Suppose you work at a Play-Doh factory. Suppose further you work in the “red division”, the part of the factory dedicated to creating, forming, and packaging red Play-Doh. All you see every day is red Play-Doh coming out of the machines.
One day, something strange happens: one of the machines in your division produces blue Play-Doh. That ain’t right. Your co-workers freak out as they contact the division manager. The manager brings in a mechanic who, after examining the machine in detail for a few hours, reports on the situation.
“Well,” states the mechanic, “nothing is wrong with your machine. The mechanisms by which it operates and produces the blue Play-Doh are identical to the other machines in this division that reliably produce red Play-Doh. There is literally no difference in the circuits, wiring, tubes, input and output operations, the program, or anything in the machines themselves.”
“Good,” you respond relieved. “That must mean the machine is simply being fed different starting materials for the Play-Doh compared to the other machines in our division. Perhaps someone accidentally poured the wrong pigments into the mix!”
“Not so fast,” replies the mechanic to your dismay. “I checked that too. The materials out of which the Play-Doh is made were also identical in this machine as in others. The same pigments were added in the same amounts and same proportions. The same flour and water were added as inputs. And so on. Every part of the machine, as well as every operation of the machine, as well as all the inputs to the machine — including Play-Doh raw materials — were identical in this machine as in others.”
You are puzzled, but an idea springs to mind. “Aha! It must be the lighting. The lighting is different in this part of the factory compared to the lighting in others, and that is what is making the Play-Doh look blue despite actually being red!”
“Nope,” states the mechanic again to your dismay. “I checked that too. In fact, I checked every environmental condition of this machine and compared it to the other machines. The environmental conditions are identical in both cases, including the lighting.”
Knowing that you are not undergoing a collective hallucination, you start to wonder about the credentials and expertise of the mechanic. Surely, you reason, he must have missed something in the process. Something changed with this machine. If literally nothing changed, it would spit out red Play-Doh just like the other machines in the division.
I suspect that the most rational conclusion you would draw is precisely the one outlined in the previous paragraph: the mechanic just didn’t complete an exhaustive survey of all the causal factors at play. But why? Why do we conclude this instead of agreeing with the mechanic that the processes were identical but nevertheless produced wildly different end results?
Here is a principle that accounts for this:
Difference Principle (DP): A difference in the effect presupposes a difference in the total cause.
The illustration of the defective Play-Doh machine helps to pinpoint what is so intuitive and seemingly undeniable about this principle. After all, if the total causes in two cases are utterly and completely (qualitatively) identical, there could be no ground or reason as to why the effects differed. The difference in the effects would be an inexplicable, brute occurrence.
There is an even further sense in which the blue is inexplicable apart from being wholly ungrounded in anything in the total cause: why was the Play-Doh blue rather than green, grey, yellow, orange, or white? If there was literally nothing in the total cause that changed between the defective machine (and its inputs) and the other machines (and their inputs) in the red division, then why was blue produced instead of orange? Why wasn’t green, or purple, or white produced? Blue is wholly arbitrary. By the very nature of the scenario, blue’s appearance couldn’t be accounted for in terms of some different causal or explanatory factor at play in the total cause or explanation. But if that is true, then we have a whole new level of arbitrariness and inexplicability: why on earth would blue be formed rather than any other color?
Here are some reasons to think DP is true:
(1) Inductive generalization
Our universal experience attests to DP’s being true. In particular, our universal experience of different effects attests to their total causes being different, and we have universal experiential support of things’ having identical effects when their causes are identical. For instance, this holds true for identical plants produced from qualitatively identical seeds that are genetically identical and that experience the same amount of sunlight exposure, soil, and water intake.
(2) Inference to the best explanation
Indeed, not only is there inductive support for DP, but DP is also the best explanation for why there is such inductive support in the first place. It is a simple principle with explanatory breadth and depth. If DP were false, we have a puzzle: why don’t, say, plants that are genetically identical and that experience identical environmental conditions turn out wildly different? Why don’t we experience all around us a sort of chaos wherein wildly different effects are produced from the same ordinary causes with which we are familiar? The hypothesis that such wild chaos is impossible best explains why we never see it obtain in actuality. If it were genuinely possible, we get a puzzle: why does it never happen?
To make this concrete, take the striking of a match in normal living room conditions (for instance, there is not an utter lack of oxygen, it isn’t raining, and so on). Curiously, the struck match always produces heat and flame rather than frost, cold, a smell of lilacs, a mouse, or a banana. Why?
Here is a simple hypothesis: such differences in the effects couldn’t occur unless there was a difference in the total cause. Because the total cause is the same in each case (the match, the match’s being struck, and the environmental conditions), the effect is the same in each case (heat and flame).
By contrast, if this hypothesis were false, we get a monstrous mystery. For then it would be genuinely possible that such differences in the effect could occur (on each occasion) despite there being no differences in the total cause. We therefore get a massive mystery why it is always the case that no such differences in the effect occur. A Bayesian argument from the repeated persistence of the same effect confirms the DP hypothesis significantly in relation to the negation of the DP hypothesis.
(3) Principle of relevant differences
The principle of relevant differences (PRD) is a useful tool — especially in disciplines like ethics.
Suppose we want to treat x and y differently in some moral way. We may want to privilege y but not x in some way, or we may want to preserve or protect y while disregarding or destroying x. However, it is only morally permissible to treat x and y differently if there is some relevant difference between x and y themselves which justifies or accounts for their differing moral status. If there is no relevant difference between them such that it justifies differential treatment, then the differential treatment is simply immoral and unjustified.
