Ancient rhetorical theory is not particularly concerned with the connecting words structuring the argumentative passages. In contemporary times, Perelman & Olbrechts-Tyteca ([1958]) do not mention connectives, nor does Lausberg (1960) in his monumental re-creation of the classical system.
Toulmin’s “layout of argument” emphasizes the role of linguistic connectives in the articulation of the element of the argumentative cell (1958) whereby the Warrant is introduced by since; the backing by on account of; the claim (conclusion) by so; the rebuttal (counter-discourse) by unless. Toulmin does not however discuss the connectives in any further detail.
Connecting words are a central issue for the linguistic theory of argumentation (Ducrot & al. 1980).

1. Indicators

Indicators are relevant to argumentative analysis on three levels

(1) Boundary indicators, helping to delineate the argumentative sequence.
(2) Internal indicators, helping to identify and articulate the argument and the conclusion within the argumentative sequence.
(3) Argument scheme indicators, helping to identify the argument scheme embodied in a specific argumentation.

All linguistic phenomena that can be exploited for any of these operations can be considered to be argumentative indicators, not only discourse particles and full semantic words. The label most often refers to the intermediate level, that of the argument-conclusion structure, where connectives play a prominent role.

1.1 Multifunctionality of connective particles

The terminology used for connectives and markers of discursive or argumentative structure is overabundant. Schematically, the framework for the discussion is as detailed below.

— Logical connectives build complex propositions from simple or complex propositions.
— Connective words belong to the category of discursive particles. From a grammatical point of view, discursive particles are conjunctions, prepositions, adverbs, interjections… Some discourse particles are particularly attached to conversational speech: well, hm, right
— Natural language connectives are multi-functional. Some connectives have essentially non-argumentative functions, even in argumentative contexts. For example, enumerative and ordering connectives, “firstly, secondly, and finally” can be used to list a series of agenda items as well as a successions of arguments. In an argumentative context, the “list effect” can itself be argumentative.

Other connectives such as since, because, so, therefore… are particularly helpful for tagging a segment of discourse as an argument or as a conclusion. However, it must be born in mind that their argumentative function although prevalent, is not exclusive.

To sum up, connectives are multi-functional particles that can signal an argument-conclusion relation.

1.2 Connective verbs

The argument-conclusion structure, “A so B” can also be articulated by a full verbal construction:

[A]; which leads me to conclude that [B]

1.3 Connectives articulating the semantic contents
of whole discourses.

Logical connectives articulate precise sets of well-defined logical propositions, whereas natural language connectives articulate not only propositions but also discourse of undetermined length:

 [A]. From this, we can conclude that [B].

In reality, connectives articulate meanings inferred from such indeterminate spans of discourse. A statement like “and so [Fr. ainsi] Commissioner Valentin jailed the whole gang” may close a novel. The left scope of so sums up all the events since the beginning of the investigation of Commissioner Valentin. The same is true for the connector but, which does not articulate propositions but semantic-pragmatic contents (example infra, §3.1); S. Orientation.

1.4 Multifunctionality of argument indicators

Argument indicators are not unifunctional words; not all their occurrences are argumentative. The discourse following so or thus is not necessarily a conclusion, and the discourse following because is not necessarily an argument pointing to a conclusion. There are non-argumentative cases of thus and because, and there are excellent arguments which feature neither therefore nor because. This means, on the one hand, that peppering a speech with because and therefore will not necessarily turn it into an argumentation. Aristotle had already spotted this strategy and rightly considered it as vain, S. Expression. On the other hand, if the interpreter waits for a so or a because to realize that he or she is involved in an argumentative situation, he or she can be said to be seriously lacking in argumentative, interpretative and interactional competence. The connective particles restrict the possibilities of interpretation by evoking a possible argumentative structure, but they are not summons addressed to a sleepy recipient to awake him from his or her interpretive torpor.
The discussion of the argumentative value of a particle must be related to the argumentative sequence itself. It must be independently defined, that is, insofar as it is organized by an argumentative question articulating discourse and counter-discourse. The argumentative character of a particle is context dependent. The fact of occurring in argumentative contexts activates its argumentative function. This general condition does not preclude the practice of the ars subtilior of reconstructing implicit arguments and conclusions.

In practice, the analysis of the connecting phenomenon should first give full consideration to the complexity of the grammar of connecting words and connected discourses:

— Their grammatical category, full words as well as discursive particles.
— Their syntactic characteristics.
— Their idiosyncratic semantic and syntactic properties.
— Their multifunctionality as argumentative particles: a particle like but can mark an argument, a conclusion, a contradiction or an argumentative dissociation.

Therefore, but, because are prime examples of particles with an argumentative function.

