I’m reading Wilfred Hodges’ Logic (1977) and I find it resonates nicely with my reading of Quine. Hodges suggests that we define “logic” as the consistency of our beliefs. That is, our a belief is “logical” if it is consistent with other beliefs. It is “illogical” to believe contradictory things, e.g., two things that can’t both be true. But he is careful to point out, right from the outset that beliefs are expressed in sentences and sentences can be ambiguous. We do not learn logic by studying beliefs directly. We learn it by studying the sentences we use to talk about our beliefs. And once we’ve learned the rules of logic, we are in a better position to maintain what Quine called our “web of belief”; we’re better able to trace the consequences of discovering the (inevitable) inconsistencies in our thinking and correcting our beliefs accordingly. That’s how we learn.
It’s also how we do science. Indeed, almost two-hundred years ago, Bernard Bolzano argued that logic constitutes a “theory of science” and should guide us in our composition of scientific “treatises”. Today, we might satisfy ourselves with the principles for composing journal articles, as long as we include the “logic” of reviewing and critiquing them. (Bolzano image of science was much slower and much more stable than ours is today so he felt that, in principle, “the sum of human knowledge” could be gather in a “single book.” It would be a very, very big book, the size of a library no doubt, but it could be written according to a consistent set of rules, namely, those of logic.
Today, we have abandoned all hope that the totality of science can be made consistent with itself, even within individual disciplines. We expect scientists to disagree with each other, sometimes even on very fundamental matters, and for these disagreements to remain open even as science progresses. Scientists are free to believe what they want, to draw their own conclusions from the evidence of their senses. What we hope, however, is that they are committed to an overarching ideal, namely, that their beliefs should be consistent. And we might add to this that, within any particular discipline or paradigm, scientists should be in broad agreement about what to believe. That is, not only is a scientist committed to personally striving for consistency of belief (logical coherence), it is assumed that since the web of belief involved is largely shared within that scientist’s community, the individual beliefs of individual scientists are formed in attempt to be consistent also with the totality of what is known about the subject.
This is a normative principle, not an empirical claim about science. Scientists should strive for consistency of belief, within themselves and among each other, but they will never perfectly achieve it. That’s what discourse is for: to achieve only a “more perfect union” of beliefs. It is the social practice through which we compare our beliefs and hold them to a certain standard. We can talk here of scholarly standards of citation, methodological standards of data collection, even stylistic and grammatical standards. But, at the end of the day, all these standards are realized in particular beliefs about the status of texts, quality of evidence, and clarity of thinking on particular subjects by particular scholars. These beliefs are then brought together and compared under a higher standard, namely, logic.
For my part, when I mention logic to students and scholars (working mainly in the social sciences) I am not talking about the sort of formal logic that Hodges’ book is a such a good introduction to. It is my sense that most scientific disciplines do not explicitly strive for that kind of logical “consistency”. Rather, in science, what is operative is something like everyday reason, even common sense. We expect each other to be “reasonable” about our beliefs and, when claiming that something is the case, to respect both the other beliefs we hold and the beliefs that are broadly held in the community. If we do challenge some of those beliefs (by insisting on others) we must acknowledge the contradiction, i.e., the inconsistency between the beliefs we hold and those that are generally held. “The civil status of a contradiction, or it status in civil life,” said Wittgenstein: “there is the philosophical problem” (PI§125). It is resolved by carefully taking apart and reweaving our web of belief to regain consistence in discourse with our peers.