This is one reason why racism is wrong: mere differences in skin color are irrelevant with respect to moral status, and hence to treat individuals morally differently merely in virtue of their skin color is to unjustifiably act wrongly. This is also why we can justify climbing, stepping on, and otherwise abusing rocks but cannot justify climbing, stepping on, and otherwise abusing (say) puppies. There is a relevant difference between them that justifies such differential treatment: the capacity to suffer and the capacity for flourishing.
But the same rational justification behind the PRD (as applied to ethics) rationally justifies DP. In other words, it seems that one cannot consistently accept and apply PRD in ethics without also accepting DP. This is because the same sort of demand for a relevant difference-making feature applies to differences in effects: the effects can only differ if there is some relevant difference in their total causes, just as our treatment of x and y can only (justifiably) morally differ if there is some morally relevant difference between them. The demand for a relevant, underlying difference that grounds the discrepancy seems the same in both cases.
(4) The PSR
If the total cause C of effect E is identical to the total cause C* of effect E*, but E and E* are different, then the difference between E and E* is inexplicable and a brute fact, since there is nothing in the explanans (the total cause) which accounts for the difference. This violates the PSR.
(5) Forms the bedrock of scientific investigation
Scientific investigation presupposes DP. When scientists find discrepancies in the effects of their experiments, they assume that there must have been something different in the experimental conditions (such as one group being the placebo and the other being the treatment group). This drives their quest for understanding the natural world and its diverse effects and causes.
The aim of my Play-Doh scenario was partly to illustrate how (in my view, at least) DP is entirely self-evident. In the scenario, you didn’t even stop to consider that maybe the mechanic was correct after all and that the total causes were completely identical. You repeatedly brought up different causal factors that could have accounted for the difference to ensure that the mechanic checked those. Having confirmed that the mechanic checked those, you didn’t conclude that the DP is false; you instead concluded that there must have been something wrong with the mechanic’s procedure, and that he must have missed some difference.
DP and Classical Theism
I take it, then, that DP is true. But it seems that classical theism is incompatible with DP. Why is that?
Before establishing this (or attempting to do so), let’s get some terminology out of the way. That’s the bullet points below:
- Total cause C1 causes effect E1. Total cause C2 causes effect E2.
- The “non-God concrete world” is the part of reality that, under classical theism, God creates and sustains (it is every concrete thing apart from God).
- The Contingency Thesis is that there is at least one thing in the non-God concrete world that is contingent, where “thing” refers to the disjunction of properties, events, objects, substances, obtaining states of affairs, and so on.
- Contingent means could have been different/otherwise.
- “God” refers to the classical theistic conception of God, not the theistic personalist conception.
- Classical theism is the conjunction of (i) God creates and sustains every concrete thing apart from God, and (ii) God is absolutely simple, purely actual, and is such that his essence and existence are identical (each of which entails that the only features of God are essential features and Cambridge (i.e. extrinsic) relations)
Here is the argument:
P1: A difference between E1 and E2 entails a difference between C1 and C2, such that the difference between C1 and C2 accounts for the difference in the effect. (DP)
P2: There is at least one x, such that x is part of the non-God concrete world and x could have been different. (Contingency Thesis)
P3: If there is at least one x such that x is part of the non-God concrete world and x could have been different, then God’s effect could have been different, where God is the cause of God’s effect.
C1 (P2, P3): So, God’s effect could have been different, where God is the cause of God’s effect.
C2 (P1, C1): So, God could have been different, such that the difference accounts for the difference in the effect.
P4: If God could have been different, such that the difference accounts for the difference in the effect, then either (i) God’s Cambridge (i.e. extrinsic) relations to something external to God could have been different, (ii) God has accidents (if the difference lies in accidental features), or (iii) God is contingent (if the difference lies in essential features).
P5: God can neither be contingent nor have accidents.
C3 (C2, P4, P5): So, God’s Cambridge (i.e. extrinsic) relations to something external to God could have been different, such that the difference accounts for the difference in the effect.
P6: But C3 is absurd.
P7: But if classical theism is true, then C3 follows.
C4 (P6, P7): So, classical theism is false.
Justification for P6
Ontologically prior to God’s act of creation, there was nothing external to God and hence no Cambridge relations in which he could stand. It follows, then, that Cambridge relations could not be that which grounds as a necessary condition the difference in the effect of God’s act, since there being Cambridge relations in the first place already presupposes as a necessary condition the effect. It’s a vicious circularity.
Here is a better way to explain it. If the existence of a different effect presupposes as a necessary condition a difference in the cause (DP), and the only candidate difference in God is a Cambridge relation to external things (C3), but there being any Cambridge relations to external things (in the first place) presupposes as a necessary condition the existence of God’s effect, then vicious circularity ensues. God’s standing in a Cambridge relation presupposes the existence of the effect of God’s act; but per DP, the very existence of such an effect presupposes a difference in the cause, which we have proven could only be a Cambridge relation. If classical theism is true, we therefore have vicious circularity: God’s Cambridge relation presupposes the effect, but the effect presupposes the Cambridge relation.
Do I claim this is a decisive refutation of classical theism?
Absolutely not. No. No way. Zero. Zilch. Nil. Nada. Nein.
My purpose in exploring this argument is not to refute, but to explore. Arguments attempted as refutations almost always end up with a clarificatory purpose, bringing to light new distinctions or precisifications that resolve purported difficulties within worldviews. This argument, then, is not some sort of knock down proof. It is an invitation — an invitation to deeper thought, unity, friendship, communion, and exploration between thinkers. It is an invitation to seek treasures.