Expectation And Certainty

[Rade]

It seems to me that 100% of all expectations (however you wish to define the term) come with some degree of uncertainty. Can anyone provide a counter argument.

[lawcat]

Anachronism is the only counter example I can think of, You expect something that has already been proven. So, I'd say not all expectations carry uncertainty because some are anachronisms.

[Rade]

Anachronism is the only counter example I can think of, You expect something that has already been proven.

But, is not proof (outside mathematical sense of the term) something impossible to come by honestly with certainty ? So, perhaps we only find expectation without uncertainty in the anachronism of mathematics ?

[CraigD]

It seems to me that 100% of all expectations (however you wish to define the term) come with some degree of uncertainty. Can anyone provide a counter argument.

Before answering this epistemological question, I must answer this ontological one: is the ideal, which is non-physical, real?

 

If I answer this question “yes”, I then conclude that formal statements such as the Peano axioms and the infinite collection of theorems that can be generated from them are real and certain. Thus the expectation that statements such as “[imath]1+2=3[/imath]” and “[imath]4+5\not=6[/imath]” are true have no degree of uncertainty.

 

If, on the other hand, I answer the question “no”, viewing the ideal as consequences of physical processes such as the neurophysiology of human brains – “emergent phenomena”, in other words – I can’t be entirely certain that statements such as “[imath]1+2=3[/imath]” are true, because, for example, I may have mistyped the expression, and failed to perceive my mistake, no matter how carefully I type and check.

 

Anachronism is the only counter example I can think of, You expect something that has already been proven. So, I'd say not all expectations carry uncertainty because some are anachronisms.

I believe informal, natural language statements about past events are somewhat uncertain, because, for example, I may miss-perceived events I witnessed, or miss-remember events I perceived accurately. No matter how carefully I research and check, I may err in my recollection of past events I recall from documents and other representations of them, or may be purposefully deceived by untrue documents or verbal statements.

 

PS: I don’t think the word anachronism is used correctly in lawcat’s post. It’s usual meaning “misplaced in time”, not “about a past event”, for example, a horse-drawn carriage on a present-day automobile road, or a story about 1965 in which a character uses a pocket-size mobile phone or the internet.

[Fluxus]

It seems to me that 100% of all expectations (however you wish to define the term) come with some degree of uncertainty. Can anyone provide a counter argument.

Ultimately, certainty is an emotion, not really an epistemic condition.

 

As such, I'm *cough* fairly confident :D that people routinely experience far greater degrees of certainty than can be justified by the amount of information available to the individual holding those expectations.

 

If we adhere to what our beliefs ought to justify, inductive processes should not produce 100% certainty. By definition, induction means you are extrapolating from a sample, and applying that information to a larger group.

 

However, if our expectation is based in deductions, we would be justified in 100% certainty. E.g. I can justifiably expect with total confidence that if I meet a bachelor, he will be unmarried.

 

Doubting deductions would require conditions that are not necessarily held, such as not being sure of the meaning of a term, or doubt about the validity of the inference. It might also require some very extreme and potentially problematic positions, such as doubting basic axioms of logic (law of identity, law of non-contradiction), doubting basic logical functions, questioning the validity of a Foundationalist belief system. You could also espouse radical relativism and proclaim that "there are no absolute truths," which is essentially a self-defeating position, since the basic claim that "there are no absolute truths" is itself an absolute truth, and relies on certain axioms to be absolutely true. I.e. you'd need to go to extremes to lose the tiniest bit of confidence in a deduction.

[Rade]

However, if our expectation is based in deductions, we would be justified in 100% certainty. E.g. I can justifiably expect with total confidence that if I meet a bachelor, he will be unmarried.

Nice reply. But, if you lived in the year 1122 AD you would have no logical reason to deduce that a bachelor was not married, not how the term was used then. Also, does not the word bachelor as relates to married apply to male-female relationships, thus, two married gay men could logically deduce that they meet the definition of a bachelor if asked the question by a female ? Deductive logic demands that the truth of the premises necessitates the truth of the conclusion. The goal is to distinguish deductively correct arguments that derive from true premises from deductively incorrect argument. Thus, use of deduction alone does not result in 100% certainty that expectations are correct, some deductions are based on false premise.

