Grasping logical truths in a flash

 

            The above conjectures about the origins of our basic logical knowledge may seem like a very strange fit with what it actually feels like when you ask yourself whether a very simple logical inference is truth preserving. You might agree with my picture of how we build up complex knowledge of logical dependence and independence of propositions: that we put together chains of steps which we know to be truth preserving or come up with descriptions of examples or counter examples which we know to be themselves logically consistent. But the claim that our knowledge that these basic steps are truth preserving or that certain scenarios are possible arises from considering some related cases or instances and performing glorified induction is nevertheless very far from your experience. For the experience of ‘seeing’ that some inference is truth preserving or some description could be true needn’t involve considering any examples, you may just think about the statement or formula in question and then come to feel certain that it is valid or that it could be true all at once when it pops into focus in a certain way.

            This is certainly a real experience, I think, and one which can confer basic logical knowledge. But I want to argue that there’s an important sense in which this knowledge is grounded in inductive investigation our linguistic norms. To make the point more vividly let’s contrast two different ways in which one could understand this process of grasping logical truths in a flash.

            The first, venerable, model for understanding that phenomenon is that of memory and perception. We do, after all, speak of ‘seeing’ that something is contradictory, or that an inference is valid. On this model the experience you have when a simple inference pops into focus amounts of a kind of perception. You have intuitive access to the realm of abstract objects and you see that a proposition living there does or doesn’t stand in a certain relation to contradiction. Or you scan the space of possible worlds with your mind’s eye and see that something is true in all of them. Or maybe objects aren’t involved at all and you perceive that the inference is valid immediately. Here we have the familiar questions about access. The logical facts are one thing, and the experience of sudden belief is another, and one wonders how it is that the one manages to co-vary with the other. Even if we take the Tractarian view of necessity, which I think makes things much easier, there is a question: how can you perceive the fact that A would never apply to something that A or B fails to apply to? Invoking perception merely focuses the question more sharply, how is this perception supposed to work? How could we perceive the range of how our norms would apply in various, mostly counterfactual, scenarios?

            The alternative hypotheses understands the experience of seeing the validity of a simple inference in a flash to that of seeing that a table is unstable or that you won’t be able to fit little triangles together to make a certain shape (in the physical sense which depends on the contingent structure of space). Both of these facts are ones which one could have the experience of grasping in a flash but our knowledge of them is grounded in empirically determined physical possibility. As people move around in the world they develop a kind of physical intuition, a sense that things are likely to fall or one thing could be made out of another or that something which looks one way will likely taste another. This knowledge is founded on unconscious generalizations from their past experiences. If they had grown up on a world with different gravity or different biology or differently curved space they would have different intuitions about the same objects. But the experience of seeing that you won’t like the gumbo you ordered or that you had better prop up the table needn’t involve any conscious experience of recalling toppling furniture or overcooked veg.

            Thus, in claiming that basic logical/linguistic knowledge of internal relations between our norms for different words comes from induction, I don’t mean to deny that the experience of learning about these relations may be one of grasping something rather than consciously reviewing instances.