Arguments consist of premises and conclusions. They can also be linked, where conclusions of individual arguments make up the premises of a 'global' argument. Some of the 'local' arguments that can make up a 'global' argument are arguments from Sign, Analogy and Cause just to name a few. Each of these have strategies associated with them that can be used to challenge them effectively, but this is beyond the scope of this discussion. For more information on these concepts, check the references section of this document.
Step one in a critical discussion is to agree to principles of behavior before you start. I recommend something like van Eemeren and Grootendorsts "Rules for a Critical Discussion". They say things like 'remember you may be wrong', 'don't use personal attacks', 'stay relevant' etc. If the one participant uses a personal attack or tries to avoid answering the question and goes off on a tangent, a charge of lack of relevance is warranted. Stay focused to avoid being distracted by these diversionary tactics.
Step two is to agree on the premises of the discussion. If the existence of Leprechauns entails evidence, then that is one place to start. You can both begin to present your evidence. And remember, there is no shame in being wrong. It's character building.
Are Leprechauns plausible, is an easier position to argue from either viewpoint because it entails using defeasible reasoning to argue whether it is likely or not that Leprechauns exist. Arguing about the fact of their existence is more difficult from the point of view of the principle of Burden of Proof. If a proponent says that something exists, and the respondents says something like 'show me the body', the proponent can always say that not all possibilities of discoveries have been exhausted. This has the weight of presumption in its favor because of the efficacy of the scientific method in fields such as the sciences (medicine, physics etc.) law and technical maintenance (electronics, automobile etc) and others not listed. The scientific method presumably works for these fields and showing that it doesn't will be a struggle for the respondent. Proponents and respondents must always be open to new information to avoid holding untenable conclusions.
The most tenable viewpoint is that because of the preponderance of evidence (positive or negative), Leprechauns either are likely or not likely to exist. There is a valid reason to doubt that Leprechauns exist beyond a reasonable doubt because of the preponderance of negative evidence regarding Leprechauns. The respondent, however, cannot show that they do not exist because the respondents definition of reasonable doubt will not be the same as the proponent believer. There is a popular phrase that goes "You can't prove a negative". This is counterintuitive but logically it depends on your requirement and acceptance of evidence.
When involved in a discussion about whether or not Leprechauns exist, the strongest arguments for the respondent in a discussion like this will come from the principle of "Negative Evidence" and "Negative Proof". One reason for this is because it will account for the 'moving goalpost' type of arguments typically found in this type of critical discussion. If the proponent tries to use equivocation (changing a previously stipulated definition or properties) or demand more evidence than is reasonable (impossible precision), the respondent can show that since they both agree that the existence of Leprechauns entails evidence, that there is no evidence where there should be or of the type there should be and therefore the preponderance of Negative Evidence (lack of evidence or evidence that suggests another cause) makes their existence reasonably implausible. In order to get around this the proponent must claim that evidence is not relevant (as in the case of faith), in which case there can be no discussion and they have disqualified themselves by getting caught in a contradiction or somehow try to disqualify the negative evidence, possibly by equivocation. Good luck with this argument in a community of Leprechaun believers, especially if their local economy or their well-being depends on it.
What follows is an analysis of the argument of the proponent. The argument is laid out using the Toulman argument model where the validity of the conclusion is supported by the premises and the premises are supported by the warrant of data. The warrant is like a the bridge between the data and the premise. Each of the properties of the support for the conclusion are labeled with a 'P' a 'W' and a 'D'.
The proponent says that Leprechauns exists and the respondent has doubt about this claim.
The proponent says that Leprechauns exist because there exists a valid presumption
P: There are documented cases in the past of Leprechaun sightings.
W: That the documents are reliable testimony and necessary if not sufficient to support the conclusion
D: newspaper article that John smith saw a Leprechaun on such and such day
D: newspaper article that Jill brown saw the evidence of Leprechaun visitation in her house.
