Communication, non-natural meaning, is about the recognition and expression of intentions. Context plays a very important role here. As listeners, we normally use the context in which a sentence is used to extrapolate its meaning, in other words the intentions of the speaker.
In the contextless vacuum in which the sentence is presented to us in this particular case, we interpret it in the way that would have the most relevance for us - with the least effort in terms of processing it and inferring its meaning. This is because we are continuously cognitively searching for relevance, especially when engaging with language. In the context that the sentence is presented, we just imagine a speaker's intention to assert:
- Paul Grice was a 20th century philosopher.
... and this being a philosophy website and all that, we are able to identify the guy that we're discussing, and attribute some kind of truth value to the statement. We derive a lot of relevance from it. But note - if we look up Paul Grice on Facebook, for example, we'll find several hundred Paul Grices, which is problematic.
Let's imagine that someone has been talking about an old guy in a retirement home. This guy is a bit dopey and openly lets off wind etc in front of the other residents and is generally also a bit uncouth, a bit rough round the edges - and his name is Paul Grice. People are sometimes mean to him. Now the woman that's speaking about him is at the cafe with her friends. To improve his standing with them she decides to lead them on by making them think that he was a famous and erudite man in his previous existence - which he wasn't. So she says to her entourage:
- Paul Grice was a 20th century philosopher.
I think we'd agree that this sentence was false. Now, if we go back to the 'sentence' that was trundled out by the computer, it is less easy to say that this sentence is meaningful. We need a context and an utterer to be able to decode who the 'intended' referent of Paul Grice is. It's not possible in this instance to say there is one. There is nothing to choose between the Paul Grice of the OP's original question, Paul Grice in the retirement home and the other thousand contenders for Paul Grice on Facebook.
A sentence is just evidence of an utterer's intention to change their listener's state of mind. Even just to be able to decode the so-called 'sentence meaning' we need to input all the evidence we have about the speaker's intention to bring the required reading to life. So the claim that "Paul Grice was a 20th century philosopher" means something is, in some tangible sense, incorrect in this case, if by that we mean that we can decode what the speaker's intended proposition was. We can't.
What we really mean when we say that the sentence has meaning, is that we are able to see what it could mean, and also that the words that were produced by the computer have a certain relevance for us. But, it is perhaps, now we've considered it this way, easier to see it as an instance of natural meaning. We've peered at a load of inky marks and seen what someone might have meant if they'd produced the same ones. But this is a bit like looking at a cloud and seeing what looks exactly like a sketch that someone might have done of a dragon. We find it relevant and can make all kinds of inferences from it, but it is not an interpretation of an ostentatious attempt to change our state of mind by another speaker.