If it is not the case that humans have freewill then God is to blame for the presence of evil.

Question

this is the rest of the question It is the case that humans have free will. Thus God is not to blame for the presence of evil.Use both the direct and indirect truthtable to show whether the above argument is valid

Answer 1

I can't easily draw a truth table in this written response, but I can talk you through how to do it!

To determine whether the argument is valid using truth tables, we should break it down premise by premise:

1. If it is not the case that humans have free will, then God is responsible for the presence of evil.
2. It is the case that humans have free will.
3. Therefore, (and this is the conclusion,) God is not responsible for the presence of evil.

Notice that premise 1 is comprised of premise 2 and the conclusion, connected in a particular way, captured by the "if... then...". We can write out the premises out using 'sentence letters', to capture their logical form (and for now ignoring their content), and that will make it clear how they all relate to each other. To do this, we just need to identify all the distinct claims and the relations between them in the argument:

1. Let the claim "It is the case that humans have free will" be represented by the letter "P".
2. Let the claim "God responsible for the presence of evil" be represented by the letter "Q".
3. And now we can write out the premises again, like this:
4. Premise 1 becomes "¬P --> Q"
5. Here, "¬" indicates the logical operation of negation, to translate the "not", and "-->" indicates the logical operation of material implication, to translate the "if... then..." in the original premises.
6. Premise 2 becomes "P".
7. The conclusion becomes "¬Q".
8. Here again "¬" indicates the logical operation of negation, to translate the "not" of the original conclusion.

So, our argument has the following logical form:

1. ¬P --> Q
2. P
3. ¬Q

This is actually famous form of an invalid argument. Let's see why!

To start, consider what it means for an argument to be logically valid. An argument is logically valid if there is no possible world in which the premises are true and the conclusion is false (at the same time, or in the same world).

Truth tables are a great way to test this out, because they set out all the possible combinations of truth and falsity for the premises and conclusion. Each 'world' is represented by a row in the truth table.

A direct truth table just writes out the scenario in the same way as the argument. I'll do my best to write out a truth table in the formatting of this box...!

P Q ¬P ¬Q ¬P-->Q

T T F F T

T F F T T

F T T F T

F F T T F

Notice that to make things easier, I started from the left with our basic propositions of P and Q, and wrote all the possible combinations of P and Q being either true or false. I then did the same for ¬P and ¬Q, and notice that if P is True, then ¬P must be false, and vice versa. Finally, I put in the meaty part of our argument, the conditional expression ¬P-->Q from premise 1, and filled that out based on the rest of the truth table.

A conditional expression is true in all cases other than where it is proven wrong. It is proven wrong only in those cases where the antecedent (the "if", before the arrow) is true and the consequent (the "then", after the arrow) is false, which occurs in row 4.

So, let's analyse the table!

Remember how we defined validity: an argument is valid if and only if there are no possible worlds in which the premises are true and the conclusion is false. So, we only need to look at the table to find out if there is any such row!

Premise 1 is represented by the last column, and is true in rows 1, 2, and 3. Premise 2 is represented by the first column, and is true in rows 1 and 2. So, we only need to look at rows 1 and 2 for worlds in which the premises are all true. The conclusion is represented by column 4, which is false in rows 1 and 2. There is at least one row where the premises are true and the conclusion is false, so the argument is not valid!

What about indirect truth tables? This is a method where you assume the negation of the conclusion and see if that assumption contradicts with the premises in any rows. Examine the truth table to check if there are any rows where all the premises are true while the negated conclusion is also true. If such a row exists, it means there is no contradiction, and the argument is invalid. If no such row exists (i.e., there is no row where all premises are true and the negated conclusion is true), the argument is valid.

So, our conclusion was ¬Q, and the negation of ¬Q is ¬¬Q, which is the same as just Q. The negation of the conclusion is therefore represented in column 2 of the truth table we made. This negation is true in rows 1 and 3. Let's check the status of the premises (columns 1 and 5) in those rows. I'll give you only the relevant rows and columns below, for ease:

P Q ¬P-->Q

T T T (row 1)

F T T (row 3)

In row 1, we can see a scenario where the premises are true and the negated conclusion is true, so there is no contradiction between the premises and the negation of the conclusion. Because there is no such contradiction, we know that the argument is invalid!

In conclusion, because the direct truth table shows a scenario where the premises are true and the conclusion is false, the argument is invalid. The indirect truth table also supports this by demonstrating that assuming the negation of the conclusion does not lead to a contradiction, reinforcing the argument's invalidity.

Answer 2

The short answer is that if there is no free will, then there is no good nor evil either, for moral judgement becomes logically impossible. Without free will we all become puppets on a stage, playing out our destined roles. Knowing what the play is really about, who is the audience or author, or why it is being staged is beyond the capacity of human beings to ever know.

That's the short answer.