The Problem with Truthmaker Maximalism

Truthmakers are roughly the things that make true certain truth bearers.  That definition is purposefully ambiguous as the exact definition of a truthmaker is dependent upon one’s notion of truth and what exactly the truth bearers are.  Nonetheless, that’s enough detail to understand the idea.

The following is called truthmaker maximalism: for every truth, there is something in the world that makes it true.  However, consider the following objection that has been raised against truthmaker maximalism in the literature:

(1)  This sentence has no truthmaker.

Suppose (1) is true.  Then, by the truth of (1) it is the case that (1) has no truthmaker.  However, that contradicts truthmaker maximalism.  If we suppose (1) is false, then (1) has a truthmaker even though it’s false.  However, that’s a contradiction in terms and so that cannot be viable either.  Thus, (1) shows that truthmaker maximalism is false.

Now, some have tried to argue against this example, but none of the responses seem very satisfying to me and so we shall go on by assuming (1) successfully shows that truthmaker maximalism is false.

The person who used to hold to truthmaker maximalism might regroup by saying, “sure, (1) shows that truthmaker maximalism is false, but then we can just stipulate that truthmaker maximalism excepting (1) is true.”  Supposing this is an acceptable move, there is a problem.  For we can now construct an infinite number of sentences that don’t have truthmakers.

Take any sentence that is true and thus has a truthmaker.  Now, conjoin that sentence with (1).  This new sentence does not have a truthmaker either.  Thus, there are an infinite number of exceptions to truthmaker maximalism.  The best route for the truthmaker proponent seems to regroup and exclude from the truthmaker maximalism definition any sentence that is (1) or contains (1) or rule out self-referential statements.


Modal Arguments and Divine Command Theory

Alexander Pruss recently posted an interesting modal argument against divine command theory.  First, I want to make some observations of modal arguments.  Then, I will discuss his specific argument.

I believe it was Inwagen in his article on modal skepticism that says he doesn’t know of a single person who has been convinced by a modal argument.  Part of the reason, I surmise, is that they often seem like a trick.  I think people often react to modal arguments in general as they do to the ontological argument, it’s simply a neat trick.  However, there are some good grounds for reacting in this way to modal arguments.  First, if you can construct a modal argument against the position the person is arguing for, then the arguments just cancel (assuming they have the same plausibility behind them, this is because it acts as a successful parody argument).  Second, it’s pretty well known that conceivability does not entail possibility.  Thus, if one is simply working from conceivability, then the argument faces more challenges.

However, Pruss is a modal skeptic himself and so his argument is all the more interesting.  The reason is this: certain modal arguments actually give an argument for the possibility premise.  As another example, Kripke gives his argument against physicalism by showing (i) that we can conceive of the situation in mind and (ii) that conceivability is the same as possibility in that case.  So if both of those portions are true, then Kripke’s argument for the possibility premise is air tight.  Pruss’ argument is in a similar vein in that he gives an argument for the possibility premise by saying, “[p]remise (3) seems to follow from divine freedom and the fact that God is under no obligation to command creatures.”

Nonetheless, this is no denial of divine freedom if God’s choice arises from His character.  To quote Pearce and Pruss (p.9) on an agreed upon point in free will studies, “a limitation on the will is not a constraint if that limitation arises from the agent’s character and/or choices in the right way.”  This seems easy enough as more recent divine command theorists like Adams have said that God’s commands flow from His loving nature.  If that is the case, this His commands flow from His character and thus they would be consistent throughout worlds without being a constraint on divine freedom.  We have now provided a premise that seems true on divine command theory, is consistent with the other premises in Pruss’ argument, and undercuts his support for the possibility premise.  Given that, divine command theory seems untouched by this argument.

What Does Explanation even Mean?

Take Pruss’ definition of the principle of sufficient reason: every contingent fact has an explanation.  Now, given my last post on showing what a term means, we can use the principle of sufficient reason as a test case.  More specifically, we will look at the word explanation.

So explanation has been taken to be synonymous with cause.  Thus: every contingent fact has a cause.  If that is true, then since libertarian free choices, they violate the principle of sufficient reason.  However, it seems like my libertarian choice really is explained by the following facts: I exist, I have libertarian freedom, and I have certain reasons to make the choice I do.  And so a casewise view of explaining a term would show that definition of “explanation” to be false.  Moreover, the same sort of thing also seems to hold for certain interpretations of quantum mechanics.

