Is this argument valid?

Thank you so much Kaiden for this answer and forgive me for the late response.

I have 2 questions if you don't mind; however, the first might sound a little weird: I was wondering how did you think of the answer to this question, as in, how did you come up with the scenario where an abstract object that depends on a concrete object necessarily exists, yet the concrete mustn't necessarily also exists. Your answer makes so much sense; I think it's because I was assuming that dependence meant that the object (in this case the concrete object) must exist to sustain the abstract. Is there a methodology to suss out these assumptions?

For the second question, I was wondering isn't this argument begging the question or circular in some sense? if the conclusion is that concrete objects exists necessarily and we derive that from the premise that abstract objects depend on concrete objects for their existence, aren't we already assuming that concrete objects exist?

[To Theo]

An un-weird and appropriate question. I haven’t been sure what to say because it’s not a common question I receive. But I’ll say this. 

My way of coming up with the scenario was to use imagination to create a counterexample. I saw that the argument was an invalid deductive argument. One way of proving such an accusation is to give and explain a counterexample. A counterexample is a description of a logically possible circumstance in which the premise of an inference is true, but the conclusion is false at the same time and in the same circumstance. 

Logical possibility here is about consistency: the sentences describing the circumstance can all be true at once, according to their form, or, seen from a different perspective, no contradiction can be derived from the sentences. 

In the case of your argument, I didn’t elaborate on my counterexamples at length in my post, but the gist is that I created a story in my head in which pizza slices and billiard racks come in and out of existence, playing a role in keeping triangle in existence. As long as the circumstance imagined is within the broad boundary of logical possibility, it can be as outlandish and goofy as you like (even defy physics and metaphysics.) Counterexamples are funny, attention catching, simple and get the job done.

For the second question…

I see what you mean. However, it seems to me that the sentence in premise 2 is not expressing the statement that there are abstract objects and that there are concrete objects. Instead, it is telling us a necessary condition of the existence of abstract objects. It is stating that abstract objects are a kind of thing that need concrete objects in order to exist. As far as the second premise is concerned, there may not actually be any concrete objects so as to fulfill the condition and, accordingly, there may not be any abstract objects. 

I think it's because I was assuming that dependence meant that the object (in this case the concrete object) must exist to sustain the abstract. Is there a methodology to suss out these assumptions?

 This assumption could be true, as far as premise 2 is concerned. Premise 2 does not require that this is true, though, which makes room for my counterexample. 

I'm glad this AI is able to work out that the argument is invalid. The example it gives using its own existence is on the right track, too. More accurately, it would be like arguing: 

1. Some AI bots exist necessarily.
2. AI bots depend for their existence on WIFI networks. 
3. So, at least one WIFI network exists necessarily. 

What really follows from the premises is that it is necessarily true that there exists some WIFI network or other. What the arguer fails to see is that the premises allow the necessity mentioned in premise 2 to be fulfilled without there being a particular WiFi network that necessarily exists. The premises allow for each particular network to exist non-necessarily, just as long as it is impossible for there to not be any network at all. 

What follows from the premises is necessarily, at least one WIFI network exists,  not at least one WIFI network exists necessarily.

Ironically, I think we trained the AI having almost of decade of discussions on logical fallacies here :)

[To Bo Bennett, PhD]

I confess it is ironic. But since you said it first, we can divide 60-40 any heat that comes our way for saying this out loud. I’ve been reading through the AI responses. The bot is very funny, I wish I could write like it does. And it is very capable.

I am aware that I am not a timely replier. I usually struggle in conversation to know what to say back to someone unless confronted with a pointed question (or a critique!).