Rationality Rules vs. Craig’s Causal Premise (p. 1)

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Rationality Rules vs. Craig’s Causal Premise

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Introduction

Stephen Woodford has a YouTube channel called Rationality Rules and he posted a video titled Creation and Causation (a Reply to Dr. Craig) responding to justifications of William Lane Craig’s premise 1’ “If the universe began to exist, then the universe has cause of its beginning,” which Craig contrasts from the less modest claim premise 1 “Whatever begins to exist has a cause of its beginning” (which Craig has had different wordings for, e.g. “Everything that begins to exist has a cause”). In this article I’ll go through Woodford’s replies.

Craig’s First Justification, Part 1: Coming into Being from Nothing

Before getting to the first justification I’ll explain some philosophical terms. A material cause is the stuff something is made out of, and an efficient cause is that which produces an effect. For example, when an artist creates a wooden sculpture, the wood is the material cause and the artist is the efficient cause.

Craig’s first justification is that “Something cannot come into being from nothing.” At 3:22 to 3:24 Woodford says that “to say that something has come into being is to say that something has begun to exist, that it’s been created” and later says the first sentence (“If the universe began to exist, then it has a cause”) is about causation, and the second (“Something cannot come from nothing’”) is about creation. But it’s really about both. For Craig, a premise like “Everything that begins to exist has a cause” includes both material and efficient causation. You can see that in this Reasonable Faith webpage but you can also see it in the very Kalam Cosmological Argument video Woodford clips from (1:08:11 to 1:08:29):

Now in the first premise, the premise doesn’t stipulate what kind of cause there has to be for what begins to exist. It’s just saying that something can’t come into existence without some sort of a cause—a material cause, an efficient cause, whatever.

So to say that the universe began to exist without a cause means beginning to exist with no efficient cause and no material cause, i.e. coming into being from nothing.

Woodford doesn’t seem to understand this, and he goes on an inadvertent tangent about quantum mechanics (which he doesn’t correctly understand) and classical causation that doesn’t really go anywhere relevant in addressing Craig’s actual claim.

In talking about quantum superposition Woodford says “we see atoms both excited and not excited at the same time (which calls into question the law of noncontradiction)” which is misleading at best. There’s quantum mechanics, which has loads of math that is very good at making successful empirical predictions, and there are various empirically indistinguishable interpretations of quantum mechanics which put forth ideas about the underlying reality behind the math. I’ll spare you the mathematical details of eigenvalues and such (I recommend David Z. Albert’s excellent Quantum Mechanics and Experience for a gentle introduction to that sort of thing) instead giving a rough general idea behind the math. In some cases we have a mathematical structure representing the state of an object (e.g. an electron) and another mathematical structure called an operator that acts on the state to tell us what measurement we’d see for a given property (e.g. if the electron would be “spin up” when measured along a particular axis) if we did a particular measurement.

In some cases, quantum mechanics will tell us “If you do that measurement, you’ll definitely get this result.” But in some cases, the state is in a superposition such that it can’t give us a definite answer as to what our measurement will be when combined with the operator, and quantum mechanics instead gives us the probabilities of the measurement results. So what’s really going on here behind the superposition math? One idea is that the object (e.g. electron) in question doesn’t have a definite property value for the property being measured until it’s actually measured. An even crazier idea, which Woodford presents here, is that the object both has the property and doesn’t have the property at the same time. However, that sort of contradiction is nowhere in the math of quantum mechanics. Mathematics can represent contradictions, and there are absolutely no contradictions in the math of quantum mechanics. The idea that a self-contradiction is present behind the math is an interpretation of quantum mechanics, and it is not a very plausible one.

Superposition confusion aside, Woodford kind of contradicts himself in this video at around 5:04 to 5:29, because he says quantum mechanics “hasn’t been shown to violate the law of conservation of energy. Every atom is accounted for; everything, so far as we know, is created from already existing material” (the conservation of energy isn’t exactly true since photon energy can be lost as space expands, but let’s ignore that for the nonce) yet he says we have billions of things “coming into being” without a “classical cause and perhaps even without a cause at all.” No, not without a cause at all, because he just conceded that all those things coming into being came from pre-existing material which means all those things had material causes.

At 5:29 to 5:40 Woodford concludes with:

Thus creation and causation are not two sides of the same coin, and it’s a mistake to treat them as such. This isn’t a distraction. It’s a refutation.

It’s a distraction because it doesn’t refute any position Craig actually put forth in the clip Woodford showed. Quantum mechanics doesn’t do anything to show that things can come into being with no efficient cause and no material cause. Nor did anything Woodford say about quantum mechanics (as flawed as it was) show that causation and creation (coming into being) aren’t closely related. Nor did Craig claim they were closely related, at least not explicitly.

