Does Contextual Nature of Knowledge Limit Applicability?

[nanite1018]

I have been thinking a lot about epistemology lately, and researching "critical rationalism", a philosophy coming from Karl Popper. This question is informed from that, but concerns the contextual nature of knowledge and its implications.

I understand that it is possible to self-consistently justify a conclusion within a certain context, for example laws of physics or the workings of a cell or what have you, based on sense-perception and the law of identity, and that these conclusions can be certain, in the sense that they are definitely true within that context of knowledge. My understanding is that, broadly conceived, the "context" of a generalization is all your perceptions in life, and your entire conceptual framework and knowledge. I accept that this is possible, without question.

My question is this: what happens in a new context? That is, how can I know that a generalization which is certain within my range of experience, for example, all the past, will remain true tomorrow, as it is a different context? Or alternatively, on the other side of the Moon (for example, Newton's laws of motion), etc.? Our knowledge is contextual, that is, every knowledge statement has the unstated parenthesis "within my context of knowledge". So how can we expand that to the future or areas wider than we have heretofore experienced?

If our generalization fails at some point, we know that there is something we do not know, that the context we had before does not include this event, and so we can expand our context and our knowledge by investigating what changed. However, prior this event, are we simply to assume that the context has not changed, even though time has passed, we are in a new location, etc.? Alternatively, if someone comes up with a theory which is identical within our context but which only differs in a context that is wider? For example if someone hypothesized Einstein's special relativity in 1860, well before the Michelson-Morley experiment, or if someone hypothesized the existence of RH factors (or, something beyond simple blood type to determine compatibility) before their had been evidence that they existed.

Is the solution to reject those claims as arbitrary? Or is it that "context" means something which cannot change prior to your experience, i.e. it includes your sense-perception, not the actual conditions (so that the context does not change until your generalization fails)? That explanation makes some sense, but there are difficulties, for example how do you explain the failure of the generalization? It had to have failed in a different context than the one where the initial generalization held initially, but by this notion of context, it did not. Contexts obviously change regularly as people make new discoveries and revisions of previous knowledge statements all the time, so it does not seem unreasonable to think that at any given time the context might be different. If that is reasonable, then how do we justify the assumption that we make in our behavior that it is not the case (until shown otherwise)?

[Grames]

It is not an assumption.

But first lets delimit the scope of 'context'. From my notes on "The Art of Thinking" lecture 6

Problem #3 Must one preface all statements with "In the present context of knowledge"

No, don't say it about everything.

Not perceptual cognition and direct memory.

Not automatized conceptual identification (that's a table)

Not axioms - they apply to all possible contexts anyway

Not mathematics - delimited subject, where everything has been reduced to axioms

Not philosophy - delimited subject, is only about fundamentals, eternal universal principles that underlie everything else and are the framework for evaluating evidence in every other field.

Not "'Atlas Shrugged' is a great novel." - principles of aesthetics are timeless, and your knowledge of the novel is perceptual so this is a truth for all contexts.

Not "There is no God" - God contradicts axioms. Since axioms are for all contexts, God's nonexistence is for all contexts.

"in the present context" does not mean that you are actually uncertain. This just tells listener/reader that conclusion is not self-evident or perceptual. It is built on an accumulation of knowledge which may not be complete. It does not mean the opposite is possible, or that conclusion is untrustworthy.

Knowledge is limited. If you think this undercuts knowledge or makes it vulnerable to overthrow you are implicitly holding omniscience as the standard of certainty.

"in the present context" is not an assertion that anything else is possible. It means: everything known supports this but I know there is more to learn, and what that more might be can't even be speculated. There is more to come and I acknowledge this. My method is right so I know what I learn tomorrow will not contradict what I have learned so far.

What is the point of making the statement "in the present context" if it leaves nothing open?

1) Intellectual honesty - highlighting an inductive conclusion

2) Declares you will entertain evidence (related and credible) for further integration

One question you ask is "what happens in a new context?" and give as an example the far side of the moon with respect to Newton's laws. It turns out the the far side of the moon was (and is) not a new context. Was there ever any basis to suspect that it would be? Newton's laws of motion are partly based on astronomical observation, and the moon is up there amongst the other astronomical bodies, so why would the moon be different? Theoretically the far side of the moon could be different enough to make a difference, but if it was there must be a reason for that. Was there any evidence, however indirect, that that reason existed? If not, then it would be entertaining the arbitrary to allow the positive assertion of some new factor to go unchallenged. You discover a new context when your existing knowledge is no longer adequate.