2. Thus, therefore, sosince, because…

So can be a conclusion marker, and many other things. It may for example, mark the resumption of a topic already introduced and forming the ratified topic of the text or of the interaction, but momentarily left aside. To make matters worse, this non-argumentative resumption can be found everywhere, and in particular in argumentative contexts. The following example is taken from a lively debate about the attribution of French nationality to immigrants living in France[1]:

I think that:: all these people— and then also the people who came thus, so [Fr. donc “therefore”] during the post-war boom years, we still owe them a certain form of respect.

No participant ever doubted that “these people” came “during the glorious thirties”. The reasoning here is that since they came during the “during the post-war bloom years”, as workers, they are therefore entitled to respect. Actually, so [Fr. donc, “therefore”], resumes a statement that is, functionally, not a conclusion but an argument. The structure is {[we owe respect to all these people, Conclusion] [they came to work (during the post-war bloom years), Argument]}, and certainly not:

* we owe respect to all these people, so [Fr. donc] they came during the post-war boom years.

The following intervention is made by a property manager, M, during a conciliation session with his tenant, T. The manager recapitulates his position: he requests a 80F (14 $) monthly increase of the rent[2].

[I asked/ Mrs. T certainly remembers\ I asked if you want uh, so uh: eighty francs if you want to get to a thousand thirty a month=]claim [that seemed very reasonable, very reasonable]modal considering the apartment/ and considering its location/ (..) you know a three room apartment let’s say all the same on the second floor’ (..) relatively comfortable\]argument
Corpus Negotiation on rents (conciliation commission), Clapi Data Base of Spoken French. Our parenthesis, italics and tagging.

T.’s claim is articulated to the context by so [Fr. donc, “so, therefore”], which sounds quite standard. But this claim is not inferred from what comes before, which has already been expressed and repeated. The so [donc] is in its classical recall, resumptive function; it just happens that the repeated segment is a claim. Thus, this is the case of a non-argumentative so, in a strongly argumentative context.

So, then… because… can be used to extract and thematize the implicit content of a sentence:

— An encyclopedic content:

All this happened in Greenland, so far in the North

— A semantically presupposed content:

S1    — Peter stopped smoking
S2    — then you know he used to smoke (in the past)?

— An implication of the act of saying such and such thing:

S1    — this dress suits you very well!
S2    — because the others don’t?

3. But

But reverses the argumentative orientation of the propositions it introduces. Nonetheless, no more than so, but is not an inherently argumentative particle, and the argumentative framework and vocabulary cannot account for all its occurrences. In particular but reverses not only argumentative orientations but also narrative and descriptive orientations.

3.1 But, reverser of narrative and descriptive orientations

Generally speaking, but serves to reverse the orientation, regardless of the kind of orientation: narrative, argumentative, or descriptive.

But is used to introduce a new narrative development:

August 27: On Friday, I remembered that the annual tax on my car was due to expire. Since I am not one of those who wait until the last minute to renew it, I went to the tax office. An employee was there, waiting for me, or almost. In just a few minutes, via the Internet, everything was done. I’m set until next year. But in the meantime…
He walked, and while he walked, tirelessly, with his head held high, rocked by his regular rhythm, he dreamed of next year […] ([3])

Such non-argumentative occurrences of but are quite common. The following passage contains perhaps the most famous but in all of French literature. Emma is the heroine of Gustave Flaubert’s novel, Madame Bovary. The whole passage is narrative-descriptive. First, it develops a semantic isotopy, “travel, love, beauty, exotic life, hammocks and gondolas”. But articulates this first isotopy to a second one, “husband snoring, children coughing, irritating screeching noises and provincial life”. It would not make sense to impose an argumentative analysis upon such a but.

Emma was not asleep; she pretended to be; and while he dozed off by her side she awakened to other dreams.
To the gallop of four horses she was carried away for a week towards a new land, whence they would return no more. They went on and on, their arms entwined, without a word. Often from the top of a mountain they suddenly glimpsed some splendid city with domes, and bridges, and ships, forests of citron trees, and cathedrals of white marble, on whose pointed steeples were storks’ nests. They went at a walking-pace because of the great flag-stones, and on the ground there were bouquets of flowers, offered you by women dressed in red bodices. They heard the chiming of bells, the neighing of mules, together with the murmur of guitars and the noise of fountains, whose rising spray refreshed heaps of fruit arranged like a pyramid at the foot of pale statues that smiled beneath playing waters. And then, one night they came to a fishing village, where brown nets were drying in the wind along the cliffs and in front of the huts. It was there that they would stay; they would live in a low, flat-roofed house, shaded by a palm-tree, in the heart of a gulf, by the sea. They would row in gondolas, swing in hammocks, and their existence would be easy and large as their silk gowns, warm and star-spangled as the nights they would contemplate. However, in the immensity of this future that she conjured up, nothing special stood forth; the days, all magnificent, resembled each other like waves; and it swayed in the horizon, infinite, harmonized, azure, and bathed in sunshine. But the child began to cough in her cot or Bovary snored more loudly, and Emma did not fall asleep till morning, when the dawn whitened the windows, and when little Justin was already in the square taking down the shutters of the chemist’s shop.
Gustave Flaubert, Madame Bovary, [1856][4]

In these two examples, but is not argumentative, it marks an isotopic shift.