So what we have done here is start off with a definition and then used real life examples to see if that definition works.  This is the strategy I suggested in the post above.  The final part of the strategy is to give a new definition of the term.  Maybe it is this: a contingent fact is explained if given the facts that are proposed as the explanation of the fact trying to be explained, it is no longer seen as mysterious how the fact that is trying to be explained obtains.

My Hands Disprove Empiricism

Consider the following argument:

(1)  If empiricism is true, then any synthetic belief is open to revision.
(2)  At least one synthetic belief is not open to revision.
(3)  Therefore, empiricism is false.

The argument is valid because it follows a standard modus tollens.  Thus, we must look at the premises.

As to (1), if a belief is synthetic then it can in theory be falsified.  For instance, Newton’s law of universal gravitation had a ton of support for it, but there were phenomena that showed Newton’s law to be incorrect and so it was abandoned.  The same is true of any other belief under empiricism since a fact that falsifies the belief would lead one to revise the belief.  Now this doesn’t mean that any anomaly must cause belief revision since Kuhn has pointed out that every theory faces anomalies, but that fact does not falsify (1).

As to (2), consider this argument for it:

(4)  At least one synthetic belief is of such a nature that it has an intrinsic defeater-defeater.
(5)  If a belief has an intrinsic defeater-defeater, then it is not open to revision.
(2)  Therefore, at least one synthetic belief is not open to revision.

Again, the argument is logically valid by means of modus ponens so we must look at the premises to see whether they are true.

As to (4), examples seem to abound of this sort.  If Quine is right that there are no such things as analytic truths, then something like “there are no married bachelors” or “if p, then p” would be great examples.  However, if we think Quine is wrong on that matter, then there are other examples still.  Consider Moore’s famous argument about his two hands: “here is one hand, and here is another.”  Now what could defeat my knowledge that I have two hands?  If I seem to wake up and find myself with only one hand, then I would suppose that a brief bit of my memory was about a dream within a dream and so I am still dreaming and once I wake up from my dream where I have one hand, I will find myself with two hands.  Moreover, if it seems to me that all of the sudden I only have one hand and I think that I was having a delusion the whole time, I would consider that present state a delusion because I have my whole life experience and immediacy of knowledge as evidence.  The same goes for skeptical arguments, etc.  This type of Moorean shift is common and seems totally appropriate.  For more examples, see Moore’s papers on the topic or consider beliefs that are usually taken as foundational in nature.

With regards to (5), if the belief that I have two hands is of such a nature that I cannot have a fact that will defeat my belief due to its intrinsic defeater-defeater, then that belief is clearly not open to revision.  For if it were open to revision, that means it could be defeated.  Since that is not the case, then (5) holds.

Therefore, (2) follows which means that (3) follows in the main argument.  Empiricism is therefore defeated; that is, if it is open to revision.

Putnam, Kripke, and Logic

So this post is going to cover a number of topics, but it will center around logic and epistemology by focusing on this article in particular.  Here is the plan of attack: I am going to summarize the article as best as I can and then provide some commentary afterwards.  As to whether you read the whole article or just my summary, that choice is yours.

Hilary Putnam is a philosopher of immense talent and wields that talent to argue for positions that are not that common.  The article above sketches the Putnam-Kripke debate on logic, epistemology, and quantum mechanics.  In particular, Putnam argues that quantum mechanics shows us that we need to revise logic as commonly conceived.  The details of the account are not particularly important since Kripke responds with a strong critique.

Kripke argues that if we accept Putnam’s argument, then we must also conclude that 2×2≥5 (see the bottom of page 7 to the top of page 11 for the details)!  Moreover, what Putnam does is assume a number of interpretations of quantum mechanics are simply wrong without arguing for such a conclusion.  Kripke retorts by saying that Putnam does not bear his burden and since his argument is missing on details, it fails as a whole.  Nonetheless, if Kripke’s argument of where Putnam’s argument leads is successful, then that seems to put the nail in the casket on the matter.

