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Posts Tagged ‘Belief’

Fallacy of Evidentialism

Posted by allzermalmer on August 18, 2013

There are two philosophers, who are taken to be generally representative of Evidentialism. These two philosophers are David Hume and C.K. Clifford. These two philosophers have two quotes that are examplars of their Evidentialism thesis. They are, respectively, as follows.

“A wise man, therefore, proportions his belief to the evidence…when at last [a wise man] fixes his judgement, the evidence exceeds not what we properly call probability.” – David Hume in “Of Miracles” (Italics are Hume’s)

“We may believe what goes beyond our experience, only when it is inferred from that experience by the assumption that what we do not know is like what we know…It is wrong in all cases to believe on insufficient evidence” – W.K. Clifford in “The Ethics of Belief

Thomas Huxley,

Huxluy Evidence

Those quotes from these three writers are taken as representative of Evidentialism, and thus the Evidentialist Principle. The statements they make might appear to carry some validity & they might even seem to be sound.

However, Karl Popper holds that they are not valid. He also doesn’t hold that they are sound. They even contradict all empirical systems or all empirical propositions. They forbid us from ever believing or holding to any empirical system or empirical proposition, they forbid us from ever believing or holding to any scientific hypothesis or scientific proposition. But the problem of Induction applies to both the truth of this matter of fact assertion and the probability of the truth of this matter of fact assertion.

Both of the propositions contain signs of being based on Induction. Hume points out that a wise man will fix their judgements on a proposition when the evidence indicates that it is probable. Clifford points out that we may infer from experience what goes beyond our experience, but this is based on hypothesis that unknown is similar to the known.

Both of the propositions show that Evidentialism is founded on Induction, or inductive inferences.

Hume, supposedly, showed that it is logically impossible to infer the unknown from the known. It is logically impossible to derive the unknown from the known. Thus, Evidentialism is founded on a logical impossibility.

“The problem of the source of our knowledge has recently been restated as follows. If we make an assertion, we must justify it; but this means that we must be able to answer the following questions.

How do you know? What are the sources of your assertion?’ This, the empiricist holds, amounts in its turn to the question,

‘What observations (or memories of observations) underlie your assertion?’ I find this string of questions quite unsatisfactory.” – Karl Popper in “The Sources of Knowledge and Ignorance

Popper presents the Evidentialist Principle, in that quote, as saying that “If we make an assertion, we must justify it“. If you make an assertion, then you must justify it, or making an assertion implies must justify the assertion. You would have to answer one question, ‘How do you know? What are the sources of your assertion?’, and have to answer another question, ‘What observations (or memories of observations) underlie your assertion?’. 

As Popper points out, the Evidentialist Principle is an answer to The Problem of Source of Knowledge. So we may suppose that Evidentialism and Induction are to be based on the Source of a proposition or an empirical proposition. It seeks that the source of a proposition to be justified.

Criticizing or discrediting a proposition because of the source has some similarity to the Genetic Fallacy: “if the critic attempts to discredit or support a claim or an argument because of its origin (genesis) when such an appeal to origins is irrelevant.”

With the Genetic Fallacy, a proposition is being discredited, or supported, because it is “paying too much attention to the genesis of the idea rather than to the reasons offered for it”. The origin, or source, of the proposition is used to discredit, or support, the proposition.

Evidentialism would discredit a proposition because the source of the proposition is without justification.

We also find that David Hume presents an example of the questions that Popper finds to be unsatisfactory.

“All reasonings concerning matter of fact seem to be founded on the relation of cause and effect. By means of that relation alone we can go beyond the evidence of our memory and senses. If you were to ask a man, why he believes any matter of fact, which is absent; for instance, that his friend is in the country, or in France; he would give you a reason; and this reason would be some other fact; as a letter received from him, or the knowledge of his former resolutions and promises…All our reasonings concerning fact are of the same nature. And here it is constantly supposed that there is a connexion between the present fact and that which is inferred from it. Were there nothing to bind them together, the inference would be entirely precarious.

