If I think, therefore I am, if I think of something that thinks, does it also exist?
The first part is an argument, and a good one, I suppose. As to the latter, yes, but because it thinks, not because you did, although that too might be a meta-property?
About the latter, under the belief that to say of something that it exists is to say of something it has properties, I would conclude that the something exists if thinking is a property. Essentially, if there is something true we can say about something, then there must be something; otherwise we couldn't say something true about it--not even accidentally, as what we would be saying isn't about something.
This is where it's paramount to make a distinction. The distinction between A and B. I've given what needs to be distinguished labels, only because it's the distinction (and not the miscommunication that could ensue by the lack of precision in our language). A would be properties and B would be some other word (oh say, "attributes")
Onward to the unicorn, to illustrate, but first, the word, "unicorn." That definitely exists. What I'm saying is that the word, "unicorn" exists. I can say something true about it. It has seven letters. I can say several true things about it. It starts with a vowel, for a second example. So, clearly, very clearly, I would imagine, it (the word) has properties. Since it's true (if it is, and I think it is) that to say of something that it has properties is to say of something that it exists, then we can be comfortable in our conclusion that the word, "unicorn" exists.
But, do unicorns exist? Statues of unicorns exist. Drawings of unicorns exist. Ideas of unicorns exist. That's all great, but if we're diverting our attention from the word to what the referent would be if there were unicorns, then we can forgo the entertainment of all those other things that exist, like statues, drawings, and ideas. So, do unicorns exist? Not what they "exist as"--such a corrupt noun-phrase, as it is, but do unicorns themselves actually exist. Yes, actually, I say, for if they do not actually exist, then they do not exist.
This is where we could turn our attention and try to see if we can successfully identify a property that unicorns have. Not what they would have if they did exist but actually have. In other words, we can look to the definition and glean it's meaning of the term and figure out that a unicorn is a white equine with a horn. A picture of an equine with a horn, we shall find, as pictures exist, but do equines with horns exist? Or, better yet, as I approach what I spoke of earlier as paramount, is the horn of an equine a property? No, it's what would be a property if it did exist. The property of an equine with a horn cannot be instantiated, and until it can, no such things ought to be considered a property of something that doesn't exist.
