Solution
The phrase "THE PALE CAST OF THOUGHT" means Serious and prolonged thinking.
In the given passage, the author describes how great thinkers engage in "habitual meditation on the vast problems that underline human life," and how their views take "a sombre and melancholy setting from 'the pale cast of thought.'" This context suggests that the phrase refers to deep, serious, and extended contemplation.
The expression comes from Shakespeare's Hamlet and refers to the way prolonged deliberation can drain action of its vigor and immediacy. In the passage, it characterizes the profound, intensive thinking process that great intellectuals engage in when contemplating significant philosophical questions.
The phrase doesn't simply indicate:
- A state of mind during sickness
- A sudden flash of thoughts
- Just an unhappy state of mind
Rather, it describes the serious, deep, and sustained intellectual effort that characterizes profound thinking.
Hence, the correct answer is Option 4: Serious and prolonged thinking.