Clear Language, Clear Mind

This will not involve many science facts as the discussion is wholly philosophical in nature. This is an epistemological, not scientific essay, it just happens to use some facts of science.

I want to show the value of thinking of things as inconsistent sets of propositions (or whatever truth carrier you like, but I like propositions) or at least implausible sets of propositions (when at least one inference is inductive (or non-deductive, if you like that term better)).

Consider this set of propositions:

1. Newton’s physics is correct.
2. Things are in a such and such way at time t1.
3. That Newton’s physics is correct and things are in a such and such way at time t1, implies that things will happen in such and such way at time t2.
4. A study found that such and such did not happen at time t2.
5. The study is correct.
6. That the study is correct implies that such and such did not happen at time t2.

This set is plainly inconsistent; it cannot be true. At least one proposition in this set is false. Suppose we are around the time when Einstein introduced his relativity theories. At that time physicists had pretty good reason to believe (1) (among others: good explanatory power, lots of empiric confirmation), and I’m sure some people called physicists who did not stop believing in Newton’s physics even when some studies found results that are contrary to the predictions of Newton’s physics given some antecedent state of affairs dogmatic. I’m fairly sure such a claim of dogmatism is often thrown around in similar cases.

My point is that it is unwise to claim someone is being dogmatic quickly. For there are many things other than some widely accepted theory that could be wrong (in this case (1)). We could be wrong about the antecedent states of affairs (in this case (2)), or wrong about what the theory predicts (in this case (3)) given that state of affairs; perhaps the scientist that make the prediction from the theory made a calculation error. Something similar applies the the study that ‘challenges’ the accepted theory (in this case (5)). So there are many things that could be wrong without the accepted theory being false. It is wise to consider that before calling people that are being epistemically conservative for dogmatic.

The method of putting the relevant propositions in an inconsistent set forces us to be made aware of some perhaps not normally discussed propositions without which the set would be consistent (or not-implausible). Usually in a moderately complex case such as the one with Newton’s physics, a set of propositions that form as inconsistent set (or implausible) will contain 5-10 propositions. In more complex cases, the sets can be much longer (such as very complex cases involving the impossibility of an infinite past which involves temporal and modal logic). In general, the more propositions we can find that together forms an inconsistent set (or implausible), the better overview, and the easier to is to make a justified decision about which proposition(s) to stop believing in in the case that one actually believes all of them. If we are to avoid inconsistent beliefs (=inconsistent objects of beliefs), then we should think of the many potentially epistemically justified ways there are to deal with a such inconsistent set.

In the above case, rejecting (4) would probably not be a wise decision, neither would it be to reject (6). If there is only one study and it is not exceptionally well done, then rejecting (5) is probably not a bad decision to begin with. If more studies (by competent scientists) confirm the first study, then sooner or later we should begin wondering if not our beliefs would have better coherence were we to reject the theory (1). But before we do that we should consider other alternatives such as (2) and (3). It would not be good if we rejected some theory and later found it that we had no grounds to do that because we were wrong about what the antecedent state of affair was (2).

This way of solving problems (which usually involve an inconsistency of we add together the relevant propositions to a set), is applicable to every topic that I have thought of. It is especially useful to very complex situations where it is hard to get an overview and it seems hard to settle on a specific solution (that is, hard to find out which proposition is the epistemically most justified to deny).

I noticed a small dissimilarity between the two words. As I have pointed out numerous times in the past, the phrase “I don’t believe that p” is ambiguous between belief in not-p and lack of belief in p. However the similar phrase for knowledge, “I don’t know that p” is not similarly ambiguous. It is however ambiguous in another way; between lack of belief in p and in not-p, and lack of knowledge that p.

“Web(s) of belief” ≡ “web”

“Object(s) of belief” ≡ “oob”

The justification of the web of belief

A web is more or less justified. The justification of a web is a function of its members in many ways. Here are some ways that I speculate may increase the justification of a web. I do not pretend to offer much argumentation for my thoughts or much certainty in the conclusions. It seems to me that it is extremely hard to have any strong evidence the beliefs about these matters. That shall not keep me from examining the matter and giving my intuitions.

