it does so because we have an imperative among our premises. Without the imperative premise, the imperative conclusion is not possible. For example, “I want you to stay dry. If you go out without an umbrella you will get wet. Therefore I want you to take an umbrella.” Not quite the same. The only way to preserve the imperative in the conclusion is to put an imperative in a premise, or else to smuggle one in with a clever turn of phrase. Or by assuming an imperative premise without stating it at all.

Review all the textbooks and tomes of formal logic from the ancient stoics to the present day and there is no accepted form of inference which gives us an imperative conclusion without an imperative premise.

Because of this, no formally valid argument can be constructed which takes as its premises observations of fact and gives as its conclusion statements of obligation. And any argument which purports to do so must either assume an unstated imperative premise, or it must disguise an imperative premise by cleverly or accidentally restating it in a way that conceals its meaning. In either case, the important point is that the premise is not actually observational in nature but imperative.

With purely indicative or observational premises, all conclusions which can be inferred will also be indicative.

Because observation is not sufficient to give us an logically deducible ethics, we will need to look to other grounds to establish ethical norms.There are a few ways this can be done, and I’ll examine some of them (including my own) in a future post. To quickly summarize some of the approaches we can take, there are a handful of subjective approaches to ethics – those based upon personal preferences, cultural or community norms or upon mutual consent. There are theistic approaches. And there are a few modern approaches.  Many of these approaches can also be organized in terms of “virtue ethics” which focus on the nature and meaning of specific virtues, versus rule-based ethics which focus on rules or prohibitions. More posts soon to come!

Comment below if there are particular approaches you’d like us to investigate first!