(Imported from Wikipedia)
Objectivism explicitly rejects the analytic-synthetic dichotomy. This dichotomy — which stems from the views of David Hume and Immanuel Kant — is the view that there is a fundamental distinction between statements that are true in virtue of meaning, alone, and statements whose truth depends upon something more (usually, upon the way the world is). Rand rejected the view that there is any such fundamental distinction, because she accepted that the meaning of a word is its referent, including that referent's every attribute. Consequently, any true proposition is in a way true in virtue of meaning, while its truth simultaneously depends upon the way the world is. In specific, Rand holds that the meaning of a non-singular term is the concept associated with that term, while this concept somehow includes or subsumes all the particulars of a given class, including all the attributes had by these particulars. Which particulars a concept subsumes, according to Rand, depends upon what the concept-coiner was discriminating from what when he or she formed the concept (this appears to be how Rand accommodates Gottlob Frege's insight that there are different "modes of presentation" of the same content). This view is a version of content externalism, similar in certain ways to the views of Hilary Putnam and Tyler Burge.
The analytic-synthetic dichotomy is intimately related to the distinction between a priori and a posteriori knowledge, as some philosophers believe that analytic truths are known a priori (i.e., they are justified independent of any experience), while synthetic truths are known a posteriori (i.e., they are justified in virtue of experience). Rand rejects the view that there is any a priori knowledge. All knowledge, she holds, including mathematical knowledge, is about the world (though possibly at some very high level of abstraction or quantization). Justification always terminates in the evidence of the senses.
The analytic-synthetic dichotomy is also related to the alleged distinction between necessary and contingent truths, i.e., the claims of a distinction between truths that could not have been otherwise and truths that could have been otherwise. Many contemporary philosophers believe that mathematical truths such as "2 + 2 = 4" are necessary (could not have been otherwise) while statements such as "There are eight planets in our solar system" are contingent (could have been otherwise). These notions of contingency and necessity have led many contemporary philosophers to elaborate metaphysical systems-building. In contrast, Objectivism holds that there is no distinction between necessary vs. contingent facts in the natural world (that is, all natural facts are necessary) and that the concept of "contingent" applies exclusively to the results of human choice (that is, there is a fundamental distinction between the metaphysical and the man-made). All facts hold in virtue of the natures or identities of the entities involved. Man-made facts hold in virtue of actions that were initiated by volitional beings ("I went to the grocery today" is a man-made fact, because I could have done otherwise). Metaphysical facts, by contrast, hold without reference to any action of a volitional consciousness.
Objectivism holds that, in a sense, all facts are "necessary": all knowledge is knowledge of identity, i.e., a statement that an entity (or aspect, potentiality, condition etc. of an entity) is what in fact it is. Many contemporary philosophers claim that, while the proposition "1 + 1 = 2" is "necessary" because true in all possible realities, the proposition "the atomic mass of hydrogen is 1" is "contingent" because it is not constant across possible worlds. Objectivism would reply that the second proposition is just as "necessary" as the first: if the atomic mass differed, the substance in question would not be hydrogen. Objectivism recognizes no legitimate meaning of "necessity" other than this one.
Additionally, Objectivism also accepts so-called "nomological" possibility and necessity. Statements of nomological possibility say that certain states-of-affairs are in accordance with natural reality in the sense that they reflect the potential of an entity to act in a certain way. For example, consider the propositions, "This glass could break" and "It could rain this weekend." These report truths, because they say that, it is in the nature of glasses that they can break (given the right circumstances) and similarly it is in the nature of the weather that it has the potential to produce rain. Objectivism analyzes counterfactuals, e.g., "If I had dropped this glass, it would break," in similar terms. Objectivism does not insist, as many contemporary philosophers do, that there must be some fact in another possible world for this proposition to correspond with, in order for it to be true. Objectivism also rejects the now-popular view that these nomological facts should be analyzed using a "possible worlds" framework that builds on a distinction between the necessary and the contingent.