The number of beliefs in a web

Imagine a web with only two beliefs whose oob logically implied each other. Think of any two logically equivalent propositions. The interconnectedness of that web is extremely high since logical implication is one of the strongest relations two oob can stand in (see below) and all the members are connected to each other by logical implication. But still it seems to me that such a web is not very justified. I suggest that we explain that by the number of beliefs in the web. If a person with the aforementioned web gave an argument to another person, the other person would (and should) respond that it is circular. It seems to me that we cannot avoid circularity in our justification (because of the infinite regress argument and that epistemic foundationalism and epistemic infinitism is false). However circularity is not much of a problem when the web contains many thousand belief as it does of any grown-up human.

The number of relations of certain kinds between the oob

The oob are truth carriers. (Just substitute your favorite truth carrier be it propositions, sentences, beliefs etc.)

We may distinguish between three kinds of relations between the oob: (1) positive relations, these are the relations that increase the justification of a web as a function of their number, and the justification of a web is partial function of the positive relations between oob, (2) negative relations, which is the opposite of positive relations; they decrease the justification of a web, (3) neutral relations, relations that have no effect on the justification of a web. We may note that this distinction is true regardless of the distribution of relations in the three categories.

Then we ask ourselves: Which relations are positive relations? Deductive relations such as (for all x, and for all y) “x logically implies y”, “x materially implies y” come to mind. Inductive relations such as “x is explained by y”, and “x gives good reason to believe y”, “x is best explained by y” seem to me to increase the justification of a web.

Similarly, which are negative relations? Basically the same of the above just with the added change that it is the negation of y. If you believe two things, and the one logically implies the negation of the other, you have an inconsistent web. It is impossible for all the oob to be true at the same time in a such web.

That a web has at least two beliefs whose oob are inconsistent does not imply that the justification of the web is zero. To see this we should simply recall that all grown-ups have inconsistent oob and that not all web of grown-ups have an equal level of justification. Hence, it is not the case that if a web contains beliefs whose oob are inconsistent, then the justification of that web is zero. Since if it was the case, then web of all grown-ups would be equally justified, all having zero justification. However, it is still the case that such inconsistent oob reduce the justification of a web, which I why we ought to change our mind when we discover that we hold beliefs whose oob are inconsistent.

I can’t think of any neutral relation, but they are not very relevant anyway, so lets disregard an example of a such. There may be no such relation for all I know.

Interconnectedness

I mentioned this in passing above but it deserves elaboration. The justification of a web is also a partial function of the interconnectedness of a web. If a web consisted of a thousand beliefs but that these were divided into 10 groups of beliefs each of whose oob did not have any positive relations with the oob of the other groups of belief, then it seems to me that the justification of that web would be very low. This seems best explainable by justification being a partial function of interconnectedness too.

If you happen to know about evolutionary peaks, good. If not I will briefly try to explain it though it is best if you know about evolutionary theory.

An evolutionary peak is a possible genome in the vicinity of which there is no other more fit genome. All mutations that could happen would result in a less fit genome (i.e. genes that replicate less than the genes in the peak genome). If evolution reaches a peak, it will stay there as it does not ‘have foresight’ (or ‘sight’) to move down the hill to another and higher peak even if there is one relatively nearby. Evolution is blind. The genome is evolutionary stable once at the hill. This continues until a change in the environment happens and another genome becomes more fit. Then evolution continues to change the genome to whatever is more fit. It is rare that a mutation occurs and thus gives evolution an opportunity to evolve change the genome into a more fit one. Evolution takes lots of time. It is even more rare that multiple mutations arise at a time.

Consider now webs of belief. A person’s web of belief is the entirety of all his beliefs. A web of belief may be more justified/warranted/better than another web of belief for a number of reasons (simplicity, coherency, lack of contradictions, mutual support, etc.). A person may change (at will but not completely free at will) his web of belief by changing its parts, either one belief at a time or many beliefs at a time. It is rare that a person changes his belief, if it is in the middle of his web of belief (=connected with many other beliefs). It is even more rarely that a person changes a lot of beliefs at one time.