When it is asked, What is the nature of all our reasonings concerning matter of fact? the proper answer seems to be, that they are founded on the relation of cause and effect. When again it is asked, What is the foundation of all our reasonings and conclusions concerning that relation? it may be replied in one word, Experience. But if we still carry on our sifting humour, and ask, What is the foundation of all conclusions from experience? this implies a new question, which may be of more difficult solution and explication.” – David Hume in “Sceptical doubts concerning the operations of the understanding” (Italics are Hume’s)

David Hume himself goes down the line of questioning that Popper brings up. For example, suppose that some assertion is made like “all ravens are black”. This assertion is what Hume calls a Matter of Fact, i.e. Synthetic proposition or Contingent proposition. It is Possible that it is true that “all ravens are black” and it is possible that it isn’t true that “all ravens are black”. This starts a line of questioning once this assertion is presented.

Question: What is the nature of reasoning concerning that matter of fact?
Evidence: The assertion is founded on the relation of cause and effect.
Question: What is the foundation of reasoning and conclusion concerning that relation of cause and effect?
Evidence: The relation of cause and effect of that assertion is founded on Experience.

These two questions follow a basic form that Popper is bringing up, and the type of basic form that Popper finds unsuitable, or the type of basic form of Evidentialism that is unsuitable. The basic reason for this is because another question follows from the answer to the previous two questions.

Question: What is the foundation of that conclusion drawn from experience?

This new question is where the Problem of Induction arises, or what Popper calls The Logical Problem of Induction.

If all Ravens are Black then justified in the relation of cause and effect. If justified in the relation of cause and effect then justified by experience. If justified by experience then experience is justified by Induction. So if all ravens are black then justified by Induction. But, Induction isn’t justified. So assertion all ravens are black isn’t justified. Therefore, Evidentialism would make it so that the assertion all Ravens are Black isn’t justified. This applies to all matters of fact, and thus all empirical and scientific assertions.

“It is usual to call an inference ‘inductive’ if it passes from singular statements (sometimes called ‘particular’ statements), such as accounts of the results of observations or experiments, to universal statements, such as hypotheses or theories. Now it is far from obvious, from a logical point of view, that we are justified in inferring universal statements from singular ones, no matter how numerous; for any conclusions drawn in this way may always turn out to be false: no matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white. The question whether inductive inferences are justified, or under what conditions, is known as the problem of induction.” – Karl Popper in “The Logic of Scientific Discovery” (Italics are Popper’s)

The Problem of Induction comes about because Induction relies on statement that is a matter of fact assertion, but this matter of fact assertion cannot, in principle, be inductively justified. So either all reasonings concerning matter of fact seem to be founded on experience or not all reasonings concerning matter of fact seem to be founded on experience.

This is a logical problem because either Induction relies on a statement that is either a contingent proposition or necessary proposition. We can call this the “Principle of Induction”. But the Principle of Induction can’t be a necessary proposition because the negation of the Principle of Induction is possible to be false. A necessary proposition can’t be possible to be false. So it is possible that Principle of Induction is true and it is possible that isn’t true that Principle of Induction is true. Therefore, the Principle of Induction is a contingent proposition.

Hume points out that matter of facts about dispositions and universal propositions are matters of facts. Thus dispositional propositions and universal propositions are contingent propositions. Dispositional propositions describe law-like behavior and universal propositions describe lawful behavior or law-like behavior. These would both be contingent propositions, and so we wouldn’t be justified, based on Induction, in asserting those dispositional propositions or universal propositions.

We wouldn’t be justified, based on Evidentialism, when it came to assertions about dispositional propositions or universal propositions. Science wouldn’t be justified, based on Evidentialism, when it came to assertions about dispositional propositions or universal propositions. But science is full of assertions about dispositional propositions and universal propositions. Therefore, science wouldn’t be justified in asserting dispositional propositions and universal propositions.