3.2 But, indicator of an unresolved contradiction

While in the standard case of an argumentative but, the inferred contradiction E1 but E2 is resolved, the coordinated construction being cooriented with E2, in other cases but articulates two anti-oriented arguments without argumentative resolution:

S1    — What shall they do today?
S2    — Some want to go to the woods, but others to the beach.

Discourse (a) sounds strange, (b) more standard:

*(a) so we’ll go to the beach.
(b) so we do not know what to do, we’ll have to talk about that

3.3 But, indicator of argumentative dissociation

S1    — I thought you wanted reform?
S2    — We do want reform, but real reform.

The concept of argumentative dissociation was introduced by Perelman & Olbrechts-Tyteca, who define it as the splitting of an elementary notion, operated by the arguer to escape a contradiction ([1958], 550-609), S. Dissociation

3.4 Other functions

— Rectification: with reference to “Beautiful blue Danube”

In Vienna, the Danube is not blue but dirty gray

— Preface to a second turn at speech, aligned with the first turn:

S1    — Once again, Peter failed to get his degree
S2    — But that’s exactly like me!

4. Other constructions articulating an argument to a conclusion

An argumentative thus can be paraphrased by a set of verbal constructions connecting an argument to a conclusion:

[Left Context]      therefore, from where, hence, that is why,      [Conclusion]                                  this means, proves, shows clearly that,
                                 one can (then) conclude that

The conclusion appears as the completion of a “connective predicate”. Markers of argumentative structure would thus be unduly restricted to “small connectives words”; other constructions, combining anaphoric terms, verbs, or substantives can play this role.

4.1 Connective predicates

Some verbs predicate a conclusion upon an argument or an argument upon a conclusion. In reality, these connective predicates are the only indisputable and univocal argumentative indicators. We must distinguish between two cases (argument is taken in the sense that it has in theory of argumentation, not as “argument of a mathematical function”, S. Argument)

(1) Conclusion Predicate: the conclusion is predicated upon the argument.
Subject (Argument) + Pred (Conclusion)

— from [Argument] I conclude (that) [Conclusion]:

V = to conclude, infer, deduce…

— [Argument] allows to deduce (that) [Conclusion]:

V = to induce, show, demonstrate…

— [Argument] proves [Conclusion]

V = to prove, demonstrate, support, corroborate, suggest, go in the direction of, motivate, legitimate, justify, entitle to believe (say, think…)

(2) Argument predicate: the argument is predicated upon the conclusion.
Subject (Conclusion) + Pred (Argument)

[Conclusion] ensues from [Argument]:

V = to ensuing, result, follow, derive…

To argue is not a conclusion predicate, but a simple verb of speech activity. In “X argues for such a conclusion”, the subject X must be [+ Human]; it cannot be an argument, a description of a state of affairs. This construction contrasts with the construction “X suggests such a conclusion” where X can be a discourse or a human, S. (To) argue.

Overlooking this set of constructions is particularly damaging in the teaching of argument.

4.2 Constructions framing an argumentation

All the words used to talk about arguments and argumentation can serve as markers of argumentative structuration and argumentative function. This class of nominal indicators includes all the ordinary lexicon of argumentation: (counter-)argument, (counter-)conclusion, point of view…, premise, objection, refutation…

this is my conclusion, a consequence, a serious objection, an argument to be taken into consideration

[D1, argument] is given as a good reason to admit, to dois stated, said for, with a view to, to make acceptable, to make, to say, to feel… [D2, conclusion]

the conclusion, the premise, the objection that…; against this point of view

We can be certain that “building the school here, the land is cheaper” is an argumentation, because it can be satisfactorily paraphrased as follows:

A good reason to build the school here is that the land is less expensive.
The fact that the land is cheaper legitimizes the decision to build the school there.

[1] Corpus Debate on Immigration, Clapi Data Base of Spoken French Num_corpus = 35]. (09-30-2013)
[2] Corpus Negotiation on Rents – Conciliation Commission), Clapi Data Base of Spoken French. Our parenthesis, italics and tagging.]. (09-30-2013)
[3]]. 07-28-2010. Our emphasis.
[4] Quoted after Gustave Flaubert, Madame Bovary. Trans. by Eleanor Marx-Aveling. Ebook, 2006.