It is not an assumption to infer that the same causes necessarily lead to the same effects. It would be an assumption to accept that some new cause is at play without evidence. Generic skepticism toward all knowledge because in the past some new cause did come into play is an example of the logical fallacy of moving from the general to the specific. Considering your context of knowledge as an entity comprised of many parts, it would be the fallacy of division to move from "knowledge has been revised in the past" to "all knowledge will be revised in the future, therefore this particular generalization is in doubt right now."

Einstein's theory and the Rh factors would be unsupported arbitrary speculations without the problems they were formulated to solve. Those problems were actually the evidence demanding that new integrations be made to accommodate an expanded context.

[nanite1018]

Okay, so the key is that until you have evidence to suggest that you are in a new context, you cannot conceivably argue that that is in fact the case because you would have no evidence to suggest it (it would be an arbitrary assertion). And so, while you could conceivably turn out to be in a different context, you have no basis for accepting that as true until you have evidence, for the same reason that you cannot use arbitrary assertions in your cognitive processes: they have no cognitive basis.

I see now my mistake. I took the belief you were in the same context as an assumption that must be justified, but in fact it is the assertion that you are in a new context that has to have some evidence for it before it can be entertained seriously. Thank you.

[Vik]

Be careful with the evidence criterion.

Consider the following proposition:

"If I let go of this pen, and the sum of forces in the opposite direction, away from the center of the earth, precisely cancelled out the force associated with gravity, the pen will float"

I have no evidence that such a thing WILL happen, but the proposition is true nonetheless. In fact, I could fill a tank with a fluid slightly more dense than the pen and the pen will float without issue.

Why isn't my proposition arbitrary? Because I've specified the relevant condition.

It's a bit like saying:

"If I let go of this pen, it will fall--provided that no forces presently unknown to me will cancel out the force associated with gravity"

And there's certainly nothing arbitrary about THAT.

[DavidOdden]

Your question is a normative, philosophical one and not a descriptive, historical one. This is the difference between those two kinds of questions: the answer to a normative question tells you how perfectly rational individuals behave given particular ultimate goals, and the answer to the historical question tells you how various individuals with varying degrees of adherence to (and awareness of) rationality did behave in the past. Practicing scientists may engage in low-level lapses of reason: a good and explicit epistemology is an essential tool in adhering consistently to reason. However, many scientists prefer to shut up and compute, and not be distracted by epistemology.

The codicile "every knowledge statement has the unstated parenthesis 'within my context of knowledge'" mildly sounds like an unscientific get-out-of-jail-free card, but it is one only if you have no normative scientific principles. The unstated context assumption does not mean that you can always plead "But I didn't know" and thus avoid responsibility for your irrationality.

The end product of your reasoning is a conceptual principle, one that is open-ended, omits measurements, and cognitively economical. "Context" is especially relevant to the cognitive function of reducing knowledge to a general principle. A hypothesized principle may be amply tested against a variety of specific instances, and the "specific instances" have a logical, conceptual relationship to the conclusion. For instance, if you were to hypothesize "All crows are black", you are invoking two open-ended concepts, "crow" and "black". It would be illogical to inspect chickens as a way of testing the hypothesis. A part of the empirical test of the hypothesis is observationally verifying that any existent that the concept "crow" refers to has an attribute subsumed under the concept "black".

In reporting your results, you provide salient information regarding the observed objects and the method of determining blackness. Thus you have to explain how you identify something as being a "crow" so that you do not include turdus merula or aplonis opaca as instances of "crow". You might identify the objects as corvus caurinus, perhaps even providing a DNA-related specification of what that refers to. The conclusion "all crows are black" then is, in fact, contextually certain. However, what you were not aware of is that there is more than one species of crow. The species corvus corax is also all black, but the species corvus albus is black and white.

