If-then sentences are closer to necessity whilst is-so is related simply to validity (though validity and necessity are in each others definitions.)
If-then can make an argument into one single sentence.
eg. Ann is a widow, so she is a woman, is an argument made up of two sentences.
But If Ann is a widow, then she is a woman, is one sentence.
If Ann is a widow, then she is a widow
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Logically necessary no matter the meaning of the words.
Ann is a widow, so Ann is sad.
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Deductively invalid
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However, it could be an enthymeme, we want to be charitable
You could add [all widows are sad]
This would be logically valid.
However, this hidden premise is not necessary
(The gap that we have to bridge is very big, so the hidden premise we add should be a strong premise)
Ann is a widow, so Ann is a woman
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Not logically valid, but deductively valid (ie. Given the definition, it is true)
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If we treat this argument as an enthymeme, we could add the hidden premise [all widows are women].
→ this would be logically valid.
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This sort of hidden premise is not logically necessary however, but it is deductively necessary. This is the measure on how strong a reason we have to presume an enthymeme.
Every deductively valid argument can be made into a logically valid one by adding deductively necessary premise.
The sort of logic we are doing is very old, eg. John Buridan ca. 1300-1360. According to the professor, the greatest logician of the middle ages.
Had an affair with the queen of france, as her logic teacher, and was killed by drowning for this.
The boundaries of logical validity:
All F are G, some H are F, so some H are G.
What are really topic neutral words?
We want to be able to clearly delineate which words are topic-neutral and which are domain specific (or non-top-neutral words).
eg. Topic neutral: all, some
Can we give a criterion for topic-neutral words?
If this is not the case then logical validity and vague boundaries.
A > B > C
Deductively valid
Logical validity depends on how we make the parts of it into topic neutral words
eg. a is more F than b, b is more F than c, so a is more F than c.
But this form doesn’t work with certain categories, like:
2 is more even than 4, 4 is more even than 6, so 2 is more even than 6
This doesn’t make sense.
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This sort of solution only works for things that can be more or less, and not either/or when being instantiated.
But if we start to add specificity to our argument, we are making the entire argument domain specific.
In everyday language we usually interpret ”some” as meaning ”not all”.
This is warm > it is not hot
is not a valid argument, however, it is a form of pragmatic reasoning.
Some A are B /> not all A are B
’Some’ > ’at least one’
If you are a man, then you are not smart. [Lorenz is a man], so Lorenz is not smart.
If there is consistency in the premises, the argument can be valid.