1st question type: "What do you mean by that?" used to get them to elucidate their view. Any question designed to get them to further explain themselves or clarify something after making a grand assertion falls here.
2nd question type: "How did you come to that conclusion?" People often assert things forcefully without actually giving any reasons for that idea. Just because something is possible doesn't mean it's plausible, let alone probable.. It's possible monkeys wrote Hamlet. Make the person give you an argument, reasons for their view, not just an opinion.
3rd question type: Leading questions. You must see the weakness in their argument. Pay attention to their response to question 2 and see if their conclusion is justified by their arguments or what presuppositions might be challenged. This step, unlike the first 2, is not automatic, it requires some insight and understanding of where you would like to lead the conversation to go. Use tact, don't come across as pushy or arrogant. "Have you ever considered..." is a good starter to this question type.
After discussions with people, review the encounter and think of ways you could have done better. Anything you didn't know or better directions you could have steered the conversation? It's also useful to spend time before interactions anticipating claims you will face and formulating responses.
When someone challenges you with a pseudo question, e.g. (who are you to...), respond with the 1st question type. Ask them to clarify what they are really asking or saying. For example, “What gives you the right to say someone else’s religion is wrong?” can be restated as “No one is justified saying one religious view is better than another.” It's easier to respond to the second statement than the first.
Statements that violate the law of noncontradiction are suicidal, they are inherently false. e.g. "My brother is an only child." He calls this "Formal Suicide." To respond to self- destructive statements first, pay attention to the basic premise, conviction, or claim. Next, ask if the claim applies to itself. If so, does it satisfy its own criteria, or is there an internal contradiction? If the exact same reasons in favor of another’s view (or against your own) defeat the reasons themselves, then the view is self-refuting. If you discover a problem, use a question (Columbo) rather than a statement to point it out.
Another type of statement is similar, it is not logically inconsistent to believe it, but any argument for it is inherently self-defeating. E.G. "It is wrong to say other people are wrong." It's possible to believe that without logical contradiction, but any attempt to argue for it contradicts itself. He calls this "Practical Suicide."
Another is "Sibling Rivalry." This is 2 objections that contradict each other, such as someone saying they believe good and evil are relative but also saying how could God allow so much evil in the world.
The 4th type of "suicide" argument is "Infanticide" which is an argument that requires what it says is false. Someone arguing against God on the problem of evil commits this because they have no grounding for their belief in absolute good and evil, only a God like the God of Christianity gives an adequate explanation for the existence of evil. Evil is not just personal preference.
Reductio ad absurdum (or simply reductio). This is a Latin phrase that means to reduce a point to its absurd conclusion or consequence. Take their view and extend it to its logical consequence to show that the view can't be true because it results in absurdity.
If someone is a 'steamroller" and rapidly fires off objections but then cuts in when you try to respond, you may need to confront that behavior and request that he do you the courtesy of letting you respond uninterrupted.
Science, as a philosophy, presupposes secular materialism, so even if its methods point to evidence for divinity or creation, scientists are forced to come up with a materialist explanation for the data, because the supernatural is a priori ruled out. For example, eyewitness testimony of Jesus' resurrection can't be real, because it's impossible for someone to rise from the dead.
If someone makes an objection that is based on something factually inaccurate, correcting the inaccuracy is in order. Specific and precise facts are more impressive and convincing than broad round estimates.
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