The videos all have this format:
- Two or more people are having a conversation which Spock overhears, and he politely joins in to inform them that they are using a particular logical fallacy.
- One of them says, "His/her argument seemed to make sense." or "But I thought he/she/[name] was making perfect sense!".
- Spock acknowledges that it may seem so, but it's still invalid. He then explains the fallacy and how the character used it.
- The conversation ends with one of the characters saying, "I should rethink what I'm trying to say!", to which Spock agrees, then tells the viewer about how "even if an argument seems to make sense."
The setting can vary from engineering, the bridge, sickbay, to even places like the brig and the mirror universe bridge.
Star Trek Logical Thinking provides examples of
- Breaking the Fourth Wall: At the end of every video, Spock talks to the viewer.
- Continuity Nod: In the video for Ipse Dixit/It Simply Is, Harry Mudd mentions the androids who he made in Star Trek: The Original Series.
- Death of a Child: Discussed in "Appeal to Emotions" when Chapel and Rand wonder if the three missing children are OK and Chapel uses the fallacy by saying that they probably are because imagining kids dying is too horrible.
- Do Androids Dream?: In the video for the Ipse Dixit Fallacy, Harry Mudd asserts that androids are inferior to humans and Spock points out that he has no evidence.
- Fantastic Racism: In the video for Ad Hominem, Sulu and Arex display prejudice against Klingons because a Klingon killed a friend of theirs.
- Fourth-Wall Observer: Spock is the only character to break the fourth wall.
- Greed: Discussed in "Argumentum ad Nauseum" when Harry Mudd insists that playing on people's greed is the best way to con them.
- Logical Fallacies: The main purpose of the episode is to educate about flawed logic.
- Share Phrase: The phrases "The argument seemed to make sense", "I thought [name/pronoun] was making perfect sense", and "I should rethink..." seem common among the non-Spock characters.
- Sick Episode: In the video for the Argumentum ad Ignorantium, a woman has a cold, and in the one about false dilemmas, a Tellarite ensign has colic.
- Signing Off Catchphrase: Every episode ends with Spock saying, "It's only logical." This is usually, though not always, preceded with "Even if an argument seems to make sense, it cannot be valid unless the form is valid and that it does not exhibit one of the logical fallacies such as [fallacy]."
- Speech Impediment: One of the science officers pronounces his "W"s as "V"s.
- Uncertain Doom: In the Appeal to Emotions video, we never find out if the missing colonists mentioned lived or died.
- Villain Episode:
- Some videos take place in the brig and feature Cyrano Jones and Harry Mudd.
- Some videos take place with the evil mirror versions of Spock and co. instead of the regular versions.
- The War on Straw: One video is about the Straw Man fallacy, demonstrated by a Lt. Kyle saying that a lieutenant's idea of checking some of the compensators is bad because realigning all of them would take too long.