The purpose of Syntax is to determine why some sentences are grammatical sentences of a language, and why others are not. However, lexical semantics often has to step in where syntax cannot. For example, in the previous post, Syntactic rules could not explain why some verbs only allowed certain argument structures. And this makes some sense. After all, it is clearly not on the structure (syntax) alone that we exclude these sentences, because they are perfectly viable with other verbs. This is well used in Computer Science, for example. An integer plus operation specifies that it requires two integers, and will not, for example, add two rational non-integers. Even more broad, in many computing languages, 2+yellow will not process (unless yellow has been named separately as a numeric object).
To go deeper down the rabbit hole, following Jackendoff, Beavers, Levin, Pinker, and others, I posit that human language is deeply grounded in a mental physics. For example, we can see that non-agentive verbs do not allow for agentive adverbs (28), language can tell when an object is affected in some way (29), and even to what degree objects are affected (30). In the first case, adverbs like ‘intentionally’ are fine with some verbs, and not with others. In the second case, verbs that entail a change of state in their object (kick) can be preceded by ‘what happened to the O is that’, whereas verbs that do not entail a change of state in their object (like run). Finally, in the third case, verbs which entail a change from state not-X to state X cannot take conative constructions (via the at particle), whereas verbs which simply entail a potentially repeatable change of state can. These two examples yield the semantic notions of agency and patienthood respectively, while the third adds more nuance (John Beavers categorizes break as taking a totally affected object, and cut as an affected object.
(28) I intentionally left my phone on during the movie.
(28b) I (*intentionally) noticed the fly in the corner of the room.
(29a) What happened to the puppy is that Sven kicked it.
(29b) *What happened to five miles is that I ran it.
(30a) I broke (*at) the bread.
(30b) I cut (at) the bread.
As well, another key notion to language is direct causation. For example, we can say that Jane broke a window if she threw a baseball at it, but not if she failed to catch a baseball thrown at a window. Moreover, we say Jeff dimmed the lights when he turns a switch down but not when he draws power to another device (say, by turning a microwave on). Our language notion of causation is not one fully grounded in actual physics, but in our mental physics, the same faculty people often use to determine guilt (the difference between murder and manslaughter, for example).
Now of course, one could argue that this is not a function of language, but rather a function of cognition. However, these distinctions are made on the fly in language all the time, with very little error, and as early as age two, suggesting it to be a natural, and not a developed function. From this, we can begin to conclude that our syntax is constrained by semantics, a semantics rooted in a conceptual physics. By investigating the mysteries of semantics, we discover how the human mind sees the world.