Maverick Christian

Introduction

In my third Maverick Christian Vlog episode I refer to a scholarly paper that is now called Folk Moral Semantics, Moral Naturalism, and Moral Descriptivism which argues for morality being non-natural. In this blog entry I’ll provide some of the technical background (like philosophical vocabulary and some formal logic) so that those of us who aren’t analytic philosophers can better understand the paper.

Why is it important that morality is non-natural? One reason is that it reveals that there is more to reality beyond the natural, physical world. Another reason is that morality being non-natural makes it so that atheism doesn’t fit in very well with the existence of morality, especially objective morality for reasons I explain in my third vlog episode. In contrast, the existence of an objective and non-natural morality makes perfect sense in a theistic worldview.

Next I’ll explain some philosophy lingo before explaining the formal logic used in the paper.

Philosophical Terminology

Deontic means “relating to obligation,” and so deontic morality refers to the “ought” part of morality. For example, an action is morally wrong for someone only if they ought not do it, and thus moral wrongness is an example of deontic morality. Axiological refers to value and disvalue, and so axiological morality refers to what is morally good and bad; e.g., justice and kindness (which are morally good) as well as cruelty and injustice (which are morally bad) fall into the category of axiological morality.

Moral semantics is about how to define moral terms. In philosophy, the word “folk” refers to colloquial stuff that laypersons use; e.g. “folk psychology” is (an albeit derogatory) term for beliefs about the human mind that ordinary people accept. In the paper, “folk moral semantics” refers to what ordinary people mean when they use terms like “morally wrong.”

A hypothetical imperative takes the form of something like, “If you want to do X, you should do Y” and describes what to do as a matter of practical necessity to accomplish some goal. For example, “If you want to do well in school, you ought to study” meaning something like, “As a matter necessity, you need to study to do well in school.” The sort of ought used in hypothetical imperatives is called a hypothetical ought. Hypothetical oughts are at their core descriptive (that is, what they are can be stated entirely in descriptive language).

In contrast, the Humean ought is that type of ought that is distinct from the purely descriptive and thus does not have only descriptive qualities. For example, someone saying, “You should not set cats on fire,” might be using this sort of ought. In the paper, the “folk moral semantics” is that sort of moral semantics that uses the Humean ought (we typically think of the moral ought as that type of ought that does not have only descriptive qualities). The gist of the Folk Moral Semantics Argument is that if we use folk moral semantics (i.e., the sort that uses the Humean ought), this leads to deontic morality being non-natural (assuming that deontic morality exists; e.g., that there is such a thing as moral wrongness).

A stipulative definition assigns a meaning to a particular word or phrase to be used in a given context (as a philosophy paper). For example, in a philosophy paper one might give a stipulative definition of “fully justified” by saying, “I will say that a belief is fully justified to denote the belief being justified to the point where one can rationally say one knows it to be true.” Stipulative definitions are often used for conveniently assigning a label to some concept and won’t necessarily match the lexical (“dictionary”) definition.

Formal Logic

Deductive Arguments

A deductive argument tries to show that it’s logically impossible (i.e. self-contradictory, like a married bachelor) for the argument to have true premises and a false conclusion, and thus that the conclusion follows from the premises by the rules of logic. If it’s logically impossible for an argument to have true premises and a false conclusion the argument is deductively valid or valid. An example of a deductively valid argument:

If it is raining, then my car is wet.
It is raining.
Therefore, my car is wet.

The above example uses a famous rule of logic called modus ponens which has this structure:

If P, then Q
P
Therefore, Q.

Another famous rule of logic is called modus tollens where “not-Q” means “Q is false.”

If P, then Q
Not-Q
Therefore, not-P.

An argument is deductively invalid or invalid if it is not deductively valid. An example of an invalid argument:

If it is raining, then my car is wet.
My car is wet.
Therefore, it is raining.

In logic lingo, a deductively valid argument with all its premises being true is called a sound argument. And since a valid argument having true premises guarantees the truth of its conclusion, a sound deductive argument has a true conclusion.

Basic Symbols and Rules of Inference

Here’s a summary of how the connectives in propositional work where p and q represent propositions (claims that are either true or false):

Type of connective	English	Symbolic Logic	When it’s true/false
Conjunction	p and q	p ∧ q	True if both are true; otherwise false
Disjunction	p or q	p ∨ q	False if both are false; otherwise true
Conditional	If p, then q	p → q	False if p is true and q is false; otherwise true
Negation	Not-p	¬p	True if p is false; false if p is true

As suggested in the above table, the symbols →, ¬, ∨, and ∧ are called connectives. It’s a somewhat misleading name since ¬ doesn’t connect propositions even though the other three connectives do. Still, it’s a popular label a lot of logic textbooks use. While the terminology varies among writers, I’ll call a single letter a simple statement and one more or more simple statements with one or more connectives is called a compound statement. For example, “¬P” and “A ∧ B” are compound statements.

The type of conditional (p → q) being used here is called a material conditional. A material conditional is equivalent to “It is not the case that the antecedent (p) is true and the consequent (q) is false,” such that the only way for a material conditional to be false is for it to have a true antecedent with a false consequent. A material conditional might seem like a pretty weak claim (in the sense that it doesn’t claim very much), since the antecedent and consequent don’t even have to be related to each other for a material conditional to be true. Thus, “If there is a married bachelor, then Minnesota is awesome” constitutes a true material conditional since it is not the case that we have a true antecedent (there is a married bachelor) with a false consequent (Minnesota is awesome). But it turns out that a material conditional is enough for modus ponens and modus tollens to be valid rules of inference, since in a true material conditional if the antecedent is true, then the consequent is true as well.

