Locke relegates almost all of science (excepting only mathematics and moral science) and most of our everyday experience to the category of opinion or judgment. Judgment, like knowledge, is a faculty concerned with identifying the truth and falsehood of propositions. It perceives apparent, rather than certain, connections between ideas. While knowledge is based on intuition and demonstration, judgment in based on probability. Probability is the appearance of agreement or disagreement by the intervention of proofs that do not lead to certainty, but, rather, to likelihood. We base our judgments of probability on the apparent conformity of propositions to our own experience and to the testimony of others.
In the final chapters of the Essay, Locke also examines reason, faith, and the relation between them. Reason is the faculty we use to obtain judgment and knowledge, the faculty that discovers connections between ideas. Faith is the acceptance of revelation and has its own truths, which reason cannot discover. Reason, however, must always be used in order to determine which revelations truly are revelations from God, and which are the constructions of man. Therefore faith without reason is entirely counterproductive. Enthusiasm, however, sometimes causes us to set reason aside in matters of faith and elsewhere. In place of reason, enthusiasm substitutes pure fancies guided only by personal conceit or impulse.
Locke ends the Essay by dividing all of human understanding up into three branches or sciences: natural philosophy, or the study of things; ethics, or the study of how best to act; and logic, or the study of words and signs.
Locke holds that we can never have knowledge when it comes to natural science. Does this mean that he thinks we should give up trying to do science? At some points, it does sound as if Locke is tending in this direction. For example, at IV.XII.11, he points out that among the truths our faculties are adapted to know, moral science (that is, the study of our duties to God, ourselves, and others) is prominent. From this he concludes that moral science is the proper object of human attention. Though Locke was primarily concerned with moral and political philosophy throughout his career, still it would be strange to find him urging us to abandon the natural sciences. He was, after all, one of the major proponents of the *new mechanistic sciences*, and its general acceptance was one of the major motivations for the Essay.
Rather than urging us to abandon science, it seems instead that Locke is simply warning us to be wary of it. At IV.xii.10, he admits that the scientist has a deeper understanding of the natures of things than the layperson, and he would certainly, then, admit that as science progresses, we as a culture gain a deeper understanding of the world. However, he cautions, we should not think that the deeper understanding science yields amounts to knowledge. It is still merely opinion or judgment. What, though, does this mean on a practical level? If we all admit that the scientist has a deeper understanding of the world, what exactly are we avoiding by refusing to call this deeper understanding knowledge? It seems that Locke is wary of a science that is too confident in its own powers. He fears a science that claims to know the inner workings of the world, rather than simply the world's observable properties. What he is telling us is not simply that we should refrain from calling science knowledge. Instead, he is telling us precisely what it is that a scientist cannot know. A scientist cannot build up systems and comprehensive doctrines and claim that they represent the truth. A scientist, in other words, cannot do exactly what the *Scholastics* and the Cartesian Rationalists thought that they were doing. Today, however, we do build up systems that purport to represent the way the world is. We claim that these systems give us knowledge. What would Locke have thought of this state of affairs? Would he admit that he was wrong, that, in fact, scientists are able to arrive at knowledge? Or would he instead claim that our culture is making a grave mistake? On the one hand, when it succeeds, modern science often does exactly what Locke demanded. Science enables us to deduce observable properties from the microstructures that cause them. Science, in other words, often discovers necessary connections. Take heat, for example. Chemistry was able to show us that heat is necessarily connected to molecular motion, by showing us that heat just is molecular motion. If molecules move in a certain pattern, heat cannot fail to arise. Given just the motion of the molecules, we can predict exactly when and how much heat will arise. In this sense, Locke would be pleased with our progress. On the other hand, no one has ever seen a molecule. We did not derive the idea of a molecule from experience, but from theoretical reasoning. Locke would have criticized our heavy reliance on theoretical concepts such as "molecule," "atom," "electron," and "wave function." The necessary connections that we have found are almost invariably between observable properties and these theoretical concepts, rather than between observable properties and other ideas we have derived from experience. Locke, therefore, would have rejected these necessary connections as useless.
We can see here how Locke's pessimism about the capacities of science ultimately rests on his rigid empiricism. It is his insistence that only experience can give rise to meaningful ideas that forces him to conclude that we will never see necessary connections in nature. He is right: if we can only derive meaningful ideas from experience, rather than from reasoning based on experience, then we can probably never discover any necessary connections between our ideas of the natural world. Remember that one of the primary arguments for his pessimistic conclusion rested on the claim that we cannot directly observe the microstructures of objects. We still cannot directly observe a great deal of the microstructures of objects, but we infer them from experiments as well as other data. Locke would not have allowed such inferences. In a way, though, this is strange since Locke did believe strongly in the powers of inference to the best explanation. He believed that this sort of inference was strong enough to ground a near knowledge in the existence of the external world. Our reasoning toward theoretical concepts, however, is also often (if not always) of this sort. It seems plausible, then, that he should have considered allowing just as much leeway in the case of knowledge of the nature of things as in knowledge of the existence of things. If inference to the best explanation can give us sensitive knowledge of the external world, could it not also give us near-knowledge of the existence of theoretical posits? If it could, then we would be able to use our theoretical concepts in reasoning about the world, and we would be able to arrive at knowledge within the natural sciences. Unfortunately, Locke does not seem to have considered this possibility.