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The argument is an enthymeme
An enthymeme is an argument with a premise left unstated. The function argument is usually told in three steps, and one of the steps between them is never written down.
Lesson · Ethics and the Arithmetic of Welfare · Virtue and method
Virtue Ethics and the Function Argument
Aristotle argues that the human good is a certain kind of activity because it is what performing the human function well comes to. Written as three sentence letters, the argument as stated has a counterexample row, and the lab finds the premise that closes it. The rest of virtue ethics, including the mean, has no structure the lab can test, and the lesson says so.
good = performing the function well
the human function is reasoning
as stated: a counterexample row
the added premise carries the weight
A function argument and its missing premise
Core ideas
What this lesson establishes
Virtue ethics is a family of views about character. The argument below is one piece of it that is also an argument in the sense this course tests.
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Validity finds the missing premise
The counterexample row names the case that the stated premises allow and the conclusion forbids. The premise that rules it out is the one to examine.
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The argument is a bridge from is to ought
A claim about what a kind of thing does leads to a claim about what is good for it. The gap in “Is and Ought” is the one that the first premise has to close.
The material
From function to good
One argument, its counterexample row, and two ways it can be completed.
Virtue ethics asks what kind of person to be before it asks what act to do. Its oldest argument for a view about the good life is Aristotle’s function argument. A flute player’s good, it says, lies in playing the flute well, and an eye’s in seeing well. A thing’s good is performing its function well. What is distinctive of human beings, shared with neither plants nor animals, is reasoning. So the human good is reasoning well.
Write three sentence letters. f is “reasoning is the human function”, g is “the human good is reasoning well” and r is “reasoning is what sets human beings apart from other living things”. The argument as told gives two premises: f → g, that if reasoning is the human function then the human good is reasoning well, and r. The conclusion is g.
The lab builds the eight rows and finds one on which both premises are true and the conclusion false: f = F, g = F, r = T. On that row reasoning distinguishes humans, and it is not the human function, so the first premise is true because its antecedent is false, and the human good is not reasoning well. Nothing in the stated premises connects what is distinctive of humans to what is their function.
f g r | f → g r | g
F F T | T T | F (the counterexample row)
any other row with both premises true has g true
Definition · Enthymeme
An enthymeme is an argument that relies on a premise it does not state. Making the premise explicit does not make the argument sound. It makes visible the thing a critic should question.
The missing premise is r → f: whatever sets a kind apart is its function. With it the argument is valid, and the lab finds no counterexample row. Aristotle supplies something like it, saying that a function is what a thing does that nothing else does. That is the premise a critic should look at. Laughing also sets humans apart, and few would say that laughing well is the human good, so distinctiveness alone looks too weak to fix a function.
The argument has a second gap, on the other side. Strip it to r and r → f, so that it ends with the claim that reasoning is the function, and ask whether it reaches g. The lab finds it does not: the row r = T, f = T, g = F is a counterexample. Here f → g is the premise that is missing, and it is the bridge from a claim about what a thing does to a claim about what is good for it, the step that “Is and Ought” asks everyone to price. A defender says that for a thing with a function, being good just is performing the function well. A critic asks why we should care about the function of a kind we belong to, which is the open question again.
Example · A tool and a person
The premise sounds compelling for a knife, whose function was given by someone who made it, and a good knife is one that cuts well. It sounds less compelling for a person, whose function, if there is one, was not assigned. The argument needs f → g to hold for kinds whose function comes from nature or nothing, and the lab can say the argument is valid with it and cannot say whether it holds.
The lab does not reach further. The doctrine of the mean, that each virtue sits between a deficiency and an excess, the role of practical wisdom in finding it, and the way character is formed by habit have no premises and conclusion to test. Any widget offered for them would be decorative, so the lesson leaves them alone, along with the history of who held which view.
Interactive
Validity by cases
Every row, every counterexample, and the form
Method
Completing an enthymeme
Five steps. The counterexample row is the guide, and the premise that excludes it is the answer.
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Give each claim a letter
Write the argument in standard form with one letter per simple sentence. Keep a claim about a kind’s function separate from a claim about its good.
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Run the table
Let the lab list every row where the premises hold and the conclusion fails. If there are none, the argument is valid as it stands.
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Read the row as a story
Say in words what the counterexample describes. It tells you what the argument assumed without saying.
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Write the premise that excludes the row
State the conditional that makes the row impossible, add it, and check that the argument is now valid.
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Price the premise
Ask who would accept it and whether it holds for every case it covers. The argument is as strong as that premise.
What the rows show
Score 0 / 0Choose the answer you can justify.
Function, reason and the human good
Three letters, two premises as stated, and the row that breaks them.
f reasoning is the human function
g the human good is reasoning well
r reasoning sets humans apart from other living things
f implies g, r therefore g: invalid, row f=F g=F r=T
add r implies f: valid, no such row
r, r implies f therefore g: invalid, row r=T f=T g=F
Two different premises are missing from the two shorter forms. The argument in the books needs both, and each can be doubted separately.
Common mistakes
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Assuming an argument from a great philosopher is valid as writtenThe first preset is the argument as it is usually told, and the lab finds the row f = F, g = F, r = T on which its premises hold and its conclusion fails. Care and prestige do not make a premise appear. A great argument is usually one whose missing premise is worth the dispute.
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Treating the added premise as a repair that costs nothingWith r → f the argument is valid, and its strength is now exactly the strength of r → f. Laughing sets humans apart and is not obviously the human function, which is the objection a critic would press.
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Taking a failure of the lab to cover the mean as a failure of the doctrineThe lab checks arguments. The mean is not stated as one, and the lesson says so instead of inventing a test. That is a limit of the method, not a verdict.
Check your understanding
✓
Finish when you can state the premise an argument from function leaves out.
Given a function argument, you should be able to formalise it with one letter per simple claim, produce the counterexample row, write the premise that closes it, and say what accepting that premise commits you to.
Note: The three letters hide a good deal. A fuller formalisation would quantify over kinds and functions, and the first-order machinery to do so arrives later in the Subject, but the gaps found here do not depend on it.