What is Logical streamlining?
- When reconstructing an argument, we should strive to display the logical relationships as clearly and simply as possible
- Somewhat messy and awkward (logically speaking). We need to:
- Eliminate extraneous material
- Make some implicit information explicit
- Supply connecting premises (according to the Principle of Charity)
Logically Streamline this Argument: “We read over and over that when all is said and done, what is best for the child is the family. But what would the elimination of the tax-credit for marriage mean? Less incentive to marry. And what would that mean? Fewer couples getting married. And what would that mean? A reduction of the proportion of children living in families.”
P1) If the tax credit is eliminated then there is less incentive to get married
P2) If there is less incentive to marry, then fewer people will get married.
C1) If the tax credit is eliminated, then fewer couples will get married
P3) If fewer couples get married, then the proportion of children living in families will be reduced
C2) If the tax credit is eliminated, the proportion of children living in families will be reduced.
P4) The proportion of children living in families should not be reduced
C3) Therefore, the marriage tax-credit should not be eliminated.
What is the Principle of Charity?
- In general, it is best to sacrifice validity to soundness when
reconstructing; an inductively sound argument is more useful than a valid but unsound one
What is a connecting premise?
P4) The proportion of children living in families should not be reduced.
… is a “connecting premise” – it needs to be made explicit in order to
make the argument valid
If we can somehow demonstrate that P4 is false (i.e., that the
argument is not sound), then we might have to reject the
conclusion, or else go back and find a better way to connect P1-P3
to the desired conclusion
What are generalisations?
- So the assertion of a conditional is often an implicit assertion of a
generalisation. - We must beware of this, especially if there is some question over whether the generalisation is a “hard” one or a “soft” one
What are the differences between these two conditionals?
1. All cats have blue eyes.
2. All siamese cats have blue eyes.
- The scope of generalisation 2 is narrower.(applies to a smaller set of things)
- Sometimes, it is useful to narrow or broaden the scope of a stated generalisation
- For precision: Soft generalisation -> Hard generalisation with narrower scope…
- For truth: False, narrow hard generalisation -> True soft generalisation
What is Relevance?
In some cases, we must exclude irrelevant information:
P1) Ichigo Ichie is usually fully booked
P2) I once went there for dinner with John Coltrane
C) Probably, Ichigo Ichie will be fully booked this weekend.
-P2 is irrelevant to C. But the inclusion of P2, if it’s false, could be the grounds for saying that the argument is not sound, even if that doesn’t affect the likelihood of C.