Speaking of which, here are those rules of inference I’ve already mentioned in symbolic form:

*modus ponens*

In English	In Symbolic Logic
If p then q p Therefore, q	p → q p ∴ q

*modus tollens*

In English	In Symbolic Logic
If p then q Not-q Therefore, not-p	p → q ¬q ∴ ¬p

In the convention I’m using, the lower case letters p, q, r,...z are placeholders for both simple and compound statements. Thus, below is a valid instance of modus tollens.

(A ∧ B) → C
¬C

¬(A ∧ B) 1, 2, modus tollens

It’s worth noting that the order of the premises doesn’t matter when using rules of inference. So below is also a valid use of modus tollens.

¬C
(A ∧ B) → C

¬(A ∧ B) 1, 2, modus tollens

Some rules of inference can be used in more than one way. Examples include disjunctive syllogism and simplification.

Disjunctive Syllogism

In English	In Symbolic Logic
p or q Not-p Therefore, q	p ∨ q ¬p ∴ q
p or q Not-q Therefore, p	p ∨ q ¬q ∴ p

simplification

In English	In Symbolic Logic
p and q Therefore, p	p ∧ q ∴ p
p and q Therefore, q	p ∧ q ∴ q

Before moving forward, I’ll introduce a quick example of how to use some rules of inference. Suppose we wanted to get C from premises 1 and 2 below:

A ∨ (B ∧ C)
¬A

B ∧ C 1, 2, disjunctive syllogism
C 3, simplification

Not too hard, right? After learning the above rules of inference, you might even have mentally “seen” that C followed from premises 1 and 2 above. Hopefully you are familiar enough with the symbols by now for me to remove the training wheels of english translation. Some more rules of inference:

conjunction

p q ∴ p ∧ q

hypothetical syllogism

p → q q → r ∴ p → r

Equivalences

In propositional logic, two statements are logically equivalent whenever the connectives make it so that they’re always the same truth-value (i.e. both true or both false). Some rules of propositional logic are themselves equivalences, such as these:

equivalence	name of equivalence

p ⇔ ¬¬p	double negation

p → q ⇔ ¬q → ¬p	transposition (also called contraposition)

¬(p ∧ q) ⇔ ¬p ∨ ¬q	De Morgan’s laws
¬(p ∨ q) ⇔ ¬p ∧ ¬q	De Morgan’s laws

Equivalence rules can be used to replace stuff “inline” whenever their equivalence appears. As an example of how to use some equivalences, suppose we want to prove ¬C ∨ ¬D from premises 1 and 2 below:

A
(C ∧ D) → ¬A

¬¬A → ¬(C ∧ D) 2, transposition
A → ¬(C ∧ D) 3, double negation
¬(C ∧ D) 1, 4 modus ponens
¬C ∨ ¬D 5, De Morgan’s laws

Conditional Proofs

The conditional is symbolized as p → q where p is called the antecedent and q is called the consequent. The conditional proof aims to prove that a conditional is true, with the antecedent of the conditional being the conditional proof assumption which is often used to help show that if the antecedent is true then the consequent is true also. The structure of a conditional proof takes the following form below:

conditional proof

a)	p conditional proof assumption
b)	... q
c)	p → q a-b, conditional proof

For example, suppose we want to prove A → (B ∧ C) from premises 1 and 2 below:

A → B
A → C

A conditional proof assumption

B 1, 3, modus ponens
C 2, 3, modus ponens
B ∧ C 4, 5, conjunction

A → (B ∧ C) 3-6, conditional proof

Notice that the validity of a conditional proof does not rely on the conditional proof assumption actually being true; rather it relies on the fact that if it is true then it properly leads to the consequent. Nothing in the proof above, for example, relies an A actually being true.

Predicate Logic

To give an example of predicate logic, consider the following symbolization key:

B(x)		=		x is a Bachelor.
U(x)		=		x is Unmarried.

The letters B and M in these examples are predicates which say something about the element they are predicating. Sometimes parentheses aren’t used; e.g. Bx being used to mean “x is a bachelor.” The symbol; ∀ means “For All” or “For Any” such that the following basically means “All bachelors are unmarried:”

universal quantification

In English	In Symbolic Logic
For any x: [if x is B, then x is U]	∀x[B(x) → U(x)]

The domain of discourse is the set of things we’re talking about when we make statements like ∀x[B(x) → U(x)], such that the “∀x” means “For any x in the domain of discourse (i.e. set of things we’re talking about here).” We can let an individual lowercase letter signify a specific element in our domain of discourse; e.g. c can signify a guy named “Charles” and we can let B(c) to signify c is B (i.e. Charles is a bachelor).

A rule of predicate logic called Universal Instantiation allows us to instantiate a universal quantification (a ∀x[...] statement) for a specific individual, like so:

∀x[B(x) → U(x)]
B(c)

B(c) → U(c) 1, universal instantiation
U(c) 2, 3, modus ponens

There’s a somewhat complicated rule called universal generalization (also called universal introduction) to get a universal quantification statement. Roughly, the idea is that if a statement contains some variable that is a placeholder for anything in the domain of discourse, we can generalize this to get “For any x, such-and-such holds true.” The universal generalization rule is fairly complicated (you can only use it under certain specified conditions) but the gist of universal generalization should be enough to follow along this proof.

∀x[A(x) → B(x)]
∀x[B(x) → C(x)]

A(t) → B(t) 1, universal instantiation
B(t) → C(t) 2, universal instantiation
A(t) → C(t) 3, 4, hypothetical syllogism
∀x[A(x) → C(x)] 5, universal generalization

And that should be all the technical stuff you need to know to read the paper that introduces the Folk Moral Semantics Argument. You still might not find it an easy read if you’re not used to analytic philosophy, but at least you have the background knowledge even if applying it is a bit tricky.