But surely Craig at least implied creation and causation were closely related when used he “Something cannot come into being from nothing” to justify premise 1’? Yes, but specifics matter; the specific relation here is one of justification, viz. “Something cannot come into being from nothing” justifying “If the universe began to exist, then it has a cause.” If the universe began to exist without a cause (efficient or material) then it came into being from nothing, and if something cannot come into being (creation) from nothing, then premise 1’ is true, and causation and creation are intimately related in that sense. Perhaps there is a sense in which creation and causation are not closely related, but they are closely related in the sense of justifying premise 1’ and nothing Woodford said about quantum mechanics etc. addressed this relation. Woodford offered a lot of distraction but no real refutation of Craig’s actual claim here.

Woodford could perhaps be forgiven for not realizing that Craig left it open whether the cause in 1’ is efficient or material (despite what Craig clearly said in the video Woodford quoted from), but even if it were an efficient cause Woodford’s reply still wouldn’t work. Suppose that by “cause” Craig only meant “efficient cause.” Would “Something cannot come from nothing” fail to justify “If the universe began to exist, then it has a cause”? No. In this context the “universe” includes all of contiguous physical spacetime, so if the universe began to exist at time t it couldn’t have a material cause because a material cause would be pre-existing material at some time t* < t, in which case the universe (which includes all of contiguous physical spacetime) existed at time t*, contradicting the claim the universe began to exist at t. So if the universe began to exist it could not have a material cause, and if it began to exist without an efficient cause also, then it began to exist without a material cause and without an efficient cause, i.e. it came into being from nothing. So “Something cannot come from nothing” still relevantly justifies premise 1’.

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Moral Ought Facts are Non-Natural

Introduction

In my third Maverick Christian Vlog episode I refer to a scholarly paper which is called A Folk Semantics Argument for Moral Non-Naturalism. In this blog entry I’ll provide some of the technical background so that those of us who aren’t analytic philosophers can better understand it.

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 math used in the paper.

Philosophical Terminology

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 semantics” with respect to morality refers to what most ordinary people mean when they use terms like “morally wrong.”

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.

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.

A category mistake (or category error) is attributing a characteristic to something that it can’t possibly have because it’s not of the right category; e.g. saying that the number six has mass or volume, when the category of abstract objects is such that they can’t have mass or volume.

Set Theory

Some Basics

Sets are collections of stuff where order and duplicates are irrelevant. For example, the followings sets are all identical.

{1, 2, 3, 4}
{1, 2, 2, 3, 4}
{4, 3, 2, 1}

There’s the empty set, sometimes symbolized as {} which is a set that has no members.

To illustrate some set operations, suppose our “universe” consists entirely of natural numbers 1 through 9. Now let A, B, and C be the following:

A = {1, 5, 9}
B = {1, 5, 7, 8}
C = {2, 3}

Symbol	Example	Explanation
∈ (element of)	1 ∈ A	For any set S, x ∈ S means that x is an element of S.
∉ (not an element of)	1 ∉ C	For any set S, x ∉ S means that x is not an element of S.
∩ (intersection)	A ∩ B = {1, 5}	Given sets S and T, S ∩ T contains all the elements x such that x ∈ S and x ∈ T.
∪ (union)	A ∪ B = {1, 5, 7, 8, 9}	Given sets S and T, S ∪ T contains all the elements x such that x ∈ S or x ∈ T.
⊆ (subset)	{1, 5} ⊆ B	Given sets S and T, S is a subset of T if and only if each member of S is also a member of T.
⊄ (not a subset)	{2, 9} ⊄ B	Given sets S and T, S is not a subset of T if and only if it is not the case that S ⊆ T.

The set “All x such that x > 3” can be symbolized like this:

{ x | x > 3 }

The set “All x ∈ A such that x > 3” can be symbolized as:

{ x ∈ A | x > 3 }

That set described above would be {5, 9}.

Relations

Unlike sets were order and duplicates don’t matter, they do matter in tuples. The following are all different from each other:

(1, 2, 3, 4)
(1, 2, 2, 3, 4)
(4, 3, 2, 1)

Those who have taken algebra might remember the tuple known as the ordered pair:

(2, 3)
(11, -3)

Relations are sets of tuples, with a binary relation being a set of ordered pairs. For example, suppose we have this set:

{Diana, Steve, Barbara}

The relation “taller-than” could consist of this set of ordered pairs, where e.g. Diana is taller than Steve.

{(Diana, Steve), (Steve, Barbara), (Diana, Barbara)}

If we symbolize our taller relation as T then we could say that (Diana, Steve) ∈ T.