The analogy is this:

Do you see the analogy? It is quite interesting I think. Similarly to evolution not having ‘foresight’/'sight’, most people do not have the necessary foresight/sight to see that another web of belief although a bit away from their current web of belief is better than their current one. And if they are at a peak or close to a peak, they will not move towards a higher peak if it is a bit away and they only change a few belief at a time. In a way it is rational to change one’s web of belief toward the nearest peak one can spot. Though ultimately it is more rational to try to spot the highest peak and then move towards it. But it is so hard to spot the highest peak (=discover which web of beliefs is the best), that we for all practical purposes cannot do so and thus stay near a local web of belief. Further, it is not humanly possible to discover with a high degree of certainty which webs of belief are the peaks and which are not. There is no known formula in which one can input all one’s beliefs (there are too many of them too) and in the output is the web of belief’s goodness rating.

But if we cannot do this with much certainty, how should we be able to say that another person has a worse web of belief than we have with much certainty? We cannot. Though we can do rough analyses and make somewhat justified claims about other people’s webs of belief. It is vary hard if not impossible for two rational and sophisticated people to discover which of them has the best web of belief. If their webs of belief are very different and are both near a local peak, then there is no way for one of them to move towards the other while continuously getting a better web of belief. He would need to change many/a lot of beliefs at once, and this very rarely happens. Arguments usually only change a single/small number of belief(s) in a person at a time. What would need to be done to change one’s web of belief so drastically, rationally, is an evaluation of all relevant arguments ‘viewed’ from both webs of belief. In the case of atheism/theism, doing so will take at least several years. It would be much better if one simply found oneself closer to the atheism peak to begin with (I did), or changed to moving toward the atheism peak without first moving towards the theism peak. But then, a person who happened to be a theist (because of, say, his parents) would most probably first move towards the theist peak than the atheist peak. That is the most rational way given a conservative principle like “change as little beliefs at a time as possible to continue gaining a better web of belief.”.

Still, given the above, I’m relatively sure that, say, a thomist (in fact it was a thomist that inspired me to write this essay) has a worse web of belief than I do and that the highest thomism peak is much lower than the highest atheism peak. But I should not claim much certainty about this.

One may talk of a reliable car. “Reliable” here clearly means a car that has a high success rate of doing what it is supposed to (e.g. getting one where one wants to go in a reasonable time). One may also talk of a reliable source of information, that is, an authority. Can we understand reliability in a similar way here? Some people think that two concepts/notions of reliability are necessary. It seems to me that we can do with just one. An authority about something is just a person that has a high success rate of telling true propositions (/have a % justified beliefs) about the matter.

As an example think of Searle’s chinese room example. Is the person in the room a reliable source?

“Imagine a native English speaker who knows no Chinese locked in a room full of boxes of Chinese symbols (a data base) together with a book of instructions for manipulating the symbols (the program). Imagine that people outside the room send in other Chinese symbols which, unknown to the person in the room, are questions in Chinese (the input). And imagine that by following the instructions in the program the man in the room is able to pass out Chinese symbols which are correct answers to the questions (the output).” (Searle, 1999, ‘The Chinese Room’, in R.A. Wilson and F. Keil (eds.), The MIT Encyclopedia of the Cognitive Sciences, Cambridge, MA: MIT Press. Found here.)

It seems to me that the answer is “yes”.

The other explication that has been offered of a reliable source is that “the person knows what he is talking about”. It seems to me that this is a constant phrase (i.e. one that is always used in almost the exactly same way). Such phrases are more often than not best understood non-literally. I suggest that a non-literal understanding/interpretation is a good idea. It could be understood as something similar to the general explication of reliability that I offered in the beginning of this essay.

However, one could insist that the phrase is meant literally and that reliability of persons /experts/authorities implies that the person knows. However it seems to me that the chinese room is a counter-example to this. The person in the room is reliable and does not know.

