His argument is a historical argument; unfortunately, I don't see how it is supposed to work at all. He starts out:
The authors claim that philosophy abandoned its relationship to other disciplines by creating its own purified domain, accessible only to credentialed professionals. It is true that from roughly 1930 to 1950, some philosophers — logical empiricists, in particular — did speak of philosophy having its own exclusive subject matter. But since that subject matter was logical analysis aimed at unifying all of science, interdisciplinarity was front and center.
But the institutionalization of philosophy does not start in the 1930s; it starts (as Soames himself explicitly recognizes!) in the nineteenth century. By the time we get to the period at which Soames starts, we already have philosophy departments and philosophy journals that have been going on for decades, and it's pretty obvious that Frodeman and Briggle would argue that the narrowing had already begun. And in fact, there is prima facie reason to think that they would be right if they did argue this way.
How did philosophy departments come about? Here's a 'prima facie history', a first-glance look at what the evidence suggests.* They originally didn't exist at all. Degrees were philosophy degrees unless they were medical, theological, or law degrees. As time there grew up chairs and lectureships and examinations specifically devoted to this or that specific field of philosophy, moral philosophy or experimental philosophy or what have you, but while departments grew out of these, the modern philosophy department did not. Philosophy was most often treated as a general field; it covered multiple 'departments'. What sense would it make to have a philosophy department, when most of your other departments are still at least sometimes seen as covering various fields in philosophy? So where did philosophy departments in particular come from?
There's an answer that has been given, and while it's controversial in parts, it is a good start for our 'prima facie history'. People started thinking of psychology as a science -- mental science. But the movement to do so was closely associated with very specific methods (structuralist, broadly speaking), and so when the push for psychology departments began to develop momentum and financial backing, as a matter of academic politics, a reaction formed among those who studied various matters relevant to the mind who thought these particular methods inadequate, and did not think that psychology could be a science, at least in that particular sense. The first clear, definite philosophy departments arose in response to the formation of psychology departments. The first clear, definite philosophy journals, associated with subject matter studied in departments devoted specifically to what was called philosophy, arose in the same way and for the same reason. It is not an accident that one of the first such philosophy journals, formed in 1876, is called Mind -- the specific reason for the journal, stated right there in the very first issue, was to serve as a forum for discussing whether psychology was a science, and if not, why not, and if so, how so.
And (continuing the prima facie history) what do we then find discussed in philosophy departments and journals entering the twentieth century? Questions relevant to whether psychology is a science. We have direct discussions of what we would call philosophy of mind. Some of those discussions get us directly into epistemological questions, as they still do, so we would get epistemology. One of the big philosophical discussions already going on was Idealism, and being an Idealist of one kind or another is one reason why you might question the idea that psychology was a science, and one's reasons for being an Idealist would be broader metaphysical reasons, so we get discussions of metaphysics -- insofar as it might be relevant to the nature of the mind. Some lines of argument about the mind and psychology get us directly into questions of logic and language; and so you begin to get those kinds of discussion, too -- slowly, and usually at first in ways closely connected to the question of the mind.
All of this is, again 'prima facie history'. The reality covers a wide variety of societies over a period of decades, each with different educational systems (occasionally very different), a large number of different players working with a wide variety of motivations. A closer look might turn up complications requiring a reassessment here and there. But, at least at first glance, it fits the obvious evidence that must be taken into account in looking at the history of philosophy-department philosophy. And note that, so far, we are still decades before Soames's starting point and already have the materials for a Frodeman-Briggle kind of argument: the terrain has already narrowed considerably: mind-focused topics like the status of psychology, epistemology (empiricism and rationalism), logic, philosophy of language. And what kinds of topics are being discussed in the 1930-1950 period when people are elaborating philosophy for the interdisciplinary unity-of-the-sciences approach? Philosophy of mind, epistemology, logical analysis, philosophy of language. And what kinds of examples do we get when Soames tells us that philosophy is not isolated from other disciplines? I list them:
(1) symbolic logic;
(2) linguistics and its relation to cognition;
(3) decision theory and what it says about beliefs;
(4) assisting of psychology in its ridding itself of behaviorism;
(5) philosophy of physics;
(6) philosophy of biology, which follows a route like that of philosophy of physics.