However, there is a larger issue at stake here and that is one on whether logic is empirical and one can adopt a logic.  On the one hand, Putnam uses illustrations of how we use to think certain mathematical truths were necessary but now we do not accept them (for instance, straight lines and non-euclidean geometry).  Another example in the paper is whether “all P are Q” implies “some P are Q”.  However, we know that isn’t the correct due to empty terms.  Namely, “all deserters will be shot on sight” does not imply that “some deserters are shot on sight” since the very rule might keep people from deserting.  However, Kripke argues that it doesn’t make much sense for empirical considerations to change our logic nor does it make any sense to adopt a logic.  In particular, there simply is reasoning and while specific systems may or may not capture accurate reasoning, it is not as if one can somehow stand outside of logic and simply adopt one logic amongst many logics.  As a great example, I recommend you read the bottom of page 13 to the bottom of page 14 (apologies as the paper gives weird formatting when I try to copy and paste for quote).

There is then talk about bivalence and the future and how this might tie into whether one can reject bivalence based upon empirical matters.  The author then tries to suggest a mediating position by saying that logic as such might be a priori, but the particular instances of logic and the details might be curtailed by empirical considerations.

On the matter of Putnam’s argument and Kripke’s response, I find Kripke’s counterargument to be solid and without any obvious objectionable point.  He seems to assume Putnam’s system and then reductio it by showing that it leads to a person concluding that 2×2≥5.  However, we certainly don’t want to do that (or, at least, I don’t want to do so), so we should reject Putnam’s argument.  Now, maybe Putnam can try to patch up his account and avoid this objection, but it’s not immediately obvious how he would do so and so we should reject Putnam’s particular argument.

As to whether logic is empirical and one can adopt a logic, I also find myself siding with Kripke on the matter.  As to the straight line example in non-Euclidean geometry, I’m not so sure this is an empirical matter.  If math just is logic, then it follows that Gauss’ discovery of non-Euclidean geometry and the implications for truths that we once thought were necessary is simply a matter of logic, not looking around at the world.  What follows then is that our logic is clarified simply by our reasoning in that our particular system of logic did not match correct reasoning.  As to the principle of subalternation for universal categories (all P are Q implies that some P are Q), this is again a matter of reasoning correctly and thus not a matter of empirical discovery.  While it certainly might be the case that someone discovered this is wrong by the whole deserter example, what seems to be going on there is that reality is reflecting logical rules and so what we are really doing is discovering correct reasoning.  However, that is not empirical matters altering or curtailing or whatever our logic, but simply reflecting the way logic is.

However, on the point of logic being overturned by empirical matters, we also have the infamous case of W.V.O. Quine.  In particular, Quine argued that logic simply is a matter of scientific investigation like every other matter and this entails that logic is open to being changed by empirical discoveries.  But to steal an example from Mike Almeida (see the fifth comment) it seems that we wouldn’t want to reject p–>p even if does solve certain empirical difficulties.  However, I’m not sure that entails that logic is a priori.  While certain empiricists might respond by saying that certain parts of logic (all?) are analytically true, we can sidestep the debate by showing that if empirical considerations can change logic then the law of non-contradiction might be dropped and so the statement could be analytically true and we could reject it in certain instances.  Another objection might be that p–>p is not known a priori but it is so confirmed a posteriori that is has an intrinsic defeater defeater for any empirical matter.  Why should that be thought to be the case though since certainly we don’t want to say that certain scientific theories have intrinsic defeater defeaters merely because they have been confirmed a number of times.  In fact, it only takes one exception to show it is false.  While it is the case that every theory runs across certain anomalies (see Kuhn’s The Structure of Scientific Revolutions), that is a sociological fact and not one that can be used to show that empiricism can be salvaged from this consequence.  If these facts conflict with empiricism, then so much the worse for empiricism.

Lastly, Stairs’ discussion of bivalence and the future does not contain a lot of meat and so I cannot really interact with it much.  He argues that if one combines presentism and indeterminism, then bivalence is not the case about the future.  However, (i) that’s not immediately obvious, (ii) he gives no real argument for the claim, (iii) there are people who hold to all three of those positions and defend them (for instance, William Lane Craig), and (iv) it doesn’t really seem like those matters are really empirical ones and thus it’s not obvious that they would provide a counterexample to Kripke’s position.

All in all, I enjoyed the article and I commend it to anybody who has time.

Feel free to register your thoughts.