Classical Theism, Philosophy, and Religion Forum / The Principle of Parsimony

**Posted by surroundx** 1/09/2018 8:10 am

How much stock do forum members put in the Principle of Parsimony?

It seems to me that, even if you somehow accepted it as a metaphysical first principle, it's application would still be contingent to some degree upon one's current (meta-)ontology.

Take Fred, who is trying to decide which of two competing hypothesis is the best explanation of some phenomenon. Call them H5 and H10 respectively, alluding to the number of assumptions/commitments that each requires. Let us further say that there is no overlap of the assumptions/commitments that constitute H5 and H10. Assuming that all other things are equal (cf. ceteris paribus), then clearly Fred should choose H5. However, if Fred already accepts 6 of H10's assumptions/commitments and none of H5's, then clearly (or so it seems to me) Fred should really choose H10 since that only burdens him with 4 extra assumptions/commitments. Thoughts?

**Posted by surroundx** 1/09/2018 8:18 am

My Fred example was more meant as a lamentation than an attempt to say something genuinely new. After all such thoughts have probably occurred to many people. Our differential ontologies wreak havoc on our attempts to adjudicate our differences.

**Posted by bmiller** 1/09/2018 2:53 pm

surroundx wrote:
Take Fred, who is trying to decide which of two competing hypothesis is the best explanation of some phenomenon. Call them H5 and H10 respectively, alluding to the number of assumptions/commitments that each requires. Let us further say that there is no overlap of the assumptions/commitments that constitute H5 and H10. Assuming that all other things are equal (cf. ceteris paribus), then clearly Fred should choose H5. However, if Fred already accepts 6 of H10's assumptions/commitments and none of H5's, then clearly (or so it seems to me) Fred should really choose H10 since that only burdens him with 4 extra assumptions/commitments. Thoughts?

""Entities are not to be multiplied without necessity" is one formulation of the principle.

In the case you cite, for Fred, H10 is not multiplying unnecessary entities (at least explicitly) since he rejects H5. In this case, Fred considers H5 unsound, so things are not really equal as far as he is concerned.

Now if H10 contained elements H7-H9 such that one would reach the same conclusion without them, then they really add nothing to the argument and probably make it worse by adding confusion. That is why I think parsimony is useful.

**Posted by surroundx** 1/10/2018 5:54 am

bmiller wrote:
""Entities are not to be multiplied without necessity" is one formulation of the principle.

In the case you cite, for Fred, H10 is not multiplying unnecessary entities (at least explicitly) since he rejects H5. In this case, Fred considers H5 unsound, so things are not really equal as far as he is concerned.

Fred doesn't reject H5 as unsound.

According to the Principle of Parsimony, Fred should reject H10 as incurring twice the number of assumptions/commitments for no added explanatory benefit.

However, it seems to me that since Fred "already accepts 6 of H10's assumptions/commitments and none of H5's", the PoP is overridden by a related Principle. I don't have a catchy name for it yet, but taking Fred's ontology into account, H10 is a lesser expansion to his ontology than H5 is since it only requires him to expand it by 4 (H10 minus the 6 he already accepts = 4) rather than 5 (H5 - 0 since he doesn't already accept any of the 5 assumptions/commitments).

Last edited by surroundx (1/10/2018 6:08 am)

**Posted by bmiller** 1/10/2018 11:30 am

surroundx wrote:
Fred doesn't reject H5 as unsound.

OK, looks like I misunderstood the scenario.

On what grounds does Fred reject H5? Are they the same grounds for rejecting 4 of H10?
What are the grounds for accepting or rejecting any of the propositions?

I had been assuming that valid and sound argumentation was the criteria.

**Posted by surroundx** 1/11/2018 8:01 am

bmiller wrote:
OK, looks like I misunderstood the scenario.

On what grounds does Fred reject H5? Are they the same grounds for rejecting 4 of H10?
What are the grounds for accepting or rejecting any of the propositions?

I had been assuming that valid and sound argumentation was the criteria.

A bit of confusion on both our parts I think. When I said that Fred doesn't reject H5 as unsound, I didn't mean to imply that he rejects it on other grounds. He doesn't reject it at all, because the scenario takes place logically prior to him coming to a decision on H5 vs. H10. The point of the scenario is rather to point out that when one takes one's ontology into account (in Fred's case making H10 preferable to H5) the PoP seems to give way to a related unnamed principle.

**Posted by surroundx** 1/11/2018 8:19 am

Or take another scenario, with H1 and H2. H1 is twice as simple as H2, and therefore preferable according to the PoP. However, if one's ontology already includes H2 to explain some other phenomenon, then it seems one should choose H2 because although prima facie more complex, it would not involve an expansion to one's ontology like accepting H1 would.

**Posted by bmiller** 1/11/2018 10:06 pm

surroundx wrote:
Or take another scenario, with H1 and H2. H1 is twice as simple as H2, and therefore preferable according to the PoP. However, if one's ontology already includes H2 to explain some other phenomenon, then it seems one should choose H2 because although prima facie more complex, it would not involve an expansion to one's ontology like accepting H1 would.

If things are not essential to an argument, then it is preferable to exclude those things. That is all that parsimony is about. It doesn't mean either should be preferred merely by the number of elements in the argument as long as all of those elements of each argument are essential to the argument.

But why would allowing oneself to prefer H1 change one's "ontology". Maybe I'm not clear what you mean by that. One's philosophy of being qua being? Maybe an example is in order.

**Posted by surroundx** 1/12/2018 4:54 am

bmiller wrote:
But why would allowing oneself to prefer H1 change one's "ontology". Maybe I'm not clear what you mean by that. One's philosophy of being qua being? Maybe an example is in order.

Take H2 to be God, and take H1 to be an even simpler explanation. If H1 is explanatorily sufficient, then H2 is not essential to an account of the phenomenon we are seeking to explain. But say that Fred is a theist, and hence he already accepts H2 on other grounds (e.g. the Leibnizian CA) but H1 is not currently in his ontology. Then for Fred, even though H1 is simpler, accepting it would involve an expansion to his ontology. Whereas accepting H2, even though it is non-essential to an explanation of the phenomenon, would not amount to an expansion of his ontology.

**Posted by bmiller** 1/12/2018 7:38 am

But then it seems the argument is actually about ontology in the first place.
Theists maintain that God is essential for things to exist. Atheists maintain that God is not essential for things to exist. The arguments contradict each other so Fred could not rationally hold that both are true. Parsimony would only tighten up each argument to be more concise.