I also note that a non-literal interpretation/understanding is consistent with a fictionalist account of the field of the matter (e.g. an error theory about ethics) because one could use the notion of justified belief

ACB:

This is an interesting point. Is there a minimum level of understanding that someone must have in order to derive justification from an authority? For example, if you are completely ignorant of music theory, and a qualified musician tells you: “A tritone is an augmented fourth or a diminished fifth”, are you justified in believing it? You do not have a clue what it means, except that it is something to do with music. Imagine the following exchange:

Layman (L): What are you talking about?
Musician (M): I’m talking about intervals.
L: What are they?
M: The distances between two notes.
L: You mean, like when two players stand five feet apart…
M: No, you fool, I mean like when you play two different notes on the piano.
L: Oh, I see. So what is this ‘fourth’ and ‘fifth’ stuff? That’s more than two.
M: No, you have to count up from the bottom note…
[Some minutes later]
L: Ah, I’m beginning to understand you now. So an augmented fourth sounds the same as a diminished fifth.
M: Yes, that’s right.
L: But what the hell is a tritone? Three tones? How can that be the same?
[Some minutes later]
L: Ah, I understand. Now I believe your original statement.
M: But why didn’t you believe it in the first place? I’m an expert in music theory, and you know I wouldn’t lie to you.

At what point would L become justified in believing M’s original statement? At the beginning? At the end? Or at some point in between? Is the acquisition of justification an all-or-nothing affair, or can it be incremental? Can any clear rules be formulated about this?

Or am I looking at this the wrong way? Should the question be, not “when would L first have justification for believing the statement”, but simply “when could he first believe the statement”?

Any thoughts would be welcome.

Emil:

I’m wondering this myself. I haven’t found any persuasive argument though. I have nothing to add.

Source.

Kennethamy in response to something about certainty:

I did not say there was such a thing as objective certainty. I said objective certainty was what Descartes was aiming at, not subjective or psychological certainty. He did not care about that. People feel certain about all sorts of things, about which they later turn out to be wrong. And people feel certain about contrary things. Subjective certainty is of no epistemological interest. Descartes presented as his prime example of objective certainty, “I exist”. So, if you are going to deny there is such a thing as objective certainty, you have to deny you are objectively certain that you (yourself) exist. That is, that it would be possible for you to be mistaken about whether you exist. Do you think it would be possible for you to believe that you exist, and still not exist? For that is what it would be for you to be mistaken that you exist.

None of your pronouncements about certainty being a useful fiction really matter. You may think what you like. But you still have Descartes argument to wrestle with, and simply saying that objective certainty is a useful fiction, or the truth with a capital T is a fiction, will really not cut it. It is the argument that is the thing, and as Socrates said, “we must follow the argument wherever she leads us”. How do you handle Descartes’s argument that it is impossible to be mistaken about whether one exists, for in order to be mistaken, one must exist? Have you a reply?

Emil in response to the above:

Not quite sure that subjective certainty is of no epistemic interest, but otherwise I agree.

Kennethamy in response to the above:

Yes. I have been told over a trillion times not to exaggerate.

Emil in response to the above:

Hahahahaha. Priceless!

Source.

[Update 11/22/09]

I note that Ben actually talked about this principle in a post on his blog, “if it’s reasonable to believe a bunch of premises, it’s also reasonable to (on the basis of the logical connection) believe the conclusions that can be validly inferred from those premises”,

[/update]

I have recently been discussing Gettier’s famous counter-examples to the JTB theory of knowledge. In his original paper Gettier argued that there are some cases where all the necessary and sufficient conditions of knowledge according to JTB theory are met, but the person in question fails to know. In the thread user ACB asked that:

If (1) the man who will get the job is Jones, and
(2) Jones has ten coins in his pocket,
then
(3) the man who will get the job has ten coins in his pocket.

But does it logically follow that if Smith is justified in believing (1) and (2), then he is justified in believing (3)? [followed by a proposed counter-example]

I and another person thought that it did follow. In other words we subscribed to the following principle about justification:

For all persons, for all propositions, P, and for all propositions, Q, that a person is epistemically justified in believing that P, and that P logically implies Q logically implies that that person is epistemically justified in believing that Q.
(∀x)(∀P)(∀Q)(Jx(P)∧P⇒Q))⇒Jx(Q)