 

Perhaps it is correct to say that deductively correct arguments yield 100% certainty of expectation ?

[Qfwfq]

You're right Rade, any man who claims to be a bachelor ought to be locked up! The very fact that it's a man making this claim is incompatible with it being a laurel berry...:lol:

 

Aside from the shortcomings of natural languages:

Perhaps it is correct to say that deductively correct arguments yield 100% certainty of expectation ?

But, as you point out, we must distinguish between the conclusion "He is not married." being uncertain and "If he is a bachelor then he is not married." being uncertain. Ignoring the other possible meanings of the word, the second assert is true and certain, regardless of whether any given man is a bachelor. In like manner, properly demonstrated theorems are true as long as the formal system is well specified. you can say that 6 + 8 = 3 is true if the arithmetic of [imath]\mathbb{Z}_{11}[/imath] is specified and it is easy to show, in this casse, that it is true with certainty.

[Fluxus]

Nice reply. But, if you lived in the year 1122 AD you would have no logical reason to deduce that a bachelor was not married, not how the term was used then...

Philosophers tend to work with statements or propositions, which are interpreted as a language-independent expression of semantic content. In contrast, "sentences" are language-specific, and the meanings of terms can change over time. If you find "statements" to be problematic and prefer to stick to sentences, then we'd be forced to time-stamp all of our claims and proofs in an attempt to index the meanings and references of the terms. Thus "circa 2011, all bachelors are unmarried" is certain.

 

To be a bit more precise there are several categories of knowledge which generally qualify for certainty. "All bachelors are unmarried" is actually an analytic statement ("true by definition," or a truth that reveals no new information) as well as a priori (its truth can be evaluated independent of experience). A deduction is when the truth of the conclusion follows from the validity of the inference. In basic propositional logic (and math), the simple example is:

 

x = y

y = z

:: x = z

 

The content is irrelevant, what matters is the validity of the inference. This would be considered synthetic a priori, since we can know the conclusion is true without any experience of x, y and z, but we learn something new about x and z. (Per Kant, mathematics is generally classified as synthetic a priori.)

 

 

Perhaps it is correct to say that deductively correct arguments yield 100% certainty of expectation ?

Well...

 

All of the above categories of knowledge claims rely on the law of non-contradiction (LNC). The Cogito of Descartes' date=' which seems to be where the skeptic's buck must stop, is ultimately only as strong as the LNC.

 

Aristotle's discussion of the LNC established it as an incontrovertible axiom in Western thought, and is supported by subsequent articulations such as the Principle of Explosion. According to this argument, if you allow a single inconsistency in your formal system, then you can prove any proposition to be both true and false, and your entire formal system becomes inconsistent and therefore useless.

 

Arithmetic offers a simple testing ground. Let's say we declare that 2+2=4 [i']and[/i] 2+2=5. As a result, you could substitute 4 and 5 at any time, and inevitably prove that any number is actually equal to any other number. E.g. 4+5=8, 9, and 10, because "4+5" can be interpreted as "4+4" and "4+5" and "5+4" and "5+5." So, you've got 4=5 and 8=9=10, and so forth. In a few steps, we can show any number to be equal to any other number. In other words, there is no way to contain the inconsistency.

 

Thus, if you express skepticism of the LNC, the effort will be self-defeating. You could never trust your conclusions, because without the LNC the truth-value of your arguments can be assigned arbitrarily. The statement "the LNC is false" is true, false, neither true nor false, both true and false, and all and neither of these simultaneously and at different times.

 

Of course, rock-solid certainty can only discourage the skeptics for so long. :D Some radical relativists may openly declare that "all knowledge is uncertain" and not care that such statements are self-defeating. Alternately, "dialetheism" is the ultimate skepticism, in that it purports that the Principle of Explosion is not necessarily applied in all cases, and that perhaps we can have and consume our logical cake. (I for one don't buy it, since there seems to be no mechanism to determine what would or would not "explode.")

