General tips:

• Most arguments are in a generally syllogistic form. This means that the conclusion should naturally follow from the previous statements. That means it’s usually not effective to try and target the conclusion.
• You often need the ideas from another person to take down an argument. Consider taking in your options before outright contradicting someone.
• If you gain an idea from someone during an argument it’s usually not going to be useful fodder for attacking their next arguments since they’d have it mind already.
• Just because two ideas are incompatible (e.g. it’s too hot today, it’s too cold today) does not always mean they can be used to argue against each other (e.g. it’s a matter of your subjective experience; no accounting for taste).
• Ideas that seem applicable to a lot of arguments (e.g. our senses can be doubted) will not work on all arguments (e.g. you can’t understand love because we can’t trust our senses is not valid reasoning).

Haunting Tips:

• Haunting characters is all about vibes. Attack them with ideas that directly conflict with their personalities:
  • Reimu is simple.
  • Suika is wild.
  • Youmu is single-minded.

Spoilerless Walkthrough:

Socrates

• Question him. His actual arguments are fairly coherent until pressed for further details.

Suika

• She’s much trickier than she lets on.
• She likes to subvert convention.

Reimu

• She already likes you so it won’t take much to get her to back down.
• Simple arguments work well on her.

Youmu

• She won’t back down so easily and has firm convictions. I would save her for last.
• Look out for her sword! Make sure you have plenty of credibility going into her argument.