“[Hume] tried to show that any inductive inference- any reasoning from singular and observable cases (and their repeated occurrence) to anything like regularities or laws- must be invalid. Any such inference, he tried to show, could not even be approximately or partially valid. It could not even be a probable inference: it must, rather, be completely baseless, and must always remain so, however great the number of the observed instances might be. Thus he tried to show that we cannot validly reason from the known to the unknown, or from what has been experienced to what has not been experienced (and thus, for example, from the past to the future): no matter how often the sun has been observed regularly to rise and set, even the greatest number of observed instances does not constitute what I have called a positive reason for the regularity, or the law, of the sun’s rising and setting. Thus it can neither establish this law nor make it probable.” Karl Popper in “Realism and the Aim of Science” (Italics are Popper’s)

The assertion “all ravens are black” isn’t justified as true under Evidentialism and “all ravens are black” isn’t jusified as probably true under Evidentialism. Hume himself points out that the wise man doesn’t fixate his judgement on an assertion in which the evidence exceeds what we properly call probability. In other words, the Evidentialist doesn’t hold to assertions in which the evidence exceeds what we properly call probability. So Evidentialist only hold to assertion in which evidence shows it is true or probably true. So “all ravens are black” is only held by an Evidentialist if evidence shows it is true or at least probably true.

Popper presents a solution to the Problem of Induction, and thus treats assertions differently from Evidentialism. Popper rejects Induction, and thus rejects Evidentialism. The source of an assertion has nothing to do with either discrediting the truth of a proposition or supporting the truth of a proposition.

Matter of fact propositions, or scientific propositions, don’t discredit or support the source of an assertion. Science doesn’t support the truth of a proposition or support the probability of a proposition. It, basically, seeks to discredit the truth of a proposition. Science seeks to show that the proposition is false, not that the proposition is true or probably true. Science always seeks to discredit it’s proposition and not to support it’s propositions. So scientific propositions are, in principle, possible to show they are false and never show they are true or probably true. This includes both dispositional propositions and universal propositions.

In other words, Evidentialism seeks both positive justifications for assertion and negative justifications for assertion. Evidentialism would be based on “full decidability”. Falsifiability, or Falsification, seeks only negative justifications for assertions. Falsifiability would be based on “partial decidability” . These negative justifications, for Falsifiability, basically state that scientific assertion hasn’t been demonstrated false as of yet. This never indicates a positive justification for the assertion being true or probably true.

“The problem of induction arises from an apparent contradiction between the basic empiricist requirement (only experience can decide the truth or falsity of a scientific statement) and Hume’s insight into the logical impermissibility of inductive decision (there is no empirical justification of universal statements). This contradiction exists only if we assume that empirical statements must be empirically “fully decidable”, that is, that experience must be able to decide not only their falsity, but also their truth. The contradiction is resolved once “partially decidable” empirical statements are admitted: Universal empirical statements are empirically falsifiable, they can be defeated by experience.” – Karl Popper in “The Two Problems of The Theory of Knowledge” (Italics are Popper’s)

For Falsifiability, the source of an assertion is irrelevant when judging whether the assertion is either true or false, and the source of an assertion is irrelevant when judging whether justified in believing that assertion is true or probably true. The source of an assertion is irrelevant for the justification of the assertion. Would have to rely on Induction, and Induction isn’t justified itself. The only justification of an assertion, specifically an empirical assertion, is that it is possible to show that assertion is false. An empirical assertion has the possibility to be shown false, but it doesn’t have the possibility to be shown true (or probably true).

Science, thus, doesn’t care of the source of an assertion. Science is justified in believing, or holding to, an empirical proposition because that empirical proposition allows for the possibility that can be shown that it is false, but hasn’t been shown that it is false yet. For example, science would be justified in believing the empirical proposition that “all ravens are orange” if wasn’t for “some ravens are black”. It would be a negative justification, since don’t have another empirical proposition that contradicts it, or shows that it is false.

