Before we can discuss why one ought to be consistent, we need to know which type of consistency is at issue. There are at least three types of consistency that people often confuse and that need to be kept distinct. I'll call them 'logical,' 'pragmatic,' and 'diachronic.' But it doesn't matter how we label them as long as we keep them separate.
1. Logical or Propositional Consistency. To say of two propositions that they are consistent is to to say that they can both be true, where 'can' expresses logical or broadly logical possibility. To say of two propositions that they are inconsistent is to say that they cannot both be true, where 'cannot' expresses logical or broadly logical impossibility.
I am blogging but not wearing a hat. My blogging is obviously consistent with my not wearing a hat since both propositions are true. But my blogging is also consistent with my wearing a hat since it is possible that I both be blogging and wearing a hat. But I am blogging now and I am not writing now are inconsistent since they cannot both be true. The first proposition entails the negation of the second, which implies the impossibility of both propositions being true.
Liberals often say that support for fetal rights is 'inconsistent' with support for the death penalty. But surely the following propositions are not logically inconsistent:
P1. Human fetuses have a right to life which cannot be overridden except in rare cases (e.g. threat to the life of the mother).
P2. Capital punishment for certain offences is morally justified.
Where is the inconsistency? (P1)and (P2) are plainly logically consistent with each other. Suppose that the right to life is grounded in the potentiality to develop into something to which one accords person-status. This is a possible view, and indeed one actually held by many. Any Aristotelian worth his salt will be able to spell it out coherently and perhaps even persuasively. Suppose also that a similarly coherent case is made for P2. One will then have made a case for the possibility of each. Joint possibility does not straightaway follow from the possibility of each, but if there is no reason to think of them as jointly impossible, then we should consider them jointly possible. On the face of it, P1 and P2 are logically consistent. They can both be true.
2. Pragmatic Consistency. By this I mean consistency in the application of a principle. Consistency in this sense is not a relation between propositions, but involves a relation between a person, a principle, and cases to which the person applies the principle.
To apply a principle consistently is to apply it to all like cases in a like manner. So if the principle is to cherish, value, and uphold human life, then perhaps the thought of those who see inconsistency in support of both fetal rights and capital punishment is that to apply this principle to the unborn but not to certain criminals is to apply it inconsistently. "How can you oppose the killing of the unborn, when you favor the killing of certain criminals? Be consistent!"
The answer to this should be obvious. The cases are dissimilar. The unborn are innocent while criminals are not. This is a difference that makes a moral difference; it is a difference that justifies a difference in treatment. No doubt principles should be applied to like cases in a like manner. But there is no inconsistency in refusing to apply a principle to cases that are relevantly dissimilar.
Principles obviously allow of exceptions. A person who fancies himself 'consistent' in opposing both abortion and capital punishment on the ground that all human life is worthy of respect will in almost all cases make an exception when it comes to killing in self-defense or killing in a just war. Now wouldn't it be absurd to accuse such a person of being 'inconsistent'? "If you were consistent in your valuing of human life, you would value the life of the jihadi who has come to decapitate you and your family, and you would not lift a finger against him."
One who opposes abortion but supports capital punishment is neither logically nor pragmatically inconsistent.
3. Diachronic or 'Emersonian' Consistency. Here is a famous passage from Ralph Waldo Emerson's "Self-Reliance" rarely quoted in full:
A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do. He may as well concern himself with his shadow on the wall. Speak what you think now in hard words and tomorrow speak what to-morrow thinks in hard words again, though it contradict every thing you said to-day. (Ziff, 183)
People routinely rip the initial clause of this passage out of its context and take Emerson to be attacking logical consistency. But he is doing no such thing. It should be clear that Emerson’s dictum has nothing to do with logical consistency and everything to do with consistency of beliefs over time. The consistency in question is diachronic rather than synchronic. A “little mind” is “foolishly consistent” if it refuses to changes its beliefs when change is needed due to changing circumstances, further experience, or clearer thinking.
It should be clear that if I believe that p at time t, but believe that ~p at later time t*, it does not follow that I hold logically inconsistent beliefs. Doxastic alteration, like alteration in general, is non-contradictory for the simple reason that properties which are contradictory when taken in abstracto can be had at different times. My coffee changes from hot to non-hot, and thus has contradictory attributes when we abstract from the time of their instantiation. But since the coffee instantiates them at different times, there is no contradiction such as would cause us to join Parmenides in denying the reality of the changeful world.
Belief change is just a special case of this. Suppose a politician changes her position for some good reason. There is not only nothing wrong with this, it shows an admirable openness. She goes from believing in a progressive tax scheme to believing in a flat tax, say. Surely there is no logical contradiction involved, and for two reasons. First, the property of believing that a progressive tax is warranted is not the contradictory, but merely the contrary, of the property of believing that a flat tax is warranted. (They cannot both be instantiated at the same time, but it is possible that neither be instantiated.) Second, the properties are had at different times. A logical contradiction ensues only when one simultaneously maintains both that p and that ~p.
Emerson’s sound point, then, is that one should not make a fetish out of doxastic stasis: there is nothing wrong with being ‘inconsistent’ in the sense of changing one’s beliefs when circumstances change and as one gains in experience and insight. But this is not to say that one should adopt the antics of a John Kerry or a Hillary Clinton or a Joe Biden. You will recall that the benighted and Biden reversed himself on the Hyde Amendment, for no good reason but for the purpose of self-promotion. So, while one ought not make a fetish of diachronic or Emersonian consistency, relative stability of views over time is a defeasible indicator of character.
Before leaving this topic, let's consider what Walt Whitman has to say in the penultimate section 51 of “Song of Myself” in Leaves of Grass:
Do I contradict myself? Very well then I contradict myself, (I am large, I contain multitudes.)
Here it appears that Whitman is thumbing his nose at logical consistency. If so, the Emersonian and Whitmaniab dicta ought not be confused.
4. Why be consistent? Ought one be consistent in any of these three senses? It is self-evident that one ought to strive to be logically consistent. For if one's beliefs are logically inconsistent, then they cannot all be true, which implies that one or more of them are false. The ideal doxastic set would consist of beliefs that are both true and consistent. Logical consistency by itself is not enough since false beliefs can be consistent. But logical consistency, though not sufficient, is necessary for true beliefs and thus a goal worthy of pursuit.
As for pragmatic consistency, consistency in the application of principles to like cases, this too seems to be a goal that ought to be pursued. Can I prove that we ought to treat like cases in a like manner? Well, can you prove its negation? If burden-of-proof considerations are relevant here, the burden is on you.
Logical and pragmatic consistency are norms partially constitutive of rationality. A rational person strives for both. Diachronic or Emersonian consistency, however, is not a rational norm or epistemic desideratum. On the contrary, one ought to change one's beliefs when new facts and arguments so warrant.