1. Statics
We defined logical modalities with reference to the relative credibilities of appearances ‘within contexts’. We will here try to clarify what constitutes a context, and its role.
In a very narrow, ‘logical’ sense, one might refer to the context of a proposition as any arbitrary set of propositions. In this sense, a proposition could be taken in isolation and constitute its own context. It might still appear to us as true (if in itself reasonable looking) or false (if obviously internally inconsistent) or even problematic (if of uncertain meaning). Likewise, for any larger set of propositions we choose to focus on exclusively. But this leads to a very restricted sense of truth or falsehood.
In practice, there is no such animal. A more ‘epistemological’ understanding of context is called for. The effective context of any proposition is not arbitrarily delimitable, but is a very wide body of information, which, whether we are conscious of it or not, impinges on our judgement concerning the proposition. It is the ‘status quo’ of knowledge at a given time, for a given individual or group.
A proposition is not just a string of words or symbols written on a piece of paper; it has to mean something to become an object of logical discussion. We cannot consider it in isolation, because our consciousness is, like it or not, always determined by a mass of present or remembered perceptual and conceptual data. This periphery is bound to affect our reaction to the proposition at hand.
It is in acknowledgement of this dependency that our definitions of logical modality must be constructed. The context of a proposition is thus all the things we are experiencing or thinking, or remember or forgot having experienced and thought — which happen to color the proposition at hand as credible or not, to whatever degree.
This is not intended as a psychological observation, suggesting that our judgment is being warped by structural or emotional factors; in some cases it indeed is, in others not. Nor is the issue what we consciously take into consideration; that may have no effect, and there may be unconscious influences anyway.
It is merely a recognition that the appearance of realism or unrealism of any proposition is always a function of a great amount of data, besides it and any artificially selected framework. The contextual data generating such a result include: perceptions, direct conceptual insights, and indirect inductions and deductions. Hence the concept of a context, as here used. It refers to the actual surrounding conditions of our knowledge.
It is hard to pinpoint precisely and with unfailing accuracy just which of the peripheral information impinges on a given proposition’s evaluation. Innumerable wordless sensations, mental images, and intuitions, are involved, and merely having had logically relevant experiences or thoughts, does not entail that they played any effective role in the present result. All we can say with certitude is that a lot of data is involved in the final display of some quality of credibility by a proposition.
The whole of logical science may be viewed as an ongoing attempt to investigate this aetiology. Its job is to find just what causes propositions to carry conviction or fail to do so, and how the totality of knowledge can be gradually perfected. We have seen its work in the domain of deduction with certain categorical propositions; now other forms are about to be analyzed. The solution to the problem of knowledge is not found in simplistic and vague pontifications, nor in a step-by-step linear guidebook, but in a vast tapestry of interlocking considerations.
2. Dynamics
The concepts of truth, falsehood, and problemacy, refer to the deployments of credibility in a static context, the ‘state of affairs’ in knowledge at a given stage. The concepts of necessity, impossibility, and contingency, refer to the changes of credibility: they consider knowledge more dynamically.
Knowledge is an evolving thing. We, human beings, are none of us ever omniscient or infallible. If our consciousness was unlimited by space, time, and structural resources, like God’s, there would be no problematic knowledge: every proposition would be true or false with finality. Just as reality is one, knowledge would be one and complete.
But reality is opened to our consciousness piecemeal, over time. We are obliged to repeatedly adapt to new factual input. Indeed, we have to actively dig into reality, if we want to approach that ultimate goal of total consciousness of everything.
We know we cannot reach that goal, since we have already missed out on enormous tracts of reality in the distant past, and the whole future is ahead of us, unexplored. We know that innumerable phenomena are happening all around us and within us, all the time, at every level (from the sub-atomic to the astronomical, from the material and physiological to the mental and spiritual); and we cannot keep track of all that. Thus, the data available to us is inevitably restricted.
Furthermore, our faculties of knowledge can play tricks on us, and draw us away from the goal. Our eyes may be myopic, our memory may fail, our reasoning may be muddled, we may be too imaginative, our mind may be moved by very subjective, emotional, considerations. We have to somehow make-do, in spite of all such imperfections in our make-up.
Our response to these limitations, if we are intent on knowing reality, is staying aware of our mental processes, and unflagging re-evaluation of what and how much we know or ignore. This is where logical modality comes into play. It provides us with labels we can attach to each and every proposition, which assign it a rank, as we proceed.
Theoretically, we take the full body of everything we have experienced or thought thus far, and order the present information in a hierarchy. Tools may be invented to increase our certainties: eyeglasses, the written word, a science of logic. The sources of information are considered: we distinguish between the fictions of our imagination and the facts of sense data, between vague and clear concepts, between fallacious and rigorous argumentation.
In practice, things are more dynamic than that. We may take some part of our data base, and hold it still long enough to evaluate it with the proper amount of reflection. But, on the whole, the process is on-going, an ad hoc response to the flux of information. Logical modalities allow us to register our value-judgments of this kind as we proceed, like a running commentary.
3. Time-Frames
Now, there are three ways for knowledge to evolve, and credibility to change. We may associate the word ‘context’ to the sum total of knowledge, the whole environment — or, more restrictively, to a given body of fundamental axioms and raw data, a framework. Here, let us use it in the latter sense.
We may not have drawn all the possible lessons from these primary givens; the process is not automatic, but has a time dimension. A proposition may be logically implicit in knowledge I already have, but it may take me time and effort to discover it.
There is always a great deal of undigested, unexploited information in our memory banks, and accessing it and assessing it demand time and skill. I mean, Philosophy, for example, requires relatively little raw data to develop considerably, because it pursues facts implicit in every existent. This is internal development, or context intensifying.