One of the basic mechanisms of Falsifiability is that works by deductive inference. Modus Tollens forms an example of deductive inference that Falsifiability uses. Given the conditional claim that the consequent is true if the antecedent is true, and given that the consequent is false, we can infer that the antecedent is also false.

If an empirical assertion is true implies another empirical assertion is true & the other empirical assertion is false, then original empirical assertion is false.

Principle of Modus Tollens:If all ravens are orange implies no ravens are not orange & some ravens are black, then not all ravens are orange. This is how the negative justification of empirical assertions works, which is deductive inference of modus tollens. It wouldn’t be possible for “not all ravens are orange” to be false. So it must be true.

The Principle of Modus Tollens is a necessary truth, which is different from the Principle of Induction. The Principle of Induction isn’t a necessary truth. It is possible that the Principle of Induction is false. So it might be true.

An assertion that is the conclusion of the Principle of Induction, or the assertion of a wise man that reviewed the Evidence, might be true. An assertion that is the conclusion of the Principle of Modus Tollens, or the assertion of a foolish man that never reviewed the Evidence, must be true.

The truth that the Principle of Modus Tollens always produces truth. It is similar to negative theology. It isn’t true that “all ravens are orange” & it isn’t true that “no ravens are not orange”. Each time saying what is true because true isn’t those false statements, since it is true that “not all ravens are black”.

The contradiction between “all ravens are orange” and “not all ravens are orange” are exclusive, they both can’t be true and no intermediary empirical propositions between them. If know that “all ravens are orange” is false then know that “not all ravens are orange” is true. All ravens are orange implied no ravens are not orange & some ravens are black. Therefore, it is necessarily true that not all ravens are orange. If Know that “not all ravens are orange” is true then “not all ravens are orange” is true. “Not all ravens are orange” is true.

Both the Principle of Modus Tollens are dealing with scientific propositions. The scientific propositions are possibly true or possibly false. If combine scientific propositions with the Principle of Induction, then scientific proposition infered might be true. If combine scientific propositions with Principle of Modus Tollens, then scientific proposition infered must be true. The negative justification allows for things that aren’t possibly not true & hold to statements that are only true, while positive justification allows for things that are only possibly true & hold to some statements that aren’t only true.

So Evidentialist like David Hume, or C.K. Clifford, would be justified in holding some scientific propositions that aren’t only true. Evidentialist would hold to both true statements and false statements. While the Non-Evidentialist, which follows Falsifiability or negative justification, would hold only to true statements. The Non-evidentialist wouldn’t be justified in asserting a scientific statement, even though conclusions drawn from it must be true.

Thus, Evidentialism is fallacious because the assertions that it concludes to be justified in holding, based on the evidence, aren’t truth-preserving. It’s conclusions of justified scientific propositions aren’t based on the evidence or derived by positive support it receives from the evidence. However, it is completely opposite with Non-Evidentialism of Falsification, or it isn’t fallacious.

The Evidentialist would be acting irrationally by seeking their justification, while the Falsifiabilist, which is necessarily a Non-Evidentialist, would be acting rationally by not seeking the Evidentialist justification.

Huxley’s assertion, in his examplar of Evidentialism, mentions that “merciless to fallacy in logic.” But we later find out that Evidentialism isn’t “merciless to fallacy in logic”, but is founded on a fallacy in logic itself. David Hume recognized this, even though exemplar of Evidentialism. Instead, he went about acting irrationally by seeking a (positive) justification of proposition by evidence & the rest of Evidentialism followed, like C.K. Clifford and Thomas Huxley. They would all go about by searching for evidence that proposition is true and end right back in the same place.

Finding Evidence

So we finally come full circle with the fallacy of Evidentialism, and find the source of the Evidentialist fallacy.