For the conclusion "All crows are black" to be reached rationally, you must rationally identify the referent of "crow". In the real world, it is scientifically (not not popularly) well-known that c. caurinus is not the only species of crow, therefore such a conclusion would be irrational and no amount of appeal to context saves the scientist from moral condemnation -- the scientist was in possession of conceptual knowledge that allows an alternative conclusion ("certain species of crow are all black", "there are multiple species of crow") and evaded that knowledge by failing to test the hypothesis against c. albus, c. cornix, which are mixed color). But in the imaginary world of toy examples, it could be the case that there is a single, very rare species of crow that is not all black, a species that is unknown to any scientist. In that imaginary world, the conclusion is arrived at rationally and satisfies the requirements of certainty.

To quote from OPAR p. 172, "Man is a being of limited knowledge - and he must, therefore, identify the cognitive context of his conclusions". Read the (imaginary) scientific report on crow color and you will see that he has identifies that cognitive context -- it has been stated that "crow" refers to the species c. caurinus. It is not necessary to burden the conclusion by stating "All instances of crow genetically identified as c. caurinus via operational test [...] have reflective spectral properties known as 'black' as defined by operational test [...]". When scientific knowledge is such that "crow" is coextensive with c. caurinus etc. then it serves the function of forming conceptual principles to simply say "crow". When you add knowledge that broadens your understanding of the concept "crow", then you cannot rely on the earlier, primitive knowledge context, and you must re-state the conclusion (or in fact substitute a rather different conclusion).

"In a new context" therefore must mean "when new knowledge is added, which materially affects your conclusion, even by expanding the known range of referents of a component concept". That new evidence might be rather indirect, for example in the pen+gravity case, you would have no experience with pens floating away from the center of the Earth, but you would have sufficient evidence that gravity operates in terms of attractions and masses (a general principle), and gravity does not just operate by the principle "things are attracted to the center of the Earth". In a non-imaginary albeit ancient scientific context, it would be arbitrary to say "If Jupiter were positioned 100 miles away from Earth, a pen will float up", i.e. if you do not have knowledge of the relevance of gravity to celestial mechanics.

[Leonid]

"My question is this: what happens in a new context? That is, how can I know that a generalization which is certain within my range of experience, for example, all the past, will remain true tomorrow, as it is a different context?"

Context of knowledge represents its identity. This is a total sum of knowledge which is available to us at the present moment. Your question belongs to the problem of induction which Karl Popper in conjunction with Hume considered unsolvable. I think the best way to resolve this problem is to invoke the Law of Identity. A thing is what it is and its interactions with other entities defined by its properties. If these properties remain unchanged with time then its physical nature and way of interaction also will be the same. A new context appears if 1. We discover new knowledge in regard to the given entities.

In such a case the new knowledge has to be non-contradictory integrated with the old one as long as previous knowledge has been proved true. For example Einstein’s theory of gravitation doesn't disprove Newton's physics but incorporates it.

2. Basic physical constants become different. (For example law of gravitation). That would mean violation of identity law which is axiomatic and therefore such a situation is incomprehensible. In any case that would be incompatible with life.

[Vik]

but you would have sufficient evidence that gravity operates in terms of attractions and masses (a general principle), and gravity does not just operate by the principle "things are attracted to the center of the Earth". In a non-imaginary albeit ancient scientific context, it would be arbitrary to say "If Jupiter were positioned 100 miles away from Earth, a pen will float up", i.e. if you do not have knowledge of the relevance of gravity to celestial mechanics.

Constant acceleration is enough to settle the first question, but it is NOT enough to settle the second.

You need a sum of forces framework--something that Galileo didn't have. Although Galileo understood that motion cannot change without a force, he didn't seem grasp its connection to acceleration.

I would argue that such connections distinguish explanatory generalizations from mere descriptive ones.

I would also argue that such connections are made possible by new concepts.

[Vik]

The codicile "every knowledge statement has the unstated parenthesis 'within my context of knowledge'" mildly sounds like an unscientific get-out-of-jail-free card, but it is one only if you have no normative scientific principles.

I see 5 such principles mentioned in your post:

You must define your concepts in terms of essentials.

You must examine instances that have a logical, conceptual relationship to the conclusion.

You must redefine your concepts when new evidence demands it.

You must clarify your conclusion when changes to your definitions demand it.

Your state of knowledge will tell you whether a claim is warranted or arbitrary.

I would add that wider generalizations must summarize or explain all narrower generalizations falling within its context.