This is a very open question. How would you start?
We could start by thinking about what the questioner means by 'logic'. By 'logic' the questioner probably means something like 'argument' or 'reasoning', although there are other kinds of 'logic', like 'maths' or 'formal logic'. Mathematical or formal logic is written in symbols (think numbers or computer code). 'Logic', even if it is not mathematical or formal, emphasises the strong link between 'steps' in the argument, and the objectivity of the argument (not emotional, the kind of argument a computer would accept). Anyone who is rational (not mad and not influenced by their emotions) should accept a truly logical argument.
So a logic is a kind of strong 'argument'. An 'argument' and 'logic' are not the same: there are 'logical' arguments and 'illogical' arguments. Think of an ‘illogical’ argument. We are interested in logical arguments, good strong arguments, the kind that would convince anyone who isn’t mad or emotional. The kind that would convince a computer.
Within 'logic' there are different kinds of argument/ reasoning, 'analytic' and 'synthetic'.
What does 'analytic' mean? 'Analysis' - drawing out what is already there in the definition. Think of an analytic statement:
If you are single you are not in a relationship/ married.
What does 'synthetic' mean? 'Synthesis' - putting together empirical evidence. Think of a synthetic argument:
All observed swans are ‘white’. Therefore all swans are ‘white’.
Which is a stronger kind of argument? Which is more useful? Which could be considered proof?
Analytic arguments are generally stronger but less useful because they don't tell you more than you already know. Both could be considered proof though.
What about the starting point of a logical argument?
'Logic' gets you from A to D, via b and c., A > b > c > D. As well as having logical steps, and argument that proved the existence of god would have to have a strong starting point ‘A’. It’s no good starting in the wrong place and continuing logically. And we can’t get to ‘A’ by logic, because we can’t offer proof for our starting point, otherwise we would always be going backwards. Imagine if we offered proof for ‘A’ (a > A > b > c > D), then we would have a new starting point ‘a’. How do we get our starting point? Well we need a starting point that everyone can agree.
So if we are to have an argument for the existence of God, we would need to have a starting point that everyone can agree (‘A’) and then strong logical steps that everyone would accept to the conclusion ‘D’ that God exists.
What starting points have people offered? Think about the design argument; the cosmological argument; the ontological argument.
Does everyone agree on these starting points? Are these strong starting points?
E.g. the design argument: the order of the universe.
E.g. the cosmological argument: everything has a cause.
Eg. the ontological argument: the essence of god
How do these arguments move to their conclusion (analytically/ synthetically)?
E.g. the design argument
The universe is beautifully ordered & everything that has order has a designer > the universe has a designer (god)
What about this further assumption? ‘Everything that has order has a designer - is this analytic or synthetic?
E.g. the cosmological argument.
Everything has a cause > the universe must have a cause. This is an analytic - drawing out what is already there. 'Everything' includes the 'universe'
What is the main weakness in logical arguments?
Starting points or steps within the argument?
Can you think of any other arguments for the existence of god? Where do they start? How do they move to their conclusion?
E.g. Religious experience
Can logic prove the existence of god? What do you think?
Even within 'logic' there are different kinds of reasoning, 'analytic' and 'synthetic'. What does 'analytic' mean? 'Analysis' - drawing out what is already there. What does 'synthetic' mean? 'Synthesis' - putting together empirical evidence.
Which is a stronger kind of argument? Which could be considered proof?
Are there analytical arguments