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Semantic holism, simply put, is the idea that words have no meaning apart from the context, or sentences, in which they are used. This can, perhaps, be better understood by looking at the meaning of holism, and contrasting it with another view of meaning, atomism.
Holism is the idea that something can be more than the sum of its parts; more specifically holism usually refers to reality. It contends that one must understand reality as a whole; that one can't start by examining the parts of reality and end up with an accurate picture. This is more easily seen if we look at biological holism. For example, a duck is more than simply a collection of "duck parts", and thus we can not break a duck down into "duck parts" and end up with an accurate picture of a duck.
Holism can be contrasted with atomism, which is the idea that everything can be broken down into smaller parts. Applied to biology one would argue that one can obtain an accurate picture of a duck by breaking down the duck into fundamental "duck parts".
Apply holism to language and we get semantic holism. The idea behind semantic holism is that every word has meaning only in relation to other words, sentences, or the language (as a whole) in which it is used. For example, semantic holists would argue that the word "tree" does not always refer to the same object for everyone. More specifically, if I say "All trees have green leaves" and you say "No trees have green leaves", there is not necessarily a disagreement. Both of us could simply be referring to different concepts of a tree. Atomism, on the other hand, would claim that one of us is wrong. Either my statement "all trees have green leaves" is false, or your statement "No trees have green leaves" is false.
There are a few criticisms of holism, which may help shed light on exactly what it is. The first one being that there is no sentence which can be thrown out as incomprehensible or irrational, unless you are the speaker. This is a consequence of semantic holism because you, as a listener, most likely don't subscribe to every assumption that the speaker is making. This leads to a second criticisim; that is, since our concepts are in a constant state of flux, and since the meaning of every word is determined by its relation to every other belief you have, you can't "translate" what you meant by a previous statement. (See indeterminacy of translation).
Jackman, Henry "Moderate Holism and the Instability Thesis" American Philosophical Quarterly, Vol. 36, No. 4, October 1999. http://www.yorku.ca/hjackman/papers/holism-and-inst.pdf
Cornwell, William "Epistemological Holism and Semantic Holism" University of Connecticut http://www.callisto.si.usherb.ca/ybouchard/symposium/2001/pdf/cornwell.pdf
Rough definition of holism from: http://dictionary.reference.com/search?q=holism
Hardcastle, Gary L. "Themes in Contemporary Analytic Philosophy as Reflected in the Work of Monty Python" http://monty.simstim.net