Sure it can. Your foregoing comment commits the logical fallacy of epistemological relativism, which is the idea that truth is either infinitely malleable, utterly irrelevant, unknowable, or nonexistent. Yet on the contrary, truth exists and is independent of what anyone thinks or feels about it.
Below are basic a priori axioms. That is, true synthetic a priori propositions; or, propositions which cannot be denied without necessitating their use in the denial.
1. I think, therefore I am. (Proof of the existential reality of one's own existence.)
If one did not exist in some form then one would not be able to even think "I do not exist."
2. Truth, and knowledge of truth, exists.
Whoever denies the existence of truth grants that truth does not exist. Yet, if truth does not exist, then the proposition "Truth does not exist" is true. And if there is anything true, then truth exists.
3. Conscious humans act. (Prof. Ludwig von Mises's Axiom of Action.)
It cannot be coherently denied that this proposition is true, since the denial would have to be categorized as an action.
As well, there are logically necessary implications of this axiom:
3. (a) With every action an actor pursues a goal; and whatever the goal may be, the fact that it is pursued by an actor reveals that he places a relatively higher value on it than on any other goal of action he could conceive of at the start of his action.
(b) In order to achieve his most highly valued goal an actor must interfere or decide not to interfere (which, of course, is also an interference) at an earlier point in time to produce some later result; such interferences invariably imply the employment of some scarce means (at least those of the actor's body, its standing room and the time absorbed by the interference).
(c) These means must also have value for an actor--a value derived from that of the goal--because the actor must regard their employment as necessary in order to effectively achieve the goal; and actions can only be performed sequentially, always involving the making of a choice, i.e., taking up that one course of action which at some given point in time promises the most highly valued result to the actor and excluding at the same time the pursuit of other, less highly valued goals.
(d) As a consequence of having to choose and give preference to one goal over another--of not being able to realize all goals simultaneously--each and every action implies the incurrence of costs. For example, forsaking the value attached to the most highly valued alternative goal that cannot be realized or whose realization must be deferred because the means necessary to effect it are bound up in the production of another, even more highly valued goal.
(e) At its starting point every goal of action must be considered worth more to the actor than its cost and capable of yielding a profit, i.e., a result whose value is ranked higher than that of the foregone opportunities. And yet, every action is also invariably threatened by the possibility of a loss if an actor finds, in retrospect, that the result actually achieved--contrary to previous expectations--has a lower value than the relinquished alternative would have had.
All of these categories--values, ends, means, choice, preference, cost, profit and loss, as well as time and causality--are implied in the axiom of action. The attempt to disprove the action-axiom would itself be an action aimed at a goal, requiring means, excluding other courses of action, incurring costs, subjecting the actor to the possibility of achieving or not achieving the desired goal and so leading to a profit or a loss. Thus, it is manifestly impossible to ever falsify the validity of Prof. Mises's axiom of action. As a matter of fact, a situation in which these categories of action would cease to have a real existence could itself never be observed, for making an observation, too, is an action.
4. Sapient humans are capable of argumentation and hence know the meaning of truth and validity. The so-called "A Priori of Argumentation". (This axiom relates strongly to axioms No. 2 and 3.)
It is impossible to coherently deny that one can argue, as the very denial would itself be an argument. In fact, one could not even silently say to oneself "I cannot argue" without thereby contradicting oneself. One cannot coherently argue that one cannot argue. Nor can one coherently dispute knowing what it means to make a truth or validity claim without implicitly claiming the negation of this proposition to be true (see axiom No. 2).
***
For more on the above, see the following works:
1. Prof. Hans-Hermann Hoppe, Economic Science and the Austrian Method (Auburn, Ala.: Ludwig von Mises Institute, 2007; originally published 1995)
http://mises.org/books/esam.pdf ,
http://webcitation.org/63rQDYtj2 .
2. René Descartes, Discourse on the Method of Rightly Conducting the Reason and Seeking for Truth in the Sciences, Part 4, p. 101 in Elizabeth S. Haldane and G[eorge]. R. T. Ross (translators), The Philosophical Works of Descartes (Cambridge, U.K.: Cambridge University Press, 1911), Vol. 1 of 2
http://archive.org/details/philosophicalwor01desc ,
http://webcitation.org/63rYLFB5m (Vol. 1);
http://archive.org/details/philosophicalwor02descuoft,
http://webcitation.org/63rYNaLr2 (Vol. 2).
3. Thomas Aquinas, Summa theologiæ, First Part, Question 2, Article 1, Objection 3; English translation: Laurence Shapcote of the Fathers of the English Dominican Province, revised by Daniel J. Sullivan, The Summa Theologica, Vols. 17–18 of Mortimer J. Adler, Clifton Fadiman and Philip W. Goetz (editors), Great Books of the Western World (Chicago, Ill.: Encyclopædia Britannica, Inc., 2nd ed., 1990), 60 vols.
See also my below article:
James Redford, "Libertarian Anarchism Is Apodictically Correct", Social Science Research Network (SSRN), Dec. 15, 2011, 9 pp., doi:10.2139/ssrn.1972733; PDF, 118091 bytes, MD5: e6de8181ad84c9d96400bb9582311c79.
http://ssrn.com/abstract=1972733 ,
http://archive.org/download/Liberta...yCorrect/Redford-Apodictic-Libertarianism.pdf ,
http://theophysics.host56.com/Redford-Apodictic-Libertarianism.pdf ,
http://webcitation.org/63xyCLjLm ,
http://pdf-archive.com/2013/09/10/r...arianism/redford-apodictic-libertarianism.pdf