Relations between different sets are also possible. Suppose we have these two sets:

L = {Reed, Scott, Clark}
F = {Sue, Jean, Lois}

And the “is-husband-of” relation is a relation from set L to set F; e.g. Reed is the husband of Sue:

H = {(Reed, Sue), (Scott, Jean), (Cark, Lois)}

An inverse of a binary relation R goes like this:

R-1 = {(y, x) | (x, y) ∈ R}

For example, the inverse of the “is-husband-of” relation would be the “is-wife-of” and be this:

H-1 = {(Sue, Reed), (Jean, Scott), (Lois, Clark)}

A relation from set A to set B is a function if each member of A is paired off with exactly one member of B. The “input” part of a function is the domain (set A) and the “output” part is called the range (set B). For instance, the “is-husband-of” relation is a function because each member L is paired off with exactly one member of F, with L being the domain and F being the range, whereas an “is-husband-of” relation would not be a function if there were polygamous marriages.

Suppose relations S and T are the following:

S = {(1, 2), (10, 11)}
T = {(2, 3), (11, 12)}

A composition of two relations S and T can be symbolized as T ∘ S, and when the relations are binary, the set of ordered pairs in such a composition goes like this:

{(x, z) | (x, y) ∈ S and (y, z) ∈ T}

In our example, T ∘ S would be the following:

{(1, 3), (10, 12)}

Suppose relation V is the following:

V = {(1, 2), (1, 3), (1, 9), (2, 3), (2, 4)}

Because the relation is binary, V(x, ⋅) is { y | (x, y) ∈ V }

Examples:

V(1, ⋅) = {2, 3, 9}
V(2, ⋅) = {3, 4}

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:

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

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

1. If P, then Q
2. P
3. Therefore, Q.

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

1. If P, then Q
2. Not-Q
3. Therefore, not-P.

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

1. If it is raining, then my car is wet.
2. My car is wet.
3. 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.

1. (A ∧ B) → C
2. ¬C

---

3. ¬(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.

1. ¬C
2. (A ∧ B) → C

---

3. ¬(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:

1. A ∨ (B ∧ C)
2. ¬A

---

3. B ∧ C 1, 2, disjunctive syllogism
4. 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

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:

1. A
2. (C ∧ D) → ¬A

---

3. ¬¬A → ¬(C ∧ D) 2, transposition
4. A → ¬(C ∧ D) 3, double negation
5. ¬(C ∧ D) 1, 4 modus ponens
6. ¬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:

1. A → B
2. A → C

---

3. A conditional proof assumption

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

7. 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:

1. ∀x[B(x) → U(x)]
2. B(c)

---

8. B(c) → U(c) 1, universal instantiation
9. 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.

1. ∀x[A(x) → B(x)]
2. ∀x[B(x) → C(x)]

---

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

And that should be all the technical stuff you need to know to read A Folk Semantics Argument for Moral Non-Naturalism. 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.

Can Objective Morality be Subjectively Perceived?

The Objection

One objection I’ve seen to objective morality on the internet, in one form or another, goes something like this: we use subjectively experienced intuition to believe in objective morality. This, somehow, is supposed to argue against objective morality or at least our justification for it. If belief in objective morality relies on subjective intuition, how can morality be objective if it’s subjectively perceived? Doesn’t the fact that supposedly objective morality is subjectively perceived mean we don’t really have any justification for accepting moral objectivism?

The answer to both questions is, “No.”

Responses

First, note that in practice, everything we know about is subjectively perceived; our own perceptions (intuitive and sensory) are all we have to go on. Yes, we can ask other people to see if they share our experiences, but the perception that there even are other people relies on, you guessed it, our own subjective experiences. At the end of the day, subjective experiences, i.e. the experiences of the self, are used to justify all of our beliefs. The fact that something is subjectively perceived thus doesn’t imply that it isn’t objectively real; e.g. my subjective experiences can report a tree existing with that tree being objectively real.

Second, some perceived truth being believed on the basis of subjectively experienced intuition doesn’t imply that the truth isn’t objective, even when people have disagreeing intuitions. If for example someone’s logic intuition told them there could be a married bachelor despite the self-contradiction, whereas your rational intuition says such a self-contradictory thing cannot exist, you’re still justified in believing that There can’t be any married bachelors is objectively true.

Or to use an example perhaps closer to real life, suppose a creationist and evolutionist look at the same data, but have differing intuitive perceptions about where that evidence points (the evolutionist thinks it’s evidence for evolution, the creationist disagrees). Does that mean there’s no objective fact of the matter about whether the data is evidence for evolution? Clearly not. Disagreeing, subjectively experienced intuitions do not imply that the intuitively perceived truths are not objective, nor do such disagreeing intuitions imply that we can’t be justified in believing them to be objectively true.

How?

So how do confused objections like, “Morality is subjectively perceived, so it’s not objective” arise? Perhaps one reason for the confusion is a conflation between moral epistemology (how moral truths are known) with moral ontology (the reality of morality; e.g. whether it’s objective or subjective). The moral epistemology may, in one sense, be subjective. But it doesn’t follow that the moral truths themselves are not objective.