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Gnostic and Agnostic Breakdown

Posted by allzermalmer on August 2, 2013

The main interest is of Agnosticism, and this by default can have some implication with Atheism and Theism.

It will be supposed that Agnosticism is about lack of knowledge or not knowing. Gnosticism will be about having knowledge or knowing. It will be supposed that to have knowledge of a claim, then that claim is Justified, True, and it is Believed.

(Gnostic) K=JTB
(Agnostic) ~K= (A1) NJTB v (A2) JNTB v (A3) JTNB v (A4) NJNTNB

There are four ways to agnosticism, but there is only one way to gnosticism.

(A1) Claim isn’t Justified & Claim is True & Claim is Believed.
(A2) Claim is Justified & Claim isn’t True & Claim is Believed.
(A3) Claim is Justified & Claim is True & Claim isn’t Believed.
(A4) Claim isn’t Justified & Claim isn’t True & Claim isn’t Believed.

(Gnostic Socrates) If Socratesl knows the claim p, then Socrates claim is Justified, True, and Believed by the Socrates.

(Agnostic Socrates) If Socrates doesn’t know the claim p, then…
(A1) Socrates claim isn’t Justified, but Socrates believes the claim and it’s True.
(A2) Socrates claim isn’t True, but Socrates claim is Justified and Believed.
(A3) Socrates claim isn’t Believed, but Socrates claim is Justified and it’s True.
(A4) Socrates claim isn’t Justified, isn’t Believed, and isn’t True.

Suppose that p is “there exists a deity”. So ~p stands for “there doesn’t exist a deity”.

(i)Kp= Socrates knows there exists a deity.
(ii) K~p= Socrates knows that there doesn’t exist a deity.

(iii) ~Kp= Socrates doesn’t know that there exists a deity.
(iv) ~K~p= Socrates doesn’t know that there doesn’t exist a deity.

Assume Socrates doesn’t know that the earth is flat. This is because Socrates knows that the earth isn’t flat. Socrates knowing that the earth isn’t flat implies that it is true that the earth isn’t flat. Socrates can’t know false things (but can believe false things), so Socrates doesn’t know that the earth is flat, especially because Socrates knows that the earth isn’t flat.

So it becomes obvious that:

(i) Kp doesn’t forbid ~K~p:: Socrates knows that there exists a deity doesn’t forbid Socrates doesn’t know there doesn’t exist a deity.

(ii) K~p doesn’t forbid ~Kp:: Socrates knows that there doesn’t exist a deity doesn’t forbid Socrates doesn’t know that there exists a deity.

(iii) ~Kp doesn’t forbid (ii) K~p :: Socrates doesn’t know there exists a deity doesn’t forbid Socrates knows there doesn’t exist a deity.

(iv) ~K~p doesn’t forbid (i) Kp :: Socrates doesn’t know there doesn’t exist a deity doesn’t forbid Socrates knows there does exist a deity.

(iii) or (iv) doesn’t imply that Gnostic, but can be Gnostic. (A1)-(A4) show some reasons on why (iii) and (iv) don’t necessarily imply, but don’t forbid, being Gnostic.

When it comes specifically to “there exists a deity”, it would mean that in order to be Agnostic on that claim, Socrates would have to take part of (iii) and (iv).

In order to be Agnostic, then Socrates doesn’t know there exists a deity and Socrates doesn’t know there doesn’t exist a deity.