Or we may receive new input of rational axioms and empirical data to consider. Here, two alternatives exist: either the new facts already existed out there, but unbeknown to us; or some change occurred in these external objects themselves, which we accordingly now absorb as new existents. These are developments fed from the outside, or context extending.
Thus, we may distinguish between three time-frames for modality change: the external time in which objects change into new objects; the interfacial time of turning our attention and sensors towards pre-existing objects — to extend context; and the internal time of mental assimilation of memory (analyzing, comparing, checking consistency) — the work of intensifying context.
The first of these essentially pertains to natural and temporal modality; the second, extensional modality; the third, is the time-frame of logical modality. But all of them, if only incidentally, concern logical modality.
4. Context Comparisons
That our definitions of truth and falsehood do not specify the context taken as being final and ideal, is not a relativistic position. It is merely intended as a statement that every proposition’s credibility is conditioned by a totality.
The given context is pragmatically accepted as a starting point for further inquiry, without thereby being regarded as ‘the best of all possible contexts’. It is subject to change, to improvement. Some contexts are to be favored over others — the exact grounds just need to be elucidated.
We might refer to the overall credibility of a context. We could perhaps consider any given context as a whole, and (of course, very roughly) sum-up and average the credibilities of its constituents, and thus get an estimate of its finality or staying-power. But, quite apart from the issue of practical feasibility, I do not think this would be of any use. The relative credibilities given within each context pertain to that context alone, and have no bearing on the relative credibilities in other contexts.
The general principle for comparing contexts seems obvious enough. Contexts are of varying scope and intensity, and it is clear that the deeper and wider the context, the closer to final will the impressions of truth or falsehood concerning any proposition in it be; and the less numerous will doubtful cases be. Thus, the bigger and more cohesive the context, the better.
The ideal context of omniscience is beyond man’s power, we can only gradually approach it. But we can say that in that ultimate, limiting case, the impressions of truth or falsehood would be final, subject to no further change or appeal; and furthermore, there would be no in-between impressions of a doubtful kind, since reality once established is determinate. Here, knowledge and reality would correspond entirely.
When we apply the above principle to one person over time, it is relatively easy to say which context is to be preferred. The more information at his or her disposal, the more this information has been carefully sifted for hidden messages, the more certain may that person be. For the individual, improvement is almost inevitable over time, because his or her context is a widening circle.
We always refer to appearance, though we can distinguish between prima-facie impressions and well-tested impressions. The two kinds of impression are essentially the same in nature, but they have different positions in a continuum stretching from subjectivity and mere belief (which still however contain seeds of objectivity and knowledge) to ultimate realism and certainty.
When, however, we compare the contexts of two (or more) people, it is not so easy to say which is better or worse. Each may have data the other lacks, and each may have thought about any item of data they have in common more thoroughly than the other. Thus, they may disagree in their conclusions, and yet both be ‘right’ for their respective contexts. And since their contexts overlap in only some respects, so that neither embraces the other as a whole, the contexts cannot be rated better or worse.
All we can do is focus on specific areas of knowledge, and consider the relative expertise of each individual in that area. If someone is a specialist in some field, we may well assign greater credibility to his or her pronouncements on the subject. On this basis, we may even trust a person we know to be generally very wise, without committing the fallacy of ‘ad hominem’.
5. Personal and Social
We must distinguish, here, between personal and social knowledge.
At the lowest level, is ‘personal knowledge’. Some people are better at knowing than others, because of their healthier faculties, or because they are endowed with more intelligence and insight, or because they are more interested, more careful, and make more of an effort, in this domain. Also, individuals inevitably have different quantities of information at their disposal, both inner and outer.
‘Social knowledge’ is an ideal. We collectively, across cultural boundaries and the generations, gradually compile a record of common knowledge, agreed upon methods, information and conclusions. It is the human heritage, our shared data bank.
An individual may admittedly have more knowledge of some field than everyone else at a given time; he may get to share it, or it may disappear with him. There may be specific disagreements at any time between groups of individuals. It may even happen that the majority of the peer group wrongly rejects an individual’s valuable contribution.
Yet, over time, the collective enterprise we call Science develops, a pool of knowledge greater and truer than any which individuals can fully match, based on a methodological consensus.
Since credibilities depend on context, individuals may assign different credibilities to the same proposition. To that extent, truth and falsehood are often ‘subjective’, since they reflect the mental abilities and dispositions of people.
Still, I may take all the premises of another person and demonstrate that his evaluations are logically incorrect even for his context. In a sense, I start off with the same context as him, and end up with a slightly different version; but in another sense, I have merely clarified the given context, brought out its full potential, without significantly altering it. If he is intelligent and honest enough, he normally bows to the evidence.
Thus, the contextuality of credibility need not imply its utter subjectivity. The evaluation can only ultimately be viewed as subjective in the pejorative sense, if it is contextually wrong.
And even then, such accusation can only be leveled fairly if the individual allowed psychological forces to sway his judgment. He may be intellectually negligent through laziness, or dishonestly evade unpleasant or frightening data or thoughts, or insincerely report his conclusions. If the error was honest, merely due to a failure to notice a connection, we can hardly criticize him, only correct him.
We get around these problems of personal weakness through the institution of social knowledge, science. This allows us to collectively ‘average-out’ the subjective vector. We mutually scrutinize and criticize each other’s contributions, until we are of one mind. There may still be collective delusion, but that at least eliminates personal deviations from logical norms.
We presume that the influence of our collective mind-sets will gradually wither away as knowledge develops further. This assumption is justified by previous developments: we have seen historical examples of liberation from ideas which seemed immovable. The notion that science is inevitably subjective, is derived from such liberations, and cannot be used to denigrate them.
Drawn from Future Logic (1990), Chapter 22.