Your side of the argument has some interesting side effects which lead me to consider the requirement that an argument have premises be faulty.
I would agree with WillO that the most accepted form of argument would be a Formal Proof. This form of argument is the most accepted because its language is the most precise, leading to a surprising resilience against vacuous arguments. Each Formal Proof starts with a finite set of axioms, which I believe can safely be compared to your word "premises" without loss of generality.
WillO's claim is that it is valid for that finite set of axioms to be the empty set, and nothing immediately comes to mind to countermand that. Forbidding the empty set also has an interesting implication: A proof with zero axioms may be deemed "invalid," but a proof with one axiom: "P or not P" magically becomes valid, even if P never appears in the proof.
Forbidding this rather absurd looking tactic is difficult. How do you claim "an axiom is assumed true," but forbid axioms that are provably true? What about proofs which depend on an unproven theory (such as the Riemann Zeta theorem)? Do all such proofs become invalid if the Riemann Zeta theorem is proven, simply because one axiom is now provably true?
I think it would be difficult if not impossible to meaningfully reject a Formal Proof with an empty set of axioms without causing a large number of undesirable artifacts. Given the popularity of that form of argument, I would say that should be case closed for the debate unless someone can find quotes otherwise.
In your comment argument, Lukas, you mentioned "Pick up any logic textbook, it will tell you that there has to be at least 1-2 premises, depending on the author" This quote caught my attention because, in context, it looked like a poor argument. WillO had cited a single source (which actually does say it can be empty: "finite sequence" is a very specific mathematical term that includes empty sequences), and you argued any textbook should contradict him, without providing one yourself, leaving him to dig through dozens of textbooks in search of a sentence to prove your point that he doesn't believe in.
However, it is true that most arguments have premisses, and often they are of small number. If it was not a rule that you have premises, might there still be some reason behind your position? I think there might be.
The number of things which can be successfully argued without premisses is vanishingly small. It's certainly not reasonable to make meaningful debate about something important like "freedom," "meaning," or "good" with an empty-set of premisses. Those words are too hard to discuss without dragging human ideals into the debate, and those do not have mathematical or logical meanings which could allow them to be manipulated in a Formal Proof.
This leaves arguments without premisses as suspect. An argument without premisses cannot prove anything which was not already in the formal system used as part of the proof. This creates a sticky situation where either:
- The listener already agrees with the speaker on the conclusion, so it does not matter how valid or invalid the argument may be. One may even say no argument took place.
- The listener disagrees with the speaker on the conclusion. If there are no premisses, then the listener must disagree with the Formal System used to prove the argument.
The latter is a bother because the issues in comparing formal systems are innumerable. It requires vastly more study and attention to detail to identify inconsistencies in formal systems than it takes to identify inconsistencies in arguments made with the formal systems. Mathematicians may debate for centuries over whether or not a particular class of proof is valid, and they literally make a living at it.
Thus, if you claim something profound from an argument with no premises, it is common for people to reject the claim outright, knowing that there is a good chance they lack the mathematical prowess to attack the formal system issues. It isn't to say that an argument without premises is invalid, but it does serve as a strong indicator to a listener that the speaker has not fully thought out the argument. There are likely premises sneaking in part-way through the argument, and someone will have to tease them out (this is known as "missing premisses"). The presence of premises is not proof that an argument is good, but the lack of premisses calls it into question.
So for the final round trip, I ask when does it make sense to make an argument with no premisses. For this, I must hand-wave away one thing which could be considered a premise: the formal system itself. No argument can be made without a system to make the argument in. If that counts as a premise, then your answer is correct. However, I see no evidence that this is a standard definition of "premise.*" So I will make the assumption that "premise" and "axioms for a formal proof" are identical while trying to make a meaningful argument with no premise.
Consider a proof style called "proof by contradiction." The goal of this style is to argue the opposite of your claim and demonstrate that doing so leads to an unacceptable proposition proven true (such as proving a contradiction). Consider that you have made an argument of your own, with premises, using a proof system which is different than mine. Consider that I agree with your premises, but not your conclusion. Clearly there is a disagreement within the proof system, but even if I am mathematician who can spend a decade dissecting your system, you wouldn't understand the results unless you too were a mathematician.
A proof by contradiction could discredit your proof system without either of us having to truly understand why the proof system is invalid. To make such a proof, I will make an argument in your proof system without premises. I will then use the proof system to generate an unsatisfactory proof. For example, if I can use your proof system to prove "It is acceptable to kill red-headed women on Tuesdays, but only if they are wearing earrings," without a single premise, that would leave your proof system highly suspect (unless that's your religion's sort of thinking!).
By making such a proof, I force your hand. You must either accept that, given any set of premises you choose, I can twist the argument into killing red-heads, or you are forced to include a special premise which forbids it in every single proof you make. The constant presence of this bothersome premise discredits the strength of your proof system, and eventually you will choose a different one.
For a less violent more mathematical example, consider "the axiom of choice (AoC)." AoC is an axiom is set theory that states "If I have a set containing non-empty "child" sets, I can create a new set by taking one element from each of the child sets." This is intuitive: if I have 10 bags with items in them, I can easily make an 11th bag by taking one item from each bag. This is so intuitive, that we often assume it as part of our formal system, as is done in the set theory called Zermelo–Fraenkel set theory with the axiom of choice (ZFC)
However, there are some very nuanced details that show up as we look at infinite sets of infinite sets. It takes years of college math to appreciate why these issues arrive, but it takes far less study to appreciate the consequences. There is a proof in ZFC which can take a sphere, cut it into 5 parts, rotate them, and re-assemble them into two spheres, each with the same volume as the original. No cheating, no empty cores, no spongy material. The math just works.
This bothers mathematicians so much that they often do not accept ZFC proofs, just because they've seen something that unnerves them and seems intuitively false. They limit themselves to ZF proof (Zermelo–Fraenkel without AoC). This proof that doubles two spheres has no premises in any proof system which has ZFC baked into it.
A classic resolution to this is to use proof systems which have ZF baked into their syntax, but not ZFC. One then adds the axiom of choice as a premise. Thus, most arguments for ZFC are made with at least one premise, but the original trouble-maker that cause people to reject ZFC based proof systems was an argument with no premises... thus showing such arguments are useful.
So, in summary: An argument with no premises is reasonable and meaningful. One purpose for such arguments is to discredit proof systems which appear to be generating undesirable relationships between premises and conclusions.
* Given that I just called you on an argument like this, claiming overwhelming literature support without actually citing any, let me know if you disagree with this claim and I'll actually go dig up a few examples or concede that part of the argument. I'm hoping you simply agree with me, because this is a linguistic topic, so there will be a lot of muddiness in the literature. I want to avoid that digging if at all possible. Clarity is good.