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Truths+Propositions
All > Sections > Illogic Primer > Truths+Propositions (3)
Definition
Propositions and their truth values are two elemental ingredients of logical reasoning.
Propositions
A proposition is an assertion that something is the case. We use sentences to express propositions. A sentence may be made of black ink, be on a page, and be four inches long. But the content of the sentence cannot be found on the page. The proposition it expresses appears to be a non-physical entity which can be in the mind.
Examples:
  1. The following sentences express the same proposition:
    1. Il pleut.
    2. Esta lloviendo.
    3. It is raining.
    4. Es regnet.
  2. The following sentences express the same proposition:
    1. John loves Mary.
    2. Mary is loved by John.
Proof: It makes sense to think of a proposition as being the meaning of a sentence. The meaning of a sentence has several components:

  • denotation: the state of affairs in the world that the sentence holds to be the case.
  • connotation: the feelings, ideas or emotions evoked in the reader by the sentence.
  • emphasis: the relative importance the writer ascribes to different elements in the sentence.

For example, in the sentence "The fire raged down the hill" the denotation of the sentence is the assertion that there is a fire buring on a hill and moving down the hill. The connotation is that this is something to be feared (the word "rage" implies anger or danger). The emphasis in this sentence is the fire itself; had we written the same sentence "Down the hill raged the fire" the emphasis would be on the hill.

Philosophers argue a lot about meaning. Some say that the meaning is the denotation only, some say it is a combination of denotation and connotation only, while others say it is all three.

Truths
A proposition can have the following truth values: true or false. "P" is true if and only if P. "P" is false if and only if not P. In other words, a proposition is true if and only if what it says about the world is in fact the way the world is. Though this correspondence view of truth has long been questioned, and especially so in these postmodern times, it remains our common sense, everyday understanding of truth.
Examples:
  1. The proposition "Snow is white" is true if and only if snow is white.
  2. The proposition "Snow is white" is false if and only if snow is not white.

Props to Stephen Downes
Many kudos to Stephen Downes, the logician who authored the lion's share of content on this page. We are extremely appreciative of his articulate and comprehensive summary of logical fallacies. Stephen Downes content is denoted by his copyright, "©Stephen Downes." A mirror of Downes original site can be found here. His blog is Half an Hour.