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Logical Analysis of Consciously Held Beliefs

Posted by allzermalmer on June 10, 2013

Axioms of Consciously Believing

Axiom: “I believe that p” if and only if “I believe that I believe that p”
EBpBBp = Bp <-> BBp

Axiom: “I don’t believe that p” if and only if “I believe that I don’t believe that p”
ENBpBNBp = ~Bp <-> B~Bp

Axiom: If “I believe that not p” then “I don’t believe that p”
CBNpNBp = B~p -> ~Bp

Axiom: If “I believe that p implies y” then “I believe that p implies I believe that y”
CBCpyCBpBy = B(p->y) -> (Bp->By)

Theorems of Consciously Believing

T1: “I don’t believe that both p and not p”
NBKpNp = ~B(p&~P)

T2: “I believe that p is equivalent to y” implies “I believe that p is equivalent to I believe that y”.
CBEpyEBpBy = B(p<->y) -> (Bp<->By)

T3: “I believe that p or I believe that y” implies “I believe that both p or y”
CABpByBApy = (BpvBy) -> B(pvy)

T4: “I believe that both p & y” if and only if “I believe that p & I believe that y”
EBKpyKBpBy = B(p&y) <-> (Bp&By)

T5: “I believe that p” implies “I don’t believe that not p”
CBpNBNp = Bp->~B~p

T6: “I believe that either p or y & I don’t believe that p” implies “I don’t believe not p”
CKBApyNBpNBNp = B(pvy)&~Bp -> ~B~p

T7: “I believe that either p or y & I believe that not p” implies “I believe that y”
CKBApyBNpBy = B(pvy)&B~p -> By

T8: If “I believe that p implies y” then “I believe that not y implies I believe that not p”
CBCpyCB~yB~p = B(p->y) -> (B~y->B~p)

T9: If “I don’t believe that p implies y” then “I don’t believe that not p & I don’t believe that y”.
CNBCpyKNBNpNBy = ~B(p->y) -> (~B~p&~By)

T10: If “I believe that I believe that p or I believe that y” then “I believe that either p or y”
CBABpByBApy = B(BpvBy) -> B(pvy)

T11: If “I believe that p implies y” then “I believe that I believe that p implies y”
CBCpyBCBpy = B(p->y) -> B(Bp->y)

T12: “I believe that I believe that p implies p”
BCBpp = B(Bp->p)

http://video.msnbc.msn.com/mitchell-reports/34510812#52158575

http://bcove.me/bqpor8gd

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Desiring, Believing, Knowing, Obligation, and Fitch’s Paradox

Posted by allzermalmer on April 26, 2013

Assume that Striving, Doing, Believing, & Knowing (SDBK) have some fairly simple properties.
Assume that (SDBK) Striving, Doing, Believing, & Knowing are two-termed relations between an Agent and a Possible State of Affairs.

It shall be a convention to treat Possible State of Affairs as Propositions. So, Φ is assumed to be an agent and  p is assumed to be a proposition.
(i) “Φ strives for p” is equivalent to saying “Φ strives to bring about or realize the (possible) state of affairs expressed by the proposition p.”
(ii) “Φ does p” is equivalent to saying “Φ brings about the (possible) state of affairs expressed by the proposition p.”
(iii) “Φ believes p” is equivalent to saying “Φ believes about or realize the (possible) state of affairs expressed by the proposition p.”
(iv) “Φ knows p” is equivalent to saying “Φ knows about or realize the (possible) state of affairs expressed by the proposition p.”

It shall be a convention to ignore the Agent and treat concepts to be considered, i.e. Striving, Doing, Believing, & Knowing (SDBK), as a “Class of Propositions” instead of Two-Termed relation.
(i) ‘Striving’ means the Class of Propositions striven for (that is striven to be realized).
(ii) ‘Believing’ means the Class of Propositions believed.
(iii) ‘Doing’ means the Class of Propositions doing (that is doing to be realized).
(iv) ‘Knows’ means the Class of Propositions known.

Simplification and Adjunction

Here are two basic rules of Logical Inference in propositional logic. They are known, respectively, as Simplification and Adjunction.

