Clarity will be served if we distinguish at least the following senses of 'absurd.' The word is from the Latin surdus, meaning deaf, silent, or stupid. But etymology can take us only so far and is no substitute for close analysis. And beware the Dictionary Fallacy.
1) Logico-mathematical. The absurd is the logically contradictory or self-contradictory or that which entails a logical contradiction. Absurdity in this sense attaches to propositions or sets of propositions. A reductio ad absurdum proof, for example, is a reduction to a contradiction. It is a way of indirectly proving a proposition. One assumes its negation and then derives a logical contradiction thereby proving the proposition.
2) Semantic. The absurd as the linguistically meaningless. Meaningful words can be strung together in meaningless ways, or meaningless words can be strung together. Example of the first: "Quadruplicity drinks procrastination." (Russell) You might object that the Russell sentence is not meaningless, but necessarily false, and because false then meaningful. Example of the second: "The slithy toves did gyre and gimble in the wabe." (Lewis Carroll). There is nothing syntactically wrong with either the Russell or the Carroll sentence.
3) Existential. The absurd as the existentially meaningless, the groundless, the brute-factual, the intrinsically unintelligible. The absurdity of existence in this sense of 'absurd' is what elicited Sartre's and Roquentin's nausea. The sheer, meaningless, disgusting, facticity of the chestnut tree referenced in the eponymous novel, for example, described by Sartre as de trop and as an unintelligible excrescence.
4) Ordinary. The absurd as the manifestly false. To be precise, 'absurd' as it is mostly used in standard English by non-philosophers refers to that which is both factually false and manifestly false. "Pelosi's assertion that there is no border crisis is absurd!" In other words, Pelosi's assertion is factually false, and plainly so. What is manifestly false as a matter of fact needn't be logically or semantically objectionable.
Item for further rumination: In Christianity construed along Kierkegaardian lines, the apparent absurdity of human existence is redeemed by the Higher Absurdity of the God-Man on the cross.
Cultural note: the hipster depicted below is a parody of the beatniks of the late 'fifties and early 'sixties. It is what Joe Average imagined an 'existentialist' must look like: a goateed cat with a beret, dressed in black, smoking a cigarette, preferably a Gitane or an unfiltered Gaulois.
Autobiographical addendum: Things didn't work out with an early girlfriend. She complained that I was an 'existentialist' who was "down all the time." I did read a lot of Camus and Sartre in those days, but my favorite existentialists were the Dane, Kierkegaard, and the Russian, Nicholas Berdyaev. Lev Shestov came later. Karl Jaspers and Martin Heidegger are only loosely classifiable as existentialists.
