An analogy can be a spoken or textual comparison between two words (or sets of words) to highlight some form of semantic similarity between them. Such analogies can be used to strengthen political and philosophical arguments, even when the semantic similarity is weak or non-existent (if crafted carefully for the audience). Analogies are sometimes used to persuade those that cannot detect the flawed or non-existent arguments.

The metaphor, according to I. A. Richards in The Philosophy of Rhetoric (1936), consists of two parts: the tenor and vehicle. The tenor is the subject to which attributes are ascribed. The vehicle is the subject from which the attributes are borrowed. Other writers employ the general terms ground and figure to denote what Richards identifies as the tenor and vehicle. Consider the All the world's a stage monologue from As You Like It:

All the world's a stage,
And all the men and women merely players;
They have their exits and their entrances; — (William Shakespeare, As You Like It, 2/7)
In this example, "the world" is compared to a stage, the aim being to describe the world by taking well-known attributes from the stage. In this case, "the world" is the tenor and "a stage" is the vehicle. "Men and women" are a secondary tenor and "players" is the vehicle for this secondary tenor.

A simile is a figure of speech comparing two unlike things, often introduced with the word "like" or "as".1 Even though similes and metaphors are both forms of comparison, similes allow the two ideas to remain distinct in spite of their similarities, whereas metaphors seek to equate two ideas despite their differences. For instance, a simile that compares a person with a bullet would go as follows: "John was a record-setting runner and as fast as a speeding bullet." A metaphor might read something like, "John was a record-setting runner. That speeding bullet could zip past you without you even knowing he was there."
Source(s):
http://en.wikipedia.org/wiki/Analogy#Rhetoric
http://en.wikipedia.org/wiki/Metaphor
http://en.wikipedia.org/wiki/Simile

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