Simplification: Because both components of a conjunctive argument are true, it is permissible to infer that either of it conjuncts is true.
(Premise): Germany Lost World War One & Germany Lost World War Two
(Conclusion): Germany Lost World War One

(Premise): Germany Lost World War One & Germany Lost World War Two
(Conclusion): Germany Lost World War Two

Adjunction: Because both premises are presumed true, we can infer their conjunction.
(Premise): Germany Lost World War One
(Premise): Germany Lost World War Two
(Conclusion): Germany Lost World War One & Germany Lost World War Two

Assume p and q are variables for two different propositions. Assume Ω stand for Class of Propositions, which can be either Striving, Believing, Obligation, and Knowing, or etc. Assume → stands for Strict Implication, Logical Entailment, Entailment, Logical Consequence.

Closed with Respect to Conjunction Elimination

Class of Propositions are Closed with Respect to Conjunction Elimination whenever a conjunctive proposition is in the Class, then those two propositions themselves are in that Class. Closed with Respect to Conjunction Elimination follows the logical inference of Simplification, but it uses one the relation of (SDBK).

Class of Propositions Closed with Respect to Conjunction Elimination:
(p)(q)[(Ω[p & q]) → [(Ωp) & (Ωq)]]

Assume that Ω stands for the Class of Propositions “know”. So the Class of Propositions (know) Closed with Respect to Conjunction Elimination means that “If (know both p & q) then logically entails (know p) & (know q)”. We can replace Ω with “Believe”, “Striving”, “Doing”, or the others listed.

Class of Propositions covered by Closed with Respect to Conjunction Elimination are: Striving (for), Doing, Believing, Knowing, Proving, Truth, Causal Necessity (in the sense of Burks), Causal Possibility ( in the sense of Burks), (Logical) Necessity, (Logical) Possibility, Obligation (Deontic Necessity), Permission (Deontic Possibility), Desire (for),

Closed with Respect to Conjunction Elimination

Class of Propositions Closed with Respect to Conjunction Introduction whenever two propositions are in the class, then so is the conjunction of the two propositions. Closed with Respect to Conjunction Introduction follows the logical inference of Adjunction, but it uses one of the relations of (SDBK).

Class of Propositions Closed with Respect to Conjunction Introduction:
(p)(q)[[(Ωp) & (Ωq)] → (Ω[p & q])]

Assume Ω stands for the Class of Propositions “know”. So the Class of Propositions (know) Closed with Respect to Conjunction Introduction means that “If (know p) and (know q), then logically entails (Know both p & q).” We can replace Ω with “Believe”, “Strive”, “Doing”, or others listed.

Class of Propositions covered by Closed with Respect to Conjunction Introduction are:
Truth, Causal Necessity (in the sense of Burks), Logical Necessity, Obligation (Deontic Necessity).

Class of Propositions possibly covered by Closed with Respect to Conjunction Introduction are: Striving (for), Doing, Believing, Knowing, Proving, Desire (for).

Class of Propositions not covered by Closed with Respect to Conjunction Introduction are: Causal possibility (in the sense of Burks), Logical Possibility, and Permission (Deontic Possibility).

Truth Class

Class of Propositions are a Truth Class if every member of it is true.

Class of Propositions Truth Class:
(p)[(Ωp) → p]

Assume Ω stands for Class of Propositions Truth Class “knows”. So the Class of Propositions Truth Class (knows) means “If (knows p) then logical entails p.”

Class of Propositions Truth Class are: Truth, Causal Necessity (in the sense of Burks), Logical Necessity, Knowing, Done, and Proving.

Theorems about Truth Classes

Theorem 1: If (Class of Propositions) is a Truth Class which is Closed with Respect to Conjunction Elimination, then the proposition, [p & ~(Ωp)], which asserts that p is true but not a member of (Class of Propositions) (where p is any proposition), is itself necessarily not a member of (Class of Propositions).