You notice immediately that all of the first four have to do with mind, language, logic, and epistemology, and in fact with very specific approaches to these things; and a closer look at the examples given for (5) shows that it's not actually a different kind of example. If Soames were trying to defend rather than oppose the Frodeman-Briggle thesis, he could hardly have chosen a better set of examples: there is actually a very narrow theme here.
Let's think about a contrast case. Really foundational work in philosophy of science gets done in the nineteenth century, with Whewell (Philosophy of the Inductive Sciences) and Mill (System of Logic) being big names. Why does this work get laid? Part of it is just the expanding success of scientific methods post-Newton. But if you look at the actual philosophical discussions, a pattern emerges: over and over again the discussions are brought back to the question of how these accounts of the sciences related to ethics. Mill, of course, was a major utilitarian. Whewell was Knightbridge Professor of Moral Theology and Casuistical Divinity; he explicitly claims here and there that his work on the philosophy of the sciences was directly relevant to moral philosophy; he was a major force behind the push to have Moral Sciences examinations at Cambridge; he was a major intuitionist opponent of the utilitarians. And while they were both interested in the subject itself, one of the primary motivations is to argue ethics and metaethics. Nor were they the only ones; you even find it in places you wouldn't expect -- Charles Darwin entered the same fray in Descent of Man arguing for intuitionism and against utilitarianism on biological grounds, for instance. Moral philosophy was queen. This is a very different from what Soames seems to suggest -- he claimed, for instance, "the study of goodness, justice and virtue" was "never" the central aim of philosophy. "Never" is an oddly strong word here -- the claim is certainly false (for instance) of very large portions of ancient philosophy. (Try to imagine a Plato who did not regard goodness, justice, and virtue as the central aim of philosophy. Or what in the world were Hellenistic philosophers mostly talking about if not primarily about "goodness, justice and virtue"?) But you don't have to go back so far. While one can argue about whether it's quite correct to call it "the" central aim, "the study of goodness, justice and virtue" was certainly far more central in the nineteenth century than you ever find it in the twentieth century.
Thus when we look at Soames's argument, it seems to say very little that's of any use. His appeal to history seems poorly designed even to address the question the appeal is supposed to address in the first place -- it claims to address the Frodeman-Briggle thesis without actually doing anything that could do so. And the historical appeal in addition raises worries of itself. If the question is the damage done by the institutionalization beginning in the nineteenth century, and is about the course of philosophy over a span of 150 years, both of which Soames explicitly recognizes, why is the history we actually get so obviously piecemeal and so heavily post-1930? If goodness, justice, and virtue were "never" central to philosophy, how does Soames reconcile this with the obvious, often explicit, emphases on moral philosophy in the eighteenth and nineteenth centuries? Part of Soames's argument is just a claim that it's important for philosophy to interact with the sciences, which is not relevant to the Frodeman-Briggle argument, since they didn't claim that it shouldn't interact with the sciences, nor even that it didn't. Soames, weirdly, talks about the idea that "philosophy was and still is isolated from other disciplines ignores much of its history"; but this is not a claim that Frodeman and Briggle made -- they claimed that philosophy was separated from society, and their only talk about "disciplines" is about the rise of disciplines and the 'democratization' of them. And how does Soames reconcile his argument with the specific facts about the history of the university in general and of philosophy departments in particular to which Frodeman and Briggle referred throughout their argument. (Noticeably, none of Soames's argument is about the institutional aspect of philosophy's institutionalization at all, despite the fact that it keeps coming up in the Frodeman-Briggle argument.) The whole argument as a response to Frodeman and Briggle is baffling, and one worries greatly that the argument is more an advocacy for the general self-congratulation with which the piece ends, than a serious attempt to examine the question.
* Those who are interested in these matters might read Edward Reed's work, From Soul to Mind; the book, by a psychologist, is an attempt to argue that philosophy in the disciplinary sense of the word is a creation of anti-psychology reactionaries. Parts of the prima facie history given here go over some of the historical points that Reed considers, although I have mostly stayed with the least controversial ones and, of course, haven't indulged in Reed's occasional sarcasm about the pompous pretensions of academic philosophers. Comparison with comments made by Frodeman and Briggle will show that there is some definite overlap between Reed and Frodeman-Briggle, although the latter account seems to be independent of the former.