
Greg L. answered 10/13/15
Philosophy Grad Specializing in Logic and the LSAT
This is one of the fundamental questions of philosophy--metaphysics in particular, and more specifically ontology. Ontology is the study of the nature of reality, existence, being, and becoming. Epistemology likewise is the study of the nature of knowledge.
Your question could be stated, "How does one know that the external world is real?" Alternately, "Are external objects real?"
Plato's Socrates denies the reality of the external world. For him, reality is not something perceived by the senses. The material world, ever changing, is merely an image or copy of the real world--the unseen and unchanging world of forms.
Berkeley and other subjective idealists assert that reality is immaterial, fundamentally mental in nature. Familiar objects such as tables are only ideas in the minds of observers, and cannot exist without being perceived.
Naïve realism (direct realism, common sense realism) theorizes that we perceive objects as they really are, we have direct awareness of the external world, and our claims of knowledge are justified.
Locke's scientific realism asserts a distinction between primary qualities and secondary qualities of objects. Primary qualities such as solidity, extension, motion, number, and figure are independent of any observer. Primary qualities exist and can be determined with certainty. Secondary qualities such as color, taste, smell, and sound are properties that produce sensation in observers but do not provide knowledge of objective facts about things.
Here is my short answer: We cannot be certain that the table is real.