The above case seems to me to be a true instantiation of the justification principle. ACB disagreed with the principle and proposed a counter-example with the alphabet which did not convince me. He then tried another counter-example that involved some mathematical propositions. That proposed counter-example did not convince me either, but it did make me think of an example that did convince me. Here’s my counter-example:

1. 1+1=2

2. 456·789=359784

Both of these propositions are true, they are even necessarily true. According to the definition of logical implication they imply each other (and themselves), since any necessarily true proposition imply any (other) necessarily true proposition.¹

Now suppose that a child is learning elemental math. Say that she has not even learned multiplication yet, however she has learned that 1+1=2 is true and she knows this. That implies that she is epistemically justified in her belief that 1+1=2. But it clear to me that she is not epistemically justified in believing that 456·789=359784. This is a counter-example to the justification principle and the principle is therefore false.

It seems to me that one could perhaps save the justification principle with some relevance logic understanding of “logical implication”. However I shall not pursue that here.

Notes

A rewrite of an earlier article “two kinds of certainty”.

-

A quick explanation of two types of certainty that people tend to confuse.

Psychological certainty

The first is the one we typically mean in normal language. It’s called psychological certainty. It’s a feeling of certainty; A confidence in something. This is the one we’re talking about when we say things like “Are you 100% sure?”. It is possible that someone is 100% psychologically certain that something is true and that the something is actually false. Psychological certainty comes in degrees. Good examples of psychological certainty and false beliefs are found in religious people and various sport fans.

Epistemic certainty

The second is epistemic certainty. This is the one that philosophers usually talk about. It’s the inability to be wrong type of certainty. If one is epistemically certain, then one cannot be wrong in some sense. This type of certainty is also called cartesian (after Descartes) certainty, infallible certainty and absolute certainty. This type of certainty does not come in degrees; Either one is epistemically certain or one is not. It is not entirely clear how to explicate this kind of certainty. Here are two proposals:

1. (∀x)(∀P)[Bx(P)∧□P⇒Cx(P)]
For all agents and for all propositions, (that an agent believes a proposition and that proposition is necessarily the case) logically implies that that agent is epistemically certain of that proposition.

2. (∀x)(∀P)[Bx(P)⇒P]
For all agents and for all propositions, that an agent believes a proposition logically implies that proposition.

Translation keys

Domains. x is agents. P is propositions.
Bx(P) means x believes that P.
Cx(P) means x is epistemically certain that P.
⇒ is logical implication.

For convenience, it smart to type p-certain and e-certain to distinguish between them.

References

http://philofreligion.homestead.com/files/CertaintyandIrrevisability.htm (About psychological and epistemic certainty.)

It is clear that when we use the phrase “It is possible that…” it is not in all cases used to express mere alethic possibility, that is, “It is logically possible that p.” [◊P] Other times it is used to express what is called epistemic possibility, that is, “For all we (or I) know p might be true.”. It preliminarily seems like a good idea to explicate this as “It is compatible with everything we know that p is true and that p is false.”.¹ But this is an improper explication as pointed out in Possible Worlds.²

Consider the example of Goldbach’s Conjecture (GC), that is, that every even number greater than 2 is the sum of two prime numbers.³ A mathematician might say that it is possible that (GC) is true. If we explicate that as suggested above, then we get that (GC) and not-(GC) is consistent with everything we know. We may formalize this explication as:

(∀P)(EP↔◊[P∧(∀n)Q₁∧Q₂∧Q₃∧...∧Q_n∧([∀Q][KQ])]) where “EP” means “P is epistemically possible”, “KQ” means “Q is known”.⁴

However, since (GC) is a mathematical proposition, then it is either necessarily true, or necessarily false. If it is necessarily true, then it’s negation is not consistent with everything we know. All necessary falsehoods are inconsistent with any proposition.⁵ If (GC) is false, then (GC) is necessarily false, and, thus it is not consistent with everything we know. If (GC) is true, then it is necessarily true, but then the claim that it is false is necessarily false and thus not consistent with everything we know. I note that this objection applies when one deals with non-contingent propositions.

The authors of Possible Worlds suggest instead that epistemic possibility should be explicated without alethic terms at all. They suggest the plain explication of: We (or I) do not know that (GC), and we do not know that not-(GC).