 

 

Thus, it's unclear where skeptics will draw the line, but it does seem that the more they question, the less validity their own skeptical inquiry can muster. Since "certainty" is ultimately an emotion, the answer is likely to vary from one individual to the next.

[Rade]

Philosophers tend to work with statements or propositions, which are interpreted as a language-independent expression of semantic content. In contrast, "sentences" are language-specific, and the meanings of terms can change over time.

Thank you for the comments. I'm not sure I understand how you find that a statement differs from a sentence ? Are not all statements declarative sentences, sure, language specific, such as the statements (1) snow is white and (2) der Schnee ist weiss. Now, both of these statements express a proposition, the whiteness of snow, thus, different statements (as declarative sentences) can be used to express the same proposition. So, I do not see how philosophers can not but use declarative sentences in any statement they make that uses words (spoken or written language). Sorry for being so dense.

 

To be a bit more precise there are several categories of knowledge which generally qualify for certainty. "All bachelors are unmarried" is actually an analytic statement ("true by definition' date='" or a truth that reveals no new information)...[/quote']OK, but I will maintain that "nothing is true BY definition". As you indicated above, the statement 'all bachelors are unmarried males' is true only cira 2011, it was not true cira 1120, and it may not be true cira 2211. At the times it will not be true, it will not be true by definition. Thus, if some statement can not be true by definition at time (t), we do not gain much by saying that it also can be true by definition at time (t+1). Yet even at the same time (t) I see a problem. For example, consider the statement at time (t):(1) men are beautify...we can say this is true by definition of beautify. However, we can also have a sense that the statement at the exact same time (t): (1) men are beautify...is not true by definition of beautify. Thus, at time (t) we have a sense that it is true by definition that men are both beautify and not beautify, and thus a violation of the law of non-contradiction.

 

IMO, when it is said that "something is true BY definition", e.g., that it is analytical and a priori, I find there is a misuse of the word "BY". For me, statements are never true BY definition, they are true BY application of deductive logic. These are two completely different ways of deciding truth for me. IMO, truth is established by the human mind well before there is consideration of assigning a definition to that which is held to be true.

 

Concerning the law of non-contradiction. Makes sense to me, but Hegel would not agree. The Principle of Explosion must be common because it is very difficult to not allow a single inconsistency in any formal argument. Perhaps I violated the principle in my above comments.

[Fluxus]

A "sentence" is an assembly of words. A "statement" or "proposition" is intended to indicate the semantic content behind the sentence.

 

"Ich bin ein Berliner" and "I am a jelly donut" are two different sentences, but express the same semantic content, thus they are the same statement.

 

It's a tool of convenience, since many philosophers accept that we don't really have such perfect and universally acceptable access to semantic content. It's less problematic when we are discussing semantic variables, since the actual semantic content is irrelevant.

 

Another way to think of it is Number : Numeral :: Sentence : Statement.

 

Thus, if you claim Q = "there cannot be truths by definition, because definitions are not stable," this applies to Q as well. Does this indicate that you believe that once Q fails, that we can claim that truths by definition are now possible? That does not seem to be the case. Thus, we say that the conditions of reality that Q purports to describe have not changed and Q is still valid -- we would just use different sentences to express the statement Q.

 

 

Concerning the law of non-contradiction. Makes sense to me' date=' but Hegel would not agree. The Principle of Explosion must be common because it is very difficult to not allow a single inconsistency in any formal argument. Perhaps I violated the principle in my above comments.[/quote']

Very cute ;) The Principle of Explosion refers to formal systems, like arithmetic, geometry or propositional logic. It's the reason why ZFC rules out certain operations, as mathematicians prefer consistency over completeness.

