Political disagreement is ultimately rooted in philosophical disagreement. So if the latter is objectively irresolvable, then so is the former. I claim that both are irresolvable due to value differences that cannot be resolved either by appeal to empirical facts or by reasoning. In illustration of my thesis, consider the the values of individual liberty and material (as opposed to formal) equality. I will assume that both are indeed values to which all of us accord respect. Even so, value conflict can arise in the form of a conflict of prioritizations. I value liberty over equality, while Peter, say, values equality over liberty. That difference suffices to put us at serious odds despite the fact that we both value liberty and equality. The conflict over prioritization — our difference as to which trumps which — makes the following aporetic tetrad objectively irresolvable:
1. Justice demands redistribution of wealth from the richer to the poorer. A just society is a fair society, one in which there is a fair distribution of the available social and economic goods.
2. Wealth redistribution requires an agency of redistribution which forces, via the coercive power of government, the better off to pay higher taxes, forego benefits, or in some other way compensate the worse off so that greater material equality is brought about.
3. Coercive redistribution violates the liberty of the individual.
4. It is wrong to violate the liberty of the individual in the way that redistribution requires.
It is easy to see that the limbs of this tetrad, despite the plausibility of each, cannot all be true: the first three, entail the negation of the fourth. Indeed, any three of them entails the negation of the remaining one. To solve the inconsistency problem, one of the propositions must be rejected. But which one? (2) and (3) are uncontroversial and so not candidates for rejection. This leaves (1) and (4).
The conservative/libertarian will reject (1) while the liberal/leftist will reject (4). Each will thus solve the problem — from his own point of view. But surely neither amounts to an objective solution to the problem since the solutions are logically incompatible and both are equally rational and equally consistent with all relevant empirical facts.
Indeed, this is why there is a philosophical problem in the first place. There is nothing illogical about the conservative or liberal positions: neither falls afoul of any logical rule or canon of reasoning. And there is no empirical fact that allows us to decide between the two positions. The difference between the positions is ultimately rooted in a value difference, specifically, a difference concerning the prioritization of liberty and equality. To the conservative, it is self-evident that liberty is such a high value that no consideration of material equality or fairness of distribution could provide any reason to violate the liberty of the individual by, for example, taxing him at a higher rate because he is more economically productive. To the liberal,on the other hand, it is is just self-evident that justice demands redistribution and so a certain amount of coercive taking of what belongs to the productive and a giving of it to the less or non-productive(for example, in the form of food stamps).
Because the doctrinal differences are rooted in a value difference, the doctrinal difference can be objectively resolved only if the value conflict can be objectively resolved. But the latter cannot be, not by any appeal to empirical facts and not by any abstract reasoning. If so, the political dispute regarding liberty and equality is objectively irresolvable.
I conjecture that all of the fundamental political problems are like this. All are at bottom philosophical problems representable by an aporetic polyad consisting of propositions which are individually plausible but not jointly consistent. If so, a certain political pessimism is the upshot. We cannot resolve our political differences by appeal to empirical facts or by abstract reasoning or by the two together. We are stuck with irreconcilable differences rooted in ultimately divergent values.
The question then becomes one of figuring how we can nonetheless continue to live with each other in some semblance of peace despite our irreconcilable differences. Federalism may be part of the answer. See my post Can Federalism Save Us?