Whether a premise is linked or convergent in relation to other premises is an essential question when argument mapping. The answer determines whether the premise is correctly placed on the map. But, surprisingly for such an important question, leading scholars cannot agree on the test to determine the answer. http://homepage.mac.com/ryanal/Philosophy/linked%20convergent%20again.pdf.

Scholars have generally agreed, however, that even when using agreed upon definitions, the determination can be difficult for students. According to Professor Tim van Gelder “this is one of the most difficult of all the concepts we will deal with.  Getting it right is one of the biggest challenges in argument mapping!” http://www.austhink.com/reason/tutorials/Tutorial_2/print.htm. Similarly, Professor Twardy observes that “[e]ven very bright students get it wrong surprisingly often.” http://www.csse.monash.edu.au/~ctwardy/Papers/reasonpaper.pdf

I have suggested that there is actually a better solution than the customary ones to this challenge. When a Transitive Inference Path argument schema is used, there is a bright-line test that suffers none of the problems of abstraction (e.g. do the premises help each other; connect in some manner; work together; synergistically enhance probative force?) of other tests.

Bright-line test: Premises are linked when they both fit within the same transitive inference path that connects the subject of the contention (aka conclusion) with its predicate. And a premise can only fit within this path if its phrasing can be adjusted such that its subject and predicate can be matched with identical terms from the adjoining premises on either side within the interlocking string of transitive premises.

With this test, the following type of simple linked/convergent problem illustrated by Professor Twardy cannot occur. http://www.csse.monash.edu.au/~ctwardy/Papers/reasonpaper.pdf

Of course, even with a transitive test, the solution is not always so obvious. What this test reveals is that the linked/convergent determination can depend on uncovering more necessary hidden premises that begin to hint at the interlocking connection. For example, in the following Rationale Transitive Inference Path (TIP) maps, the determination and resulting placement of the premise in question might not be at first apparent, as shown in the first map, until  another premise in the path is uncovered, as shown in the second map.