 

Inconsistencies don't wind up affecting informal positions to the same extent, in no small part because typically we don't apply such strict formal operations to them. An inconsistency is generally seen as an error or hypocrisy rather than a devastating shortcoming, and the extent of the flaw depends on how critical that particular idea is to the whole. It would be fallacious to refute every fact, claim and argument ever uttered by Michael Pollan just because you saw him buy Froot Loops at the supermarket.

 

Hegel's dialectic was really more about "combining opposites" than with "contradictions" in the logical sense. In strictly logical terms, a "contradiction" is a statement or argument that always returns False, e.g. "A & ~A". "Master + Slave" are interdependent opposites, which Hegel believes dialectically resolve to Equality. He was not suggesting that X can be both true and false simultaneously, or that we could arbitrarily assign truth-values to statements.

[Rade]

A "sentence" is an assembly of words. A "statement" or "proposition" is intended to indicate the semantic content behind the sentence.

But I am confused, because not all sentences allow for a statement to be formed, well, at least that is what my textbook on Symbolic Logic (G. Hardegree, 1994) suggests. So, the sentence, "shut the door" is an assembly of words, but it is NOT a logical "statement" because it is not capable of being either true or false. Because all logical arguments must be formed from sentences that also are statements, all logical arguments must be capable of being true or false, otherwise they are commandments, not arguments.

 

In your reply you appear to combine "statement" and "proposition" as if they are not distinguished, that they both are intended to indicate semantic content, but, this is not my understanding, again from Hardegree. Thus, "Ich bin ein Berliner" and "I am a jelly donut" are two different sentences, WHICH ALSO ARE TWO DIFFERENT STATEMENTS (because they are capable of being true or false). Thus, they express the same semantic content because THEY EXPRESS THE SAME PROPOSITION about what I am, not because they are the same statement, as you suggest in your reply. A sentence may or may not be capable of being true or false, whereas a statement is always a declarative sentence that is so capable. The relationship of statement to proposition would be like [the word door : the object door :: statement : proposition]. I would appreciate comment where my thinking is off in how I interpret what Hardegree says in his textbook.

 

Thus' date=' if you claim [i']Q[/i] = "there cannot be truths by definition, because definitions are not stable," this applies to Q as well. Does this indicate that you believe that once Q fails, that we can claim that truths by definition are now possible? That does not seem to be the case.

But why not the case ? If Q is a logical argument composed of statements that must be capable of being true or false, then I am logically compelled to accept that truths BY definition are now possible, and my argument falsified. So, what I need to see are examples where definitions ARE stable over time, I cannot think of any. So, while Q is capable of being true OR false this is not the same as saying it must be both true AND false. Thus, I would argue that while Q is capable of being true OR false, it just so happens to true 100% of the time.

 

But, let me concede for sake of argument that an example can be found of a stable definition over time, now I would argue R = "there cannot be truths BY definition, because assignment of truth is always prior to assignment of definition, even if definitions are stable over time".

 

==

 

Thank you for the comment concerning Hegel and non-contradiction. However, I thought Hegel rejected Aristotle on this point, especially with his comment that everything depends on "the identity of identity and non-identity". This is directly opposite the Law of Identity suggested by Aristotle, that [A = A]. For Hegel, [A = A and not-A] given his statement about the identity if Identity. What am I missing in my understanding ?

 

A question, how would you think Hegel would resolve as the dialectic of ["Matter + Antimatter"] ...what word do you think he would use ?

[belovelife]

impetali

[Fluxus]

I haven't found people to be all that strict about distinguishing "statement" and "proposition," but am fine with separating the two if it makes my comments easier to understand.

 

Regardless, by coincidence "I am a jelly donut" is still an analytic statement (albeit an "analytic falsity" as opposed to "analytic truth."). It's declarative, can be assigned a truth-value (unlike "shut the door,") has the same semantic content as "ich bin ein berliner," and its veracity and/or status as analytic is derived from its semantic content, as opposed to linguistic factors like reference shifts or synonyms. I.e. you at least know that I operate a computer, that donuts do not operate a computer, thus via this "analysis of the concepts alone" you already know that I am not, in fact, a jelly donut.

