Your whole post: good point.
BTW, mt wife’s only 5 foot 1/2 inches 
And mine is 4’ 10" - my little spitfire is the inspiration for my twisted argument above.
I think the prof’s concept of modal realism is wrong. I’m no expert here, Smears would be the better one to ask. But if the statement that the truth is a null-set is true in one possible world but not in other possible worlds (which your prof seems to admit), there is no reason to assert that the statement, “there is no truth” holds true. It may in some possible worlds, but not all. Since we have no effective means to assay whether or not we are in such a world (aside from pragmatic epistemology, which I imagine your prof rejects) we may well be in such a world. But lacking a meaningful assay, we also cannot be sure that we aren’t in such a world.
Given meaningful epistelomogies that assert a useful/meaningful conception of the truth, it therefore behooves us to ask why we ought accept his conception of the truth?
Thinking modally as you suggest:
Consider the proposition: “the professor who said ‘there is no truth’ exists”. Isn’t his existance at least contingently true in our world? Doesn’t he exist?
The statement ‘there is no truth’ was transmitted and is now being considered. (I’m pretty sure that’s what is happening here). What is the truth value of this proposition: “Human language exists.” ?
I could go on, but the fact he uttered the statement we are now discussing provides some category of truth for these propositions.
Did the proffessor actually say, “There is not, Ruth” 
in response to being asked if there is mayo in his sarnie.
So…
The only truth we have is what we experience (or percieve to) and this is ultimately limited firstly by our own interpretation and then further by our presentation of it to others - and then further by how others interpret that and so on. So if truth exists it is that which is not consciously realised or shared?
As soon as truth is glimpsed it is misunderstood and therefore no longer true. ](https://www.ilovephilosophy.com/uploads/default/original/2X/7/7c349bf1053f368a5729d053e1e91215f22ce66c.gif "Brick wall"){kind=small}
Well if that’s true…wait… I think I must have misunderstood it.
Could you explain it again, and again, and again?
I would if I was in any way close to the truth, but I misunderstand most things more than most 
While we need to hold onto our truths tentatively because they are always subject to revision or replacement, that does not mean we must deny the idea of having any truths - there are different views of how truth-claims can be tested/considered truth (see my eariler post in this topic). You have to be able to live your life: balance your checkbook, enjoy a meal, cross the street safely, teach children, make commitments (even if they have to change over time) - I don’t think one can actually live their life so skeptically (neither did David Hume by the way). The idea of truth is not a parlour game.
“Let us not pretend to doubt in philosophy what we do not doubt in our hearts.”–C.S. Peirce
Perhaps, then, I should say that truth is so subjective/relative/conditional that it does not lend itself well to being shared/explained/communicated without total misrepresentation?
there are billions of truths when you think about it , in depth
When it comes to “truths” is it not better to drink about it… in deep, deep depth?
Truth in minds is nothing more then a word.
Truth in reality must be everything.
Truth in law will be a unity.
Truth is a word. Truth is a fact. Truth is a law.
Truth is logical even it is out of your imagination.
Truth is ironic even you denied it.
Truth is always one.
A Pyramid of Lives
Lives are in different levels.
The only truth in the universe is reality.
A Life in Lives
Lives is the only principle.
The only truth on the Earth is the same.
A Family in Reality
Lives are a unity in the universe.
The only truth for all of us is a family of the Earth.
Teru Wong
“There is no truth”
It’s true.
Alcohol is the only truth with value