In logic, consistency and inconsistency are important concepts. They are also relational concepts in that a claim, by itself, is neither consistent nor inconsistent. It can only be consistent or inconsistent relative to another claim.
Two claims are consistent when both can be true at the same time. For example, the claim “lying is sometimes acceptable” is consistent with the claim “lying is sometimes unacceptable.” This is because both claims could be correct.
Two claims are inconsistent when both cannot be true at the same. They can, and this is important to note, both be false at the same time. For example, the claim “national health care would do more good than harm for America” is inconsistent with the claim “national health care would do more harm than good for America.” This is because while these claims cannot both be true at the same time, they could both be false. National health care might, for example, be neutral in terms of overall benefits and harms.
While people sometimes use “inconsistent” and “contradictory” interchangeably, they do not mean the same thing. If two claims contradict each other, then one must be false and the other true. For example, the claims “God exists” and “God does not exist” are contradictory claims. If one is true, the other must be false.
Because of the nature of inconsistent claims, if someone makes inconsistent claims, then at least one of their claims must be false (and it is worth remembering that all their claims might be false). Similarly, if a person accepts principles that are inconsistent or entail inconsistent claims, then at least one of the principles must be flawed. This assumes, of course, that principles have truth values. Not surprisingly, theories must also be internally consistent-a theory that has inconsistencies must contain at least one false claim.
The fact that two (or more) claims are inconsistent does not show which of them is false—the inconsistency just shows that they all cannot be true at the same time. Sorting out the true from the false is another matter entirely.
Given that logically inconsistent claims cannot be true at the same time, it is irrational to accept such claims when their inconsistency is known. This can be used a basic method of argumentation.
Step 1: Show that two claims made by a person or principles held by a person are inconsistent.
Step 2: Conclude that both cannot be true/correct.
For example, suppose Kelly seems to accept the that people should be treated equally but also asserts that certain people should receive special treatment. On the face of it, there seems to be an inconsistency here: If people should be treated equally, then certain people should not receive special treatment. But, if some people should receive special treatment, then all people should not be treated equally. Therefore, one of the principles must be incorrect.
While this method is logically solid it suffers from the usual weakness of logic as a persuasive device. People can, of course, simply hold to inconsistent claims and refuse to be persuaded that at least one of them must be false.
Of course, the fact that there is an inconsistency does not show which claim or principle is mistaken—it just shows that at least one must be incorrect. Unless, of course, there is a reasonable way to respond to the charge of inconsistency.
As with most attacks and criticisms, there are ways to respond to a charge of inconsistency. One way is to abandon one of the inconsistent claims or principles. Obviously, the least plausible claim or principle should be the one rejected. For example, Kelly might decide to abandon the principle that some people should receive special treatment and stick with the principle that people should be treated equally. This is obviously not much of a defense. However, if there are excellent reasons to reject one (or more) of claims, then this would be the logical thing to do.
In some cases, it is possible to respond to the charge of inconsistency by dissolving the inconsistency. This can be done by showing that the inconsistency is merely apparent. This is achieved by arguing that the claims/principles are consistent. For example, Kelly might present the following reply: treating people equally requires providing special treatment to certain groups or people. For example, allowing equal access to public facilities requires provided some people with special treatment in the form of ramps and special parking. Thus, the inconsistency has been dissolved.
While logical consistency and inconsistency are straightforward, things can get complicated when other philosophical views some into play. For two claims to be logical consistent they must be true or false (but not both at the same time). If the claims are relative, subjective or without any truth value, then the situation becomes rather problematic.
Relativism is the view that the truth of a statement depends on the culture. This relativism is most often presented in the context of ethics and aesthetics. Obviously, cultures with different moralities will present claims that are inconsistent with each other. Assuming relativism is correct, the truth of such ethical claims depends on the culture, so a claim can be true in one culture and false in another.
Even on the assumption that ethical relativism is true it is still possible to apply a charge of inconsistency—but only within that culture. For example, in the 1800s American social morality (as expressed in the Declaration of Independence and countless speeches) held that all men are equal. Yet, slavery was also accepted by the culture, thus making it at least morally tolerable. Obviously, the acceptance of slavery and the professed value of equality are inconsistent with each other. Hence, one of those views must be mistaken—within the context of American culture.
Of course, a culture could accept as a moral principle that moral inconsistency is morally acceptable. In that case, the charge of inconsistency would bear no weight (assuming that relativism is correct).
Subjectivism is the view that the truth of a statement depends on the individual. As with relativism, this view is most often presented in the context of ethics and aesthetics. Individuals with different moralities will obviously present claims that seem to be inconsistent with each other. For example, one person might claim that abortion is morally acceptable while another person endorses it. If ethical subjectivism is true, the truth of each moral claim depends on the individual, so a claim can be true for one person and false for another. In this case, inconsistency is not a problem because it simply cannot occur between individuals. Everyone is correct because morality is subjective.
However, even if subjectivism is true, a person can be charged with inconsistency in their claims. However, a person could hold that moral inconsistency is perfectly acceptable and if subjectivism is true they would be “right.”
Nihilism is the view that claims have no truth value—they are neither true nor false. As might be suspected by now, nihilism is most commonly presented in ethics and aesthetics. If moral claims are neither true nor false, then there is no possibility of logical inconsistency between moral claims Hence, if moral nihilism is correct, then inconsistency in regard to moral claims and principles is impossible.
“…Kelly might present the following reply: treating people equally requires providing special treatment to certain groups or people. For example, allowing equal access to public facilities requires provided some people with special treatment in the form of ramps and special parking. Thus, the inconsistency has been dissolved.”
I think this is somewhat dangerous semantic territory. I would say that “treating people equally requires providing special treatment to certain groups or people.” is not about treatment, but about guaranteeing outcome.
I happen to be a tall person, one who has a lot of difficulty flying “coach” on airlines, and even in trying to comb my hair in public restrooms without having to bend over. I would still claim that the airlines treat everyone equally – you purchase the seat you want for the price they ask; I don’t believe that my height entitles me to any special accommodation, despite the fact that it seems patently unfair that the 5’3 woman sitting next to me can have a far more enjoyable flight than I, unless I spend considerably more money than she has to.
Of course, I would wholeheartedly support a move by the airlines to offer height-based seating – that if you fly coach and are over 5’10”, you can be seated in a section with more legroom for the same price – but I don’t consider that “treating people equally”. It’s treating people unequally, but perhaps for a very good reason.
I think that Kelly can accept that people should be treated equally, but allow that that principle might require some exceptions in certain situations.
(In fact, I proposed the idea of “variable height-based legroom on flights” on a forum once, after a particularly painful cross-country red-eye flight. I was flamed mercilessly, even by people who support “equal outcome” accommodations for a wide variety of personal differences. It led me to this “exception to the rule” idea, because once you open those floodgates, “equal treatment” becomes an absolutely undefinable and constantly debated concept.)