Are these truth functors (4 examples)

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Reply Fri 29 May, 2009 03:31 pm
I am to determine if the following sentence functor's are truth-functors. There were 10. These four I'm not sure about, but this is how I'd answer.
Always grateful for the help I get here. Am I right on these 4?

1. If [A] or , and [not-A], then .

This is also not a truth-functor. That is because of the relationship A has to B. I could write If [the Blue Jays won the series in 1992] or [3 Independent MP's were elected in the last Canadian federal election], and [the Blue Jays did not win in 1992], then [3 Independent MP's were elected in the last Canadian federal election]. The relationship between A, B simply does not follow that in the negation of A, B is a necessary consequent. The sentence is entirely dependent upon my choice of constituent sentences and where I choose sentences that have only 2 possibilities If [the Republican's took control of the Senate in 2006] or [the Democrats took control of the Senate in 2006], and [the Republicans did not take control of the Senate in 2006], then [the Democrats took control of the Senate in 2006]. Because of our knowledge we know it can either be the Democrats or the Republicans at this moment in time, but there is nothing in the sentence alone that justifies this. What if there was a third party as there is in Canada. What then? This cannot be a truth-functor.

2. That [A] is caused by the fact that and the fact that [C].

Not a truth-functor. This is not a truth-functor. That [the Senate Democrats increased their number of seats in the 2008 election] is caused by the fact that [Democrats picked up some previously held Republican seats] and the fact that [Democrats did not lose any of their own seats]. Each of the constituent sentences are true, but does that validate the compound sentence. But the latter two constituent sentences (through true) were not necessarily the cause of the first constituent sentence.

3. Whether or not [A], it is raining.
This is a truth-functor. That it is raining will be maintained whether or not anything.
-Whether or not [their are clouds in the sky], it is raining.
-Whether or not [Margaret Atwood is a Canadian novelist], it is raining.
-Whether or not [This sentence-functor is a truth-functor], it is raining.
The whether or not encompasses any constituent sentence it seems and does not alter that it is raining. But what if the constituent sentence were "It is raining."

4. [A] because [A].

This is not a truth-functor. When because is defined as for the reason that, not truth value can be determined on a truth table
-[Pizza Hut provides menus] because [Pizza Hut provides menus].
The constituent sentence is true (Pizza Hut does provide menus). But it cannot be said that [Pizza Hut provides menus] because [Pizza Hut provides menus] is false. So why is this no a truth-functor. Perhaps because in no circumstances can it be true. In no circumstance will A be the reason for A.
 
goapy
 
Reply Sat 30 May, 2009 01:19 am
@Horace phil,
Horace;65599 wrote:

1. If [A] or , and [not-A], then .

This is also not a truth-functor. That is because of the relationship A has to B. I could write If [the Blue Jays won the series in 1992] or [3 Independent MP's were elected in the last Canadian federal election], and [the Blue Jays did not win in 1992], then [3 Independent MP's were elected in the last Canadian federal election]. The relationship between A, B simply does not follow that in the negation of A, B is a necessary consequent. The sentence is entirely dependent upon my choice of constituent sentences and where I choose sentences that have only 2 possibilities If [the Republican's took control of the Senate in 2006] or [the Democrats took control of the Senate in 2006], and [the Republicans did not take control of the Senate in 2006], then [the Democrats took control of the Senate in 2006]. Because of our knowledge we know it can either be the Democrats or the Republicans at this moment in time, but there is nothing in the sentence alone that justifies this. What if there was a third party as there is in Canada. What then? This cannot be a truth-functor.


Your justification for #1 seems convincing, but I remember the definition of a truth-functor as being a sentence-functor which has a full truth table.

[(A v B) & ~A] -> B

is a tautology. It seems to have a full truth table:

Code:
[(A v B) & ~A] -> B
T T T F FT T T
T T F F FT T F
F T T T TF T T
F F F F TF T F
^
The whole sentence is true regardless of the truth values of
the components.
I suppose it could be argued that if the sentence variables were replaced with declarative sentences, that the whole sentence would be true not because of the truth-values of those declarative sentences, but rather because of the truth-functional connectives of the tautology. But I still think it is a truth-functor. I could be wrong.

Also, since the whole sentence is a conditional (if/then) sentence, consider the logical force of material implication. '(A v B) & ~A' is the antecedent. The meaning of the sentence (and material implication) is IF the antecedent condition were met, it would be sufficient for the consequent. You ask "What if there was a third party as there is in Canada. What then?". Well, that condition is not the antecedent condition that is contained in the antecedent. If you suppose some other antecedent and conclude that the consequent must be false, you're committing the fallacy of denying the antecedent.

Some background on sentence-functors and truth-functors:

Code:A sentence-functor is defined to be a string of English words and sentence variables, such that if the sentence variables are replaced by declarative sentences, then the whole becomes a declarative sentence with the inserted sentences as constituents.

A sentence-functor which has a full (as opposed to a partial) truth-table is called a truth-functor. Some sentence-functors are not truth-functors because sometimes the truth-values of the constituent sentences are not enough by themselves to determine the truth-value of the whole. For example:

I know that [A].

has only a partial truth-table:

A | I know that [A]
-------------------
T | ?
F | F

Suppose that [A] is the declarative sentence 'The sky is green'. Whatever the truth-value of 'The sky is green', such truth-value by itself is not enough to determine the truth-value of the whole sentence 'I know that the sky is green', because if 'The sky is green' is true, such truth has no impact on the truth value of knowing that the sky is green.
 
 

 
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