The main point of Peter Geach's paper, "Assertion" (Logic Matters, Basil Blackwell, 1972, pp. 254-269) is what he calls the Frege point: A thought may have just the same content whether you assent to its truth or not; a proposition may occur in discourse now asserted, now unasserted, and yet be recognizably the same proposition. This seems unassailably correct. One will fail to get the Frege point, however, if one confuses statements and propositions. An unstated statement is a contradiction in terms, but an unasserted proposition is not. The need for unasserted propositions can be seen from the fact that many of our compound assertions (a compound assertion being one whose content is propositionally compound) have components that are unasserted.
To assert a conditional, for example, is not to assert its antecedent or its consequent. If I assert that if Tom is drunk, then he is unfit to drive, I do not thereby assert that he is drunk, nor do I assert that he is unfit to drive. I assert a compound proposition the components of which I do not assert. I assert a relation between two propositions without asserting either of them.
The same goes for disjunctive propositions. To assert a disjunction is not to assert its disjuncts. Neither propositional component of Either Tom is sober or he is unfit to drive is asserted by one who merely asserts the compound disjunctive proposition.
On one view of logic, it studies propositions and the relations between them such as entailment, consistency, and inconsistency in abstraction from the concrete mental acts in which the propositions are accepted, rejected, or merely entertained. Logic is thus kept apart from psychology. If so, then assertion, as a speech act founded in the mental act of acceptance, is external to logic. If this were not the case, then how would one account for the validity of the following obviously valid argument?
a) If Tom is drunk, then Tom is unfit to drive
b) Tom is drunk
Therefore
c) Tom is unfit to drive.
For the argument to be an instance of the valid argument form modus ponendo ponens, the protasis of (a) must be the same proposition as is expressed by (b). But then the assertoric force that (b) carries when the argument is given by someone cannot be part of the proposition. For the assertoric force is no part of the proposition that is the protasis of (a).
So if formal logic studies propositions in abstraction from the concrete episodes of thinking in which they are brought before minds, then assertion is external to formal logic.
But according to the NYT, a philosopher with a cult following among the cognoscenti rejects the above view:
[Irad] Kimhi argues that this view is wrong, and that the distinction between psychology and logic has led our understanding of thinking astray. Consider that the following statement does not, according to the standard view, constitute a logical contradiction: “It’s raining, but I don’t believe it’s raining.” Why? Because the first part of the sentence concerns a state of affairs in the world (“it’s raining”), whereas the second part concerns someone’s state of mind (“I don’t believe it’s raining”).
Kimhi wants to rescue the intuition that it is a logical contradiction to say, “It’s raining, but I don’t believe it’s raining.” But to do this, he has to reject the idea that when you assert a proposition, what you are doing is adding psychological force (“I think … ”) to abstract content (“it’s raining”). Instead, Kimhi argues that a self-conscious, first-person perspective — an “I” — is internal to logic. For him, to judge that “it’s raining” is the same as judging “I believe it’s raining,” which is the same as judging “it’s false that it’s not raining.” All are facets of a single act of mind.
I haven't read Kimhi's book, and I am not sure I should trust the NYT account, but Kimhi seems to be recycling Kant in a confused way. At B 132 of Critique of Pure Reason, Kant writes, "It must be possible for the 'I think' to accompany all my representations; for otherwise something would be represented in me which could not be thought at all, and that is equivalent to saying that the representation would be impossible, or at least would be nothing to me." (NKS tr.)
Consider a propositional representation. One's awareness that it is raining need not be accompanied by an explicit act of reflection, the one expressed by 'I think that it is raining,' but it must be possible that this reflection occur. Thus there is a necessary connection between the propositional representation 'It is raining' and Kant's transcendental unity of apperception. The latter could be described as " a self-conscious, first-person perspective — an “I” — [that] is internal to logic." But it is a transcendental I, one common to all cognitive subjects, and not the psychological I of a particular cognitive subject. Kimhi seems to be speaking of the latter.
Kant's Ich denke points us back to Descartes' cogito. The Frenchman discovers that while he can doubt many things, he cannot doubt that he is doubting these things. He can doubt the existence of the cat he 'sees' — using 'see' in a strictly phenomenological way — but he cannot doubt the existence of his 'seeing' as a mental act or cogitatio. His doubting is a thinking, but it is not a believing. The Dubito ergo sum is but a special case of the generic Cogito ergo sum. His doubting that he has a body is not a believing that he has a body but it is a thinking in the broad Cartesian sense that subsumes all intentional states or mental acts.
Accordingly, the 'I think' that must be able to accompany all my representations does not have the specific sense of 'I believe.' Belief is one type of mental act among many. One who believes does not doubt, and conversely. But both think. The 'I think' expresses an explicit reflection on the occurrent intentional state one is in, whether one is doubting, believing, wishing, hoping remembering, etc.
So there is a defensible sense in which there is an I internal to logic, but this is the transcendental I of the original synthetic unity of apperception, not the I of the psychophysical subject in nature. If there is an I internal to logic, it is the I of the transcendental prefix, the 'I think ___' which must be able to accompany all my representation. But this 'I think ___' of the transcendental prefix does not have the sense of the ordinary language 'I think so' which means 'I believe so.'
One consequence of Kimhi’s view is that “It’s raining, but I don’t believe it’s raining” becomes a logical contradiction. Another consequence is that a contradiction becomes something that you cannot believe, as opposed to something that you psychologically can but logically ought not to believe (as the traditional cleavage between psychology and logic might suggest). A final consequence is that thinking is not just a cognitive psychological act, but also one that is governed by logical law.
In other words, the distinction between psychology and logic collapses. Logic is not a set of rules for how to think; it is how we think, just not in a way that can be captured in conventional scientific terms. Thinking emerges as a unique and peculiar activity, something that is part of the natural world, but which cannot be understood in the manner of other events in the natural world. Indeed, Kimhi sees his book, in large part, as lamenting “the different ways in which philosophers have failed to acknowledge — or even denied — the uniqueness of thinking.”
The above strikes me as based on a confusion of the transcendental 'I think' with the psychological 'I believe.' It seems to me that one can have a reflective awareness as of rain falling without believing that rain is falling. What is impossible, and contradictory, is to have a reflective awareness as of rain falling without thinking (in the broad Cartesian sense that subsumes specific types of mental act) that rain is falling.
The transcendental I's thinking is governed by logical law, but not the thinking of the empirical I in nature. So the distinction between psychology and logic does not collapse. To the extent that I can make sense of what Kimhi is saying on the basis of the NYT article he seems to be trying to naturalizer Kant's transcendental ego. Good luck with that.
Perhaps talk of a transcendental I is nonsense if it is supposed to be a real entity that thinks; but only a transcendental I could be internal to formal logic.
If anyone has read Kimhi's book, his comments would be appreciated.