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TL;DR: How can we use syntactic phenomena that target subject to design tests for subjecthood (or even possibly derive a cross-linguistic definition of subject)?

I am reading Van Valin's An Introduction to Syntax. It has many interesting examples of "syntactic phenomena that target subject", for example, reflexivization, relativization, wh-question and cleft formation and so on.

To my understanding, such phenomena often always target the subject but not necessarily exclusively so; they can sometimes target other grammatical relations, such as English cleft formation, which can certainly target direct objects as well as subjects, as demonstrated by the following sentences:

  1. It was his soni who _i stole the product.
  2. It was the productj that his son stole _j.

which are clefts both possibly formed from:

  1. His son stole the product.

Say we want to know whether his son or the product is the subject of this sentence. Relying solely on the fact that subjects can be clefted in English does not help us determine which of the two NPs is the subject. It is better to test with yet another syntactic construction until only one of the NPs is eligible to a construction, such as matrix-coding-as-object:

  1. I believe his soni _i to have stolen the product.
  2. *I believe the productj his son to have stolen _j.

Since matrix-coding-as-object applies to his son but not to the product, now we are more confident that his son is the subject in (3).

The above process is what I think is the utilization of syntactic phenomena that target subjects, which are observations that certain types of constructions only involve subjects (or potentially other grammatical relations as well), as tests for subjecthood in a sentence. By transforming a given sentence into constructions of one or more of these "certain types", we see if the resulting constructions are grammatical or not, and determine the subject based on such results. The more tests we apply, the more confident we are about our judgment. Is this process correct, or canonical in linguistics?

From tests for subjecthood, can we possibly derive a cross-linguistic definition of subject? I personally don't consider this possible, since we are only "more confident" about a constituent being the subject of an examined sentence with increasing number of tests we apply; we are never 100% confident.

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    Many of the tests for subjecthood in English give different results in borderline cases. For instance, in sentences with there-insertion, the verb doesn't agree with there (There {is a/are 3} deer in the yard), but there is targeted by Subject-Raising (There is believed to be a deer in the yard). Every rule, phenomenon, alternation, syntagma, construction -- whatever you call it -- has its own set of input, output, and boundary conditions. Plus, ergative case systems have no single concept that includes what "subject" does in an accusative system. And then there's Indonesian. – jlawler Aug 3 '17 at 23:12

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