5.5 Simplifying Propositions Into Standard Logical Form - From "The Reasonable Person" by Mark Grannis
One of the key steps in thinking and arguing logically is reducing down language into standard logical form. Humans speak in different types of modes and expressions and this isn't always conducive to understanding the meaning behind those expressions as a logical proposition. And so rephrasing what someone is saying into its simplest logical form helps to get at the heart of the power, or lack thereof, of their thinking. "Recall our 'golden rule' for dealing with ambiguity of terms: 'To unmake an ambiguity, make a distinction.' To apply a similar principle to propositions, we might say, 'To clarify a confusing proposition, ask questions.'"
There are four steps which can help us simplify information into standard logical form. Now this may involve the changing of words or terms, and that is okay, as long as the deeper meaning is the same.
1) "Our first step should be to unpack any language that is figurative rather than literal:" Here we have to see to the deeper meaning of a metaphorical language. If I say that "It's raining cats and dogs outside.", it is necessary to see beyond the phrasing to its actual meaning. We could translate this to: "The weather right now is producing a lot of rain."
2) "Second, identify the subject and predicate we will use in our translated proposition." Here we must precisely identify what the subject and predicate are. In other words, what is the thing itself versus what is being attributed or denied of that thing. Brackets here can be used to enclose subject and predicate (which often contain more than one word). "Also remember that both subject and predicate can be as complicated as they need to be in order to permit the use of a linking verb as the copula." We could then put the example in a form like this: {The weather right now} is {producing a lot of rain}.
2) "Second, identify the subject and predicate we will use in our translated proposition." Here we must precisely identify what the subject and predicate are. In other words, what is the thing itself versus what is being attributed or denied of that thing. Brackets here can be used to enclose subject and predicate (which often contain more than one word). "Also remember that both subject and predicate can be as complicated as they need to be in order to permit the use of a linking verb as the copula." We could then put the example in a form like this: {The weather right now} is {producing a lot of rain}.
3) "Third, remember to add 'tw' or 'twi' as appropriate to change both subject and predicate into units that operate like nouns." To keep the standard form of subject, verb to be, and predicate, we must use "that which" or "that which is" to keep the predicate as a noun. We could continue with the example like this: All {The weather right now} is {that which produces a lot of rain}.
4) "Fourth, identify the quality and quantity of the proposition."
When determining the quality of the propositions it is tempting to convert everything into a universal affirmative proposition, but we really should ask if the original statement is affirming or negating the subject and predicate of each other. If it implies a negating then we should use the universal negative E instead of A. "Try not to make the common rookie mistake of forcing every natural-language statement into an affirmative form, because some statements, like 'Cheaters never win,' or 'You can't always get what you want,' clearly suggest a negative form."
For quantity one must determine whether the subject and predicate involved are involving all or only some in their distribution. This, again, can be hidden by tricky phrases and words.
When determining the quality of the propositions it is tempting to convert everything into a universal affirmative proposition, but we really should ask if the original statement is affirming or negating the subject and predicate of each other. If it implies a negating then we should use the universal negative E instead of A. "Try not to make the common rookie mistake of forcing every natural-language statement into an affirmative form, because some statements, like 'Cheaters never win,' or 'You can't always get what you want,' clearly suggest a negative form."
For quantity one must determine whether the subject and predicate involved are involving all or only some in their distribution. This, again, can be hidden by tricky phrases and words.
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