Proof: Suppose the contrary, [p & ~(Ωp)], is a member of (Class of Propositions), i.e. suppose that (Ω[p & ~(Ωp)]) is a member of (Class of Propositions). Since (Class of Propositions) are Closed with Respect to Conjunction Elimination, the propositions p and ~(Ωp) must both be members of (Class of Propositions), so that the propositions (Ωp) and (Ω(~(Ωp))) must both be true. But the fact that (Class of Propositions) is a truth class and has ~(Ωp) is true, and this contradicts the result that (Ωp) is true. Thus from the assumption that [p & ~(Ωp)] is a member of (Class of Propositions) we have derived contradictory results. Hence, that assumption is necessarily false.

Theorem 2: If (Class of Propositions) is a Truth Class which is Closed with Respect to Conjunction Elimination, and if p is a true proposition which is not a member of (Class of Proposition), then the proposition, [p & ~(Ωp)], is a true proposition which is necessarily not a member of (Class of Propositions).

Proof: The proposition [p & ~(Ωp)] is clearly true, and by Theorem 1 it is necessarily not a member of (Class of Propositions).

Omnipotent and Fallibility

Theorem 3: If an Agent is all-powerful in the sense that for each situation that is the case, it is logically possible that that situation was brought about by that Agent, then whatever is the case was brought about (done) by that Agent.

Proof: Suppose that p is the case but was not brought about by the agent in question. Then, since (doing) is a Truth Class Closed with Respect to Conjunction Elimination, we conclude from Theorem 2 that there is some actual situation which could not have been brought about by that Agent, and hence that Agent is not all-powerful in the sense described. Hence, that assumption is necessarily false.

Theorem 4: For each Agent who is not omniscient, there is a true proposition which that Agent cannot know.

Proof: Suppose that p is true but not known by the Agent. Then, since (knowing) is a Truth Class Closed with Respect to Conjunction Elimination, we conclude from Theorem 2 that there is some true proposition which cannot be known by the Agent.

Knowability Paradox

Theorem 5: If there is some true proposition which nobody knows (or has known or will know) to be true, then there is a true proposition which nobody can know to be true.

Proof: Similar to proof in Theorem 4.

Proved True Never Proved

Theorem 6: If there is some true proposition about proving that nobody has ever proved or ever will prove, then there is some true proposition about proving that nobody can prove.

Proof: Similar to the proof in Theorem 4, using the fact that if p is a proposition about proving, so is [p & ~(Ωp)].

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Yoruba Epistemology

Posted by allzermalmer on June 2, 2011

This is blog is based on the epistemology of an African tribe called the Yoruba. Here is some general information on the Yoruba. They are found in the western Africa country known as Nigeria.

The Yoruba epistemology is one that we can call, in western language, an empiricist epistemology. This means that knowledge, for the Yoruba, derive from the senses. This belongs to that of sight, touch, taste, smell, and hearing. An empiricists epistemology also relies on induction. This moves from past observations to predictions of future observations based on the past.

The Yoruba break epistemology down into two different categories. These are Imo and Igbagbo. Imo is similar to what we call, in the west, but not exactly the same, as knowledge. Igbagbo is similar to what we call, in the west, but not exactly the same, belief.

In the west, we put knowledge down into propositional knowledge. Propositional knowledge would be something like this, “Water is made up of two hydrogen atoms and one oxygen atom.” In western epistemology, we consider knowledge to be of the propositional sort. However, with propositional knowledge, this is mostly secondhand. This means, someone experiences something and they tell you what they experienced. Thus, with the example of water, someone experiences this and tell us about and hold universally. So, following the water example, a chemist experiences that water is made up of two hydrogen atoms and one oxygen atom (and I will skip over the problem with that for now). Thus, when we are students in a chemistry class, our chemistry teacher teaches us the proposition, “water is made up of two hydrogen atoms and one oxygen atom”. Now we are said to have propositional knowledge. We never experienced it, but we were taught it.We are said to have knowledge that water is made up of two hydrogen atoms and one oxygen atom.

For the Yoruba, though, that would not be knowledge per se, that would not be Imo, per se. For the Yoruba, you would need to have experienced such a thing to have