This is a long-ass quote, but it's a good one to keep around for the next time we have someone talking about the "irrationality" or "illogicalness" of natural languages and existing conlangs; the alternative would be preserving the entire thread, which I think is of dubious value. (In that vein, I've left out part of the reply specific to the particular case.)
Salmoneus wrote:1. 'Reason' is not just avoiding contradictions.
The Law of Non-Contradiction (LNC) is only one of the three most widely (but not universally) accepted axioms of thought. It is more commonly accepted than the Law of the Excluded Middle, but less commonly accepted than the Law of Identity. The LNC by itself will not get you very far at all. Most people nowadays would also add some form of law of continuity (or define the LI to include it) (i.e. if it was true yesterday that it was raining on the 1st March 1582, it'll be true tomorow that it was raining on th 1st March 1582), but that's more controversial.
2. Avoiding contradictions is not necessary.
Logicians tend not to care about avoiding contradictions and inconsistencies per se - that's a metaphysical theoretical issue, not a practical logical one. What logicians are concerned about is the principle of explosion - ex contradictione quodlibet. This says that if you accept one contradiction, you must accept all contradictions, and indeed all propositions: if one contradiction can be proven, every possible proposition is true. Such a result is trivial (it makes everything true), and therefore useless, because a practice of argument that equally confirms all possible propositions is of no practical use.
[to backtrack a moment: inconsistency is when you claim a thing, and also claim the negation of the thing. Contradiction is when you claim both a thing and the negation of the thing simultaneously.]
Now, the principle of explosion follows from the operations of classical logic. Therefore, contradictions cannot be permitted in classical logic. But classical logic is only one of a wide array of possible, and useful, logics. [NB: there is no 'logic', only 'logics']. Some non-classical logics, known as paraconsistent logics, allow you to hold inconsistent propositions as true without inviting trivialism. This can be done either by directly casting aside the LNC by changing the assumptions that normally result in the principle of explosion, or by reducing the ability to move from inconsistency to contradiction (allowing you to keep inconsistency, the LNC and the POE) (i.e. restricting the ability to move from <p> and <~p> to <pv~p>).
Paraconsistent logics are seeing increasing use in many fields of philosophy, mathematics, computer science, and physics (such as in several mathematical approaches to quantum physics). Perhaps the most basic example is calculus, which as originally formulated by both Leibniz and Newton tacitly ignores the POE (early calculus was necessarily inconsistent, though need not be contradictory under some paraconsistent regimes), and though I gather that mathematicians have invented various excuses for this since, it's hard to avoid the conclusion that these are just excuses... formal interest in paraconsistency was revived in th 20th century following Goedel's proof that only inconsistent (and hence either trivial or paraconsistent) mathematics could be complete.
3. The LNC is very little use in practice
The LNC, even if accepted, only prohibits a thing being true and false in exactly the same way. This is largely irrelevent for human behaviour and beliefs. Because if someone wants to believe both <p> and <~p>, and you ask what they really mean by that, they inevitably mean that the truth of <p> leads them to do one thing, and the truth of <~p> leads them to do another, different thing as well, and this asymmetry of response shows that the two propositions are not being considered in exactly the same way. Or, at least, for any purported contradiction, it can always be argued that the two things are not intended in exactly the same way. This makes the LNC of almost no use in practical reasoning when dealing with anyone other than the most utterly, gibberingly insane (indeed, the LNC is also widely understood as a psychological truth - even the insane don't believe a thing and its negation in the same way at the same time).
4. Non-paraconsistent logic and non-dialethaeist metaphysics do not entail one another
Logic isn't about what's really true. Logic is just about permitted rules of inference from premises. It is possible to accept the LNC as a rule of argument while believing in metaphysically true contradictions; contrariwise, it is possible to deny the existence of true contradictions while also denying the necessity of the LNC as a rule of argument. So any argument against true contradictions does not serve as an argument for non-paraconsistent logic; and contrariwise, any argument for the utility of non-paraconsistent logics does not serve as an argument for the metaphysical claim that there are no true contradictions. [however, the belief that there are true contradictions is a pretty reasonable basis for rejecting non-paraconsistent logics, needless to say!]
So, it's really important to point out that the claim "contradictions are what's logically impossible; to embrace them is to embrace irrationality" is completely false. It is not logically impossible for contradictions to be true. It is 'logically impossible' within non-paraconsistent logics for contradictions to arise in a valid argument. These are not the same thing at all. Logic has no power over metaphysics, it only describes it. Specifically, employing a non-paraconsistent logic it is impossible to prove a contradiction (because a contradictory conclusion can never arise in a valid argument). But at the same time, employing a non-paraconsistent logic it is possible to prove that there are true propositions that cannot be proven employing a non-paraconsistent logic (thanks, Goedel!). Therefore it follows that, employing a non-paraconsistent logic, it is illogical to believe that it is (demonstrably) impossible for a contradiction to be true. (it may, however, be true that there are no contradictions, just impossible to demonstrate it logically). The metaphysics cannot be proven by the logic: even in non-paraconsistent logic, you can choose to adopt a contradiction as a premise. Non-paraconsistent logic just warns you that if you accept that contradiction as a premise, your conclusions won't be interesting - that doesn't mean, of course, that either the premise or the conclusions are not true. Logic concerns the preservation of truth (if you start with true premises, your conclusions cannot be false), not with the truth or falsehood of premises themselves.
5. Embracing contradictions is not to embrace irrationality
"Rationality" is not well defined. But most commonly it refers either to thinking that is internally guided by reason - calculating one's plans and beliefs through a process of logical deduction from premises - or that is externally in accordance with reasons - the process of determining one's plans and beliefs that most completely results in the outcomes that were desired. It is a pleasant nostrum to imagine that these two definitions are equivalent - that deductive reasoning is the best way to pursue desired outcomes - but in fact it's demonstrably false in many situations (because deductive reasoning itself has a cost, and heuristic-instinctual responses may be close enough to optimal to be 'cheaper' than the cost of a marginally superior but considerably more expensive (in time and effort) deductive reasoning process.
Importantly, however, your theory doesn't hold for either conception of rationality. In the internal conception, there are times when paraconsistent logics are part of deductive reasoning - when you are presented only with 'facts' that you know to be inconsistent but cannot further investigate the truth of, for example, a clever paraconsistent logic enables you to still use those facts to 'solve' many problems, while classical logic just instantly explodes and doesn't let you derive any conclusions whatsoever. Externally, because paraconsistent deductions can be more useful than classical ones, they can be preferred as tools in obtaining the optimal outcomes.
[these two concepts broadly correspond to traditional theoretical and practical reason, btw, though I don't think they're quite the same?]
6. Hardly anything is really irrational
It's nice to say that reason should guide our actions. But the sad truth is, the guidance offered by reason is limited, for the simple reason that hardly anything we ever see or do is genuinely irrational (in the 'internal' sense mentioned above), or else almost everything is irrational (in the 'external' sense mentioned above) but nothing can be shown to be so.
Something is only illogical when the conclusions do not follow securely from the premises. But virtually all errors in real life do follow from the premises - it's just that the premises are wrong. But believing a false premise is not illogical or irrational, but only misinformed. The problem is even greater when it comes to irrationality in the sense of self-defeating behaviour - not only can we never prove the truth or falsity of all the premises involved, but we have no independent evidence regarding what the individual values. If rationality is judged by efficiency in meeting the individual's desires, nothing can per se be irrational, inasmuch as it may be justified by an undeclared desire. And those desires themselves are neither 'rational' or 'irrational'. As Hume observes, it is not irrational to prefer the destruction of the world to the raising of my little finger...