 

Another way to consider analytic statements is "true by analysis of the concepts," or (per the Stanford Encyclopedia of Philosophy) "those whose truth seems to be knowable by knowing the meanings of the constituent words alone." It is not the act of defining that determines its truth or falsity; it is that we already know what the words mean, thus we know whether or not terms are equivalent without needing any additional information, concepts, arguments and so forth.

 

So in terms of certainty, the way to doubt it would be to doubt either the communicative efficacy of a specific utterance and/or its intended semantic content (which can be repaired), or the efficacy of language in general (in which case you would, in theory, have a very difficult time examining or communicating this belief).

 

 

But why not the case ? If Q is a logical argument composed of statements that must be capable of being true or false, then I am logically compelled to accept that truths BY definition are now possible, and my argument falsified. So, what I need to see are examples where definitions ARE stable over time, I cannot think of any....

I'm trying to point out that since you agree that it is a permanent condition that "definitions are not permanent," you are essentially using a sentence to communicate specific semantic or propositional content to others. Q is inconsistent when viewed as a sentence, but consistent when viewed as a proposition.

 

If you state that "there are no permanent truths, because there are no statements or propositions, we only have sentences" you are, in fact, relying on your ability to successfully access and communicate semantic content. Otherwise your position would be false the instant we change any definition in that sentence -- and in being falsified, it is proven true. Thus when we interpret this position strictly, it is inconsistent.

 

Or: Suetonius wrote in Latin. We do not claim "I do not read Latin, therefore Suetonius must be wrong." We translate the work (or have someone translate it for us), attempt to gain access to the same semantic content as a native Latin speaker, and judge it on the meaning rather than the original sentences.

 

In comparison, consider "sentences and utterances rely on terms that change, thus do not consistently express the same propositions at all points in time." We further presume that I am attempting to access a proposition, rather than saying this is only true as long as the words hold the same meaning. This is consistent and also explains why the sentence "all bachelors are unmarried" might not be true in the year 2050.

 

Again there may be issues here in how accurately we can truly express propositional content (e.g. Quine's indeterminacy of translation, Gadamer's hermenutical focus on historical context as interfering with interpretation). However, partial inaccuracy does not necessarily demonstrate complete failure, and only becomes problematic in this matter iff such concerns impede our own knowledge of an analysis of a statement, proposition, identity claim, definition etc on the conceptual content alone.

 

 

Thank you for the comment concerning Hegel and non-contradiction. However, I thought Hegel rejected Aristotle on this point, especially with his comment that everything depends on "the identity of identity and non-identity". This is directly opposite the Law of Identity suggested by Aristotle, that [A = A]. For Hegel, [A = A and not-A] given his statement about the identity if Identity. What am I missing in my understanding ?

I'm not an expert on Hegel, I never particularly liked his work. With that caveat, my best guess is that Hegel was talking about "Sameness" and "Difference," which are opposing yet interdependent concepts. (e.g. http://www.sunypress.edu/p-4474-identity-and-difference.aspx)

 

Though I am not too familiar with his argument, Graham Priest does try to make the case that Hegelianism incorporates or is based on specific dialethias (again, "true contradictions" that do not subsequently "explode"), though others in the field debate this view.

 

 

A question, how would you think Hegel would resolve as the dialectic of ["Matter + Antimatter"] ...what word do you think he would use ?

"Annihilation" I presume? ;)

 

Offhand I don't know Hegel's views on science. AFAIK he focused more on using dialectics to explore metaphysics, theology and sociopolitical dynamics. I could be wrong, but I don't think he intended it to be used in place of the scientific method.

[Rade]

Fluxus...a pleasure learning from you.

[Rade]

...you at least know that I operate a computer, that donuts do not operate a computer, thus via this "analysis of the concepts alone" you already know that I am not, in fact, a jelly donut.

Yes, this matches what I was trying to say..that true knowledge is only via analysis of concepts, never via analysis of definitions. That is why imo the statement..all bachelors are unmarried males" is not true BY definition, but is true BY analysis of concepts.