While Wolffian school had relegated the question of truth to the practical or applied side of logic, Hoffmann understood its value and insisted placing it in theoretical side. Corresponding with this exalted place, Hoffmann's actual investigation of truth is surprisingly thorough, even if it ultimately fails as a reliable evidence for truth.
First of all, Hoffmann delineates the topic by noting that we are not speaking of moral truth, which means correspondence of a speech or writing with author's intentions. Instead, it is truth as the correspondence of one's actual thoughts with actual things that Hoffmann has in mind. Furthermore, this subjective truth is dependent on still further notion of objective truth or correspondence of possible thoughts with actual things – this objective truth, Hoffmann says, is reducible to the notion of reality or actuality.
Hoffmann notes the paradoxical nature of ascertaining the possibility of objective truth. Such ascertainment can only happen through some general proof, but it is just these human tools of proof that are in question in this investigation. Human ability of deduction or inference must then be applied to itself in order to show its own validity, which makes the whole endeavour rather circular. Hoffmann notes that this is just inevitable and even distinguishing feature of all basic principles – proofs for them must be of completely different sort than proofs of common propositions.
The first and foremost task is to investigate the formal principles by which human beings prove things – that is, what we would call rules of inference. We already know that we feel forced to accept these rules, but this does not mean that the rules would work also with actual things. It is the explicit task of the three highest principles to provide this required link of ideas with things, while other principles might just connect ideas with one another.
Beginning with the highest principle of non-contradiction, Hoffmann notes that the only way to justify it is to show how impossible it would be to think against it. Suppose we consider the proposition ”something both is and isn't”. This proposition must be accepted as either true or false, both true or false, neither true or false or epistemically uncertain. The last possibility can be ignored, since uncertainty concerns only the status of a thinker and not the proposition itself.
We are then left with four options, of which we would like to show the falsity to be the most convincing. We cannot really state that the proposition would be both true and false, since we cannot understand what that means. If we accepted that it is neither true or false then the proposition wouldn't even be a proposition, which must always be either one – and we would have nothing to think about at all. The final possibility would be that the proposition is true, but accepting something as merely true already presupposes that we can use the (epistemic) principle of non-contradiction of propositions, which in turn is based on the (ontological) principle of non-contradiction of entities.
We might be skeptical about Hoffmann's desire to base epistemic principle of non-contradiction on ontological principle of non-contradiction, but it was quite common in his days. Hoffmann's proof is then a sort of trilemma: either there is nothing to think about, when we discuss of ontological contradictions, or then ontological contradictions just are beyond our capacities to think – or then we must just accept the principle of non-contradiction.
One might say that this is a rather good proof that the principle of non-contradiction is natural rule for us, since we cannot even imagine what it would even be like, if world did not follow it, but that it does not really justify that the principle also holds with real things. Hoffmann accedes this point and asks us then to think about such a thing that would both be and not be – since we cannot do it, we cannot even say anything about it and it would thus lie completely outside the realm of meaningful discussion, in which notion like truth can only be applied.
Hoffmann's apparent attempt has been to prove the validity of the principle of non-contradiction, but what he has been capable of proving is more like incapacity to speak of the truth of contradictions and the existence of contradictory things, except by denying them – quite good result in itself, since it makes evident that when discussing truth, one can just assume that no contradictions exist. The only remaining worry is that some other type of intelligence might find contradictions quite acceptable and would be capable of speaking about them, thus making it possible to connect the existence of contradictions with the idea of truth. Hoffmann's only remark is that while it is verbally possible to accept the existence of such thinkers, from the viewpoint of out notion of truth such thinkers would be speaking mere absurdities. In other words, such thinking would be quite alien to our way of thinking and our notion of truth and we would be quite justified to deny that their thinking has anything to do with truth.
While we must thus accept the principle of non-contradiction, as valid among all things we have the ability to think of, in case of the two other highest principles we must accept some restrictions. In a sense, we might be able to use the very same method as we used in justifying the highest principle. Suppose, for instance, that we must think about two features, A and B, always as combined together, but that in actual fact A and B would not be combined in some thing, but it would be A without any B – say, while we must think that force is always connected to some substance, there would be a force that would not be connected to a substance. The problem in thinking about such a possibility would be that we would have to think about a contradiction – we would be naturally forced to think about the necessary connection of force and substance, which makes us incapable of even holding the notion that forces could exist without substances. Again, this proof merely pushes the possibility of things, which would cancel the validity of the second principle, outside the realm of meaningful discussion. Furthermore, Hoffmann holds, the second principle works only when the two properties are both positive, that is, when we are referring to two ideas we must always think together. If, on the other hand, the other idea is only negative, that is, actually a mere lack of an idea, the necessity to think of an idea together with a lack of another idea might just be a result of our limited conceiving ability – Hoffmann is here probably thinking of our incapacity to think of properties of God in a positive manner.
The justification of the third basic principle of proof follows a similar pattern as the justification of the second principle. Hoffmann asks us to consider two ideas we find repugnant to connect and then asks us to try and think that the two would be actually connected – the result is that there is actually no subject to talk about, since the two ideas cancel one another. Just like with the other principles, the justification removes all discussion of such combination of incompatibles beyond field of meaningful discussion about truth. And just like with second principle, Hoffmann notes that the third principle can be used only in restricted manner – we might be seduced by our inability to sense or perceive a connection of two properties to think that they would be incombinable even in realms surpassing mere senses. The restrictions on the two latter principles also make metaphysics often into a mere probable discipline, Hoffmann concludes – we cannot be completely certain whether some seemingly incompatible combination of properties cannot truly be actualised.