Argument from Tradition, more or less.
P: There exists a cultural belief that Leprechauns exist.
W: All these people wouldn't believe if it weren't true. They can't all be wrong.
D: Collectively all these people have reasons to believe
D: A lot of people believe that fire burns, and in fact it does
Argument from Popularity.
P: We can see the effects of leprechauns in our environment
W: If Leprechauns exist, we should see their effects since we presuppose they are doing things
D: Unexplained things happen all the time, especially things that have been determined to be characteristic of Leprachauns
Argument from Cause.
P: There exists an artifact of a Leprechaun pipe
W: Leprechauns are known to smoke pipes
D: the artifact is in the museum
Argument from Sign.
P: There is independent evidence of leprechaun like beings in other cultures, even if descriptions vary.
W: Since there is independent evidence in other cultures, it creates a presumption that supports the evidence in this one.
D: In the Appalachians there beliefs in magical beings that live in the mountains
D: In Nordic cultures, there are beliefs in magical beings called Trolls.
Argument from Precedence.
P: Leprechauns are like foxes. They clever, quick and can hide easily
W: Leprechauns are clever and hard to catch.
D: Foxes are considered to be clever and hard to catch.
Argument from Analogy, inherently weak and easy to refute.
P: Leprechauns are supernatural beings making them difficult to find
W: Leprechauns would use their powers to their advantage.
D: The supernatural factors exist because no one has proved that they don't
Argument from Ignorance.
P: Leprechauns are supernatural beings making them difficult to understand
W: Because of their supernatural abilities it makes their world view impossible for us to understand because we cannot possibly share their perspective because we are not supernatural.
D: Supernatural factors exist because no one has absolutely refuted evidence suggesting that they do.
Argument from Ignorance
Laid out like this, it is easy to see where to start with the argument. In a face-to-face discussion with people that are not familiar with structured discussion, it is much harder. The warrant and the data are rarely presented without a request, but to challenge the argument effectively, they must be revealed. The concept of the "unstated premise" is similar to the warrant, and you must look for these as well. It usually constitutes figuring out what is inferred, or what factors a statement depends on but has not been addressed so far.
The respondent should challenge the conclusion by rebutting the premises of the proponent using critical questioning according the strategy most effective for the type of argument that is being refuted. In the process of rebutting the premises of the proponent, it is usually necessary to challenge the warrant and the data. Sometimes the warrant is valid but the evidence is not. The respondent should avoid making claims where possible for a couple of reasons. The first reason is that it is preferable to shift the burden of proof to the other party. Many logical fallacies do this very effectively. The second reason is that whoever asks the questions is in control of the discussion.
The respondent should try to get the proponent to commit to statements that support the respondents conclusion. In doing so, the respondent can get the proponent to make contradictory claims, it which case the proponent must retract or commit to an untenable conclusion. For example, getting the proponent to commit to the premise that in the case of four witnesses of a robbery, there will be four conflicting stories that agree to some degree. The respondent can use this to point out that testimonial evidence is weak compared to other forms and an example of this is the "telephone game" that children play. Another example is to get the proponent to admit that in cases where there was a strong presumption in favor of the supernatural, it was later proven that there were natural causes. Such is the case with schizophrenia and Germ theory.
References:
Toulman, Stephen. 2003. The Uses of Argument. 2nd ed. Cambridge University Press
Walton, Douglas N. 1995. Argumentation Schemes for Presumptive Reasoning. Lawrence Erlbaum
Walton, Douglas N. 2005. Fundamentals of Critical Argumentation. Cambridge University Press.
Walton, Douglas N. 1996. Argument from Ignorance. Pennsylvania State University Press.
Damer, T. Edward. 2004. Attacking Faulty Reasoning. 5th ed. Wadsworth Publishing
Freeley, Austin J. 1993. Argumentation and Debate: Critical Thinking for Reasoned Decision Making 8th ed. Wadsworth Publishing Company
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