What I want to argue is that the commandment is to place tzitzit on a garment that I wear as a normal garment, and if I wear a garment only in order to become obligated in the commandment, it still has to count as “the corners of their garments.”
And in the summer, a wool garment does not really count as “their garments,” because nobody wears it as a garment.

It seems to me that this reasoning is quoted in the name of Rabbi Yosef Shalom Elyashiv of blessed memory.

Ohad, no tzitzit garment at all (except for a tzitzit undershirt) is something you would wear just like that; it doesn’t look like a garment and it isn’t comfortable. So why should it matter why you’re wearing it?

Rabbi, look here at a scan from a book called Chazon Ish:

http://212.199.162.70/viewtopic.php?t=40049#p455719

In my opinion, the questioner is right, based on what is brought there.

With a regular garment, there is benefit from wearing it, but with a wool garment there is no benefit from wearing it, and therefore according to Tosafot it is exempt from tzitzit.

(Though even with a regular garment that one wears only for the sake of tzitzit, it still requires clarification what exactly the benefit of wearing it is.)

If a wool garment is not considered a garment and is exempt from tzitzit, that has nothing to do with the question whether one wears it only in order to fulfill his obligation. In any case it is exempt from tzitzit, full stop.

That isn’t correct.

As I understand it, “benefit from wearing” can be expressed in several ways. A person wears a garment in order to keep warm, to protect himself from rain, to look nice, to signal social status, and so on.
If someone wears a wool garment in the summer for his own enjoyment, say in order to look elegant (an expensive wool frock coat), he would certainly become obligated in tzitzit.

Here we are talking about a garment that is worn only in order to become obligated in tzitzit. With such a garment, one can distinguish and say that if the garment is not wool, there is apparently some benefit in it (I’m not entirely clear why), whereas if the garment is wool, then there is no benefit from wearing it in the summer.
What is the problem with that?

On the contrary, if one wears the garment only in order to become obligated in tzitzit, then perhaps even with wool one can put tzitzit on it. So this whole discussion is being conducted in a flawed way. It has nothing to do with whether you wear it in order to become obligated in tzitzit or just wear it. The question is whether a wool garment is obligated in tzitzit or not. That’s all.

The question whether a wool garment is obligated in tzitzit or not is of course a discussion in its own right.
I am arguing that there is another separate discussion about the definition of the commandment: that the commandment applies only to what is considered a garment, meaning something that people wear as clothing (for the reasons Aharon mentioned), and wearing a piece of wool in the summer does not fall under the definition of a garment. The fact that one wears it in order to become obligated in the commandment does not change the fact that this is not the kind of garment the Torah spoke about.
In the winter, that piece of wool is considered a garment, no matter its form (in response to Ish), because it actually keeps me warm in the winter and I benefit from it, and therefore it is obligated in tzitzit.

Just to sharpen the point: what I meant in my first sentence is that the discussion whether a wool garment is obligated in tzitzit or not is a discussion from the angle of the material of the garment—which materials are obligated in tzitzit.
And the second discussion, in my claim, is from the angle of the garment’s purpose. What is it being worn for?

All this was clear to me. I just don’t see what it has to do with the introduction that nowadays people wear it only in order to become obligated in tzitzit. You are claiming that wearing a wool garment does not obligate one in tzitzit, unless this is done in the winter to protect ourselves. The same claim could be made about any four-cornered garment worn nowadays, regardless of whether it is wool. It is not worn for any other purpose, it is not comfortable, and it serves no purpose other than creating an obligation of tzitzit. Its material makes no difference, because it is not a garment in any sense.

Just a note: all my life I have greatly wondered about the “frock-coat wearers” in the Lithuanian Haredi community.

The frock coat should have been obligated in tzitzit, and in order to exempt it they round off one of its corners, while they fulfill the commandment of tzitzit with a special garment they wear under the shirt.

With the outer garment there is benefit from wearing it, and with the inner garment there is not.
Common sense says to put tzitzit on the frock coat and give up the small tallit.

That is certainly true. I too have always wondered about this. Rabbi Yoel Bin-Nun wears a suit with tzitzit on it.

You can use a tzitzit undershirt; in my opinion it’s quite comfortable, though it’s been a long time since I wore a regular undershirt without it.
In any case, I recall that some claim it is less preferable because of sweat, as opposed to a small tzitzit garment.

“The same claim could be made about any four-cornered garment worn nowadays, regardless of whether it is wool. It is not worn for any other purpose, it is not comfortable, and it serves no purpose other than creating an obligation of tzitzit. Its material makes no difference, because it is not a garment in any sense.”

Exactly. My claim applies to all materials as well (I also mentioned this in one of my comments above).
It’s just sharper in the case of wool, because the halakhic decisors write that it is preferable to wear wool.

In the winter, every material is a plus because it adds warmth and I benefit from it, and therefore every material is obligated in tzitzit; then the consideration of the halakhic decisors comes in, that wool is preferable in order to satisfy all opinions.
In the summer, in my view there is no point at all (maybe there is no commandment in it?) in wearing any garment of any material that you would not otherwise wear. The only thing left is a tzitzit undershirt, because people do wear an undershirt in the summer as a garment.

We are repeating ourselves. Everything has been clarified. I said at the outset that the reasoning is plausible, and something along these lines already appears in Tosafot, though there it is not about the type of garment but about the general issue of wearing something in order to become obligated. Tosafot say that one who does not wear such a garment will not be punished in a time of divine anger, because there is no evasion here. But their assumption is that wearing in order to become obligated is also obligated in tzitzit, and that indeed seems to be the view of all the halakhic decisors. About this it was said: just because we draw analogies, should we act on them?

There is thin merino wool that can be worn in the summer, and some people do wear it in the summer even if they have nothing to do with tzitzit. What makes wool warm is the air pockets it contains that retain heat, but with the right structure it can actually be very suitable for summer. Silk, for example, is not suitable for summer at all.