Assuming Hoffmann's justification of the three highest principles of inference have been accepted as bridging the gulf between ideas and things, we can then accept the rest of the principles justified through these three principles. Often these sub-principles, such as Hoffmann's version of the principle of sufficient reason, rely on some necessary connection or incompatibility of ideas, which can then be accepted as a proper pattern of inference in realm of things also through the use of second or third main principle – thus, because we must always think changes of a thing either as caused by external agents or as happening through spontaneous action of the thing, in a meaningful discussion of truth this connection should be thought to hold also between all things.
One can do little with mere inference patterns or one needs some material propositions as premisses of one's inferences. A simple set of these is provided again by the highest principles – through the second and the third principle we can accept as immediately true axioms all propositions combining things we necessarily connect and separating what we necessarily separate. Yet, this is not enough, Hoffmann admits, and we must also defend the general reliability of our experience, and more precisely, of sensations, on which experience is based.
Hoffmann's defence of sensations is divided into three parts. Firstly, we must know that we can distinguish sensations from other similar mental events, such as imaginations. Hoffmann's justification for this seems overtly simple: we can identify sensations as being produced by external objects. In other words, in sensing the human consciousness is passive, that is, it is incapable of saying what to sense – in comparison, imaginations might be produced by free choice. Problem is that we often still appear to be able to confuse sensations with various other mental occurrences. Hoffmann himself admits as much and delineates four cases where confusions might happen: when we are sick, when we are dreaming, when our sensations are obscure and when we are mixing implicit inferences with our sensations (in the last case Hoffmann is referring to the famous case of a square tower that looks round from a distance).
The first two cases Hoffmann dismisses quickly just by saying that we are well able to recognise sickness and dreams – since he is not explaining his point, it is difficult to say whether he means that an external observer could do it or whether he thinks there truly are some clear marks, by which a sick or dreaming person could recognise one's condition. The case of obscure sensations Hoffmann can clear up pretty quickly by noticing that obscure sensations do not produce as much confidence and can therefore be discarded because of the doubt they produce.
The final case is perhaps the most intriguing. Hoffmann notices that in affirming something as round, we are actually saying that it has no angles. Yet, we cannot straightaway sense lack of anything – we can merely not be able to sense something. This lack of sensation might then be caused by various things – there might not be anything to sense, but the thing to be sensed might also be far away etc. When we then move from a sensation of tower containing no angles to a proposition that the tower has no angles, we are not just perceiving, but using this perception as a ground for an unjustified inference – the unreliability of the proposition is then no proof against the reliability of sensations. Hoffmann also notes that all causal propositions must be based on similar inferences, because we cannot literally see one thing causing something else – an important acknowledgement of a Humean statement.
Supposing then we accept that Hoffmann has some evidence fo supposing that we do reasonably well distinguish sensations from imaginations, we come to the second question: is there actually any object behind a sensation? This is the place where Hoffmann can criticize the two other leading theories of body-soul-interaction: Leibnizian pre-established harmony and occasionalism. Hoffmann attacks Leibniz' theory, because according to it we could actually never distinguish sensations from imaginations, since both are actually produced by the soul itself. Here Hoffmann apparently doesn't notice that sensations might be so obscure that we never really notice they have actually been produced by ourselves. Yet, Hoffmann has a separate argument against that point: if the difference between sensation and imagination is only that one is more obscure than the other, then this difference is only one of degree and one could easily overcome it through careful clarification. We are here approaching the Kantian idea that sensation with its passivity is completely different in nature from more active events of mental life and thus in need of a clear demarcation from latter.
Occasionalism doesn't pose as much a challenge to Hoffmann. Supposing God would make us experience sensations – something he could well do, Hoffmann admits – we would have to imagine that he wants to deceive us into believing that things exist. Yet, this appears to contradict God's good will, so there is no reason to believe that these things would not exist.
The final question concerning sensation is then whether sensation reveals accurately what features an object has. Here Hoffmann has an easy answer. What do we mean by saying that e.g. proposition ”grass is green” is true? Surely it can only mean that when we observe certain object, called grass, this object produces in us the sensation of green. Generally, with such propositions based on immediate sensations, truth means merely the accordance of the proposition with other sensations (actual or possible). All we need to see, then, is that sensations are reliably consistent in the sense that what we once perceive as green is in similar conditions still green.
Now, all of the arguments thus far have aimed at defending the possibility of objective truth, that is, at showing that in an ideal case a person following these rules of inference and having sensations could make reliable conclusions. Problem is whether we can still prove the possibility of subjective truth, that is, can we show that we are actually in a position where e.g. we can reliably follow our intuitions about connections between ideas. Hoffmann's answer is that certainty lies in the inner sensation, in other words, in our capacity to be aware of our own ideas as states of our mind. If we have vivid enough sensations of our idea, we can be convinced that our mental capacities are working fine and that we can rely on them in constructing truth claims.
Problem of Cartesian demon is still lurking. What if some powerful being would have made us think that we are reliably perceiving something, even though we are not? Hoffmann's peculiar answer is that according to his beliefs such a being could only be God, and if God wants us to believe something, then we know that belief is good for us, even if it is not literally truth. The answer belies Hoffmann's pietistic background, but also has an interesting pragmatist twist: if it works, why bother fixing it.
This concludes the theoretical part of Hoffmann's work. Yet, we are still only halfway through his massive book, since we still have all of the practical side to investigate. I shall begin with the question of using experience correctly.