Transitive Inference Path (TIP) argument visualization relies on the “transitivity of predication.” I hesitate expounding on this relation because it leads down a rabbit hole. (Only logicians and philosophers dare tread deeply in that dark place.) But I will share what I have gleaned from standing at the entrance looking in. (The following explanation reflects my understanding largely drawn from the works of Angelelli, such as Predication Theory: Classical vs Modern and the works of Cocchiarella, such as Conceptual Realism and the Nexus of Predication. http://traumstadt.org/angelelli.pdf; http://www.formalontology.it/essays/nexus.pdf

Predication is saying something about its subject. Argument mapping is a visualization of predications designed to reflect paths of inference (e.g. inferential networks). And, in its ontological sense, “predication has been a central, if not the central, issue in philosophy since at least the time of Plato and Aristotle.” (“Philosophical Perspectives on Quantification in Tense and M odal Logic”, in Handbook of Philosophical Logic, vol. 2, eds. D. Gabbay and F. Guenthner, D. Reidel Pub. Co., Dordrecht, 1983, pp. 309-353.) So it must be central to argument mapping as well.

The critical question for a Transitive Inference Path is whether predication is transitive. As an attorney, the standard answer to any question is…it depends. And, in this instance, that is actually a pretty good answer. From a classical (pre-Fregean) perspective, it depends on which type of predication to which you are referring. (Don’t ask me about substitutivity!)

Aristotle states “for all we affirm of the predicate will also be affirmed of the subject.” Categoriae. But, as an attorney, it is always good to also check the fine print. And in this case, Aristotle qualifies his statement. This transitivity relation only applies to predication of a thing “as of a subject.” Categoriae. (According to Angelelli, some literature obscures this fine print or misses it altogether.)

This qualification limits transitivity to essential predication where something is “said of” a subject rather than accidental predication where something is “in” a subject. (I told you this was a rabbit hole.) Paul Crice and Alan Code use the terms IZZing and HAZZing to express these distinctions. http://faculty.washington.edu/smcohen/433/GriceCode.pdf.

Consider the following example:

The apple is red. Red is a color. So an apple is a color.

In this instance, the predication is accidental with the apple HAZZes the color red. So this type of predication is not transitive.

But, in the following example, the predication is essential so that it is transitive.

The apple is red. Something that has the quality is red is the color of a fire truck. So an apple is the color of a fire truck.

A helpful perspective in ensuring that a Transitive Inference Path is correctly structured is seeing that “even accidental predication [HAZZing], implicitly involves some kind of essential predication [IZZing] (i.e., classification).” http://faculty.washington.edu/smcohen/433/GriceCode.pdf.

For example, an apple HAZZes something that IZZes red.

So when creating a Transitive Inference Path, be careful that the linkage between the co-premises is phrased to represent an essential predication to maintain the transitivity as shown below.

Generally, just cut the sentence in half starting with the verb, add “something” or “someone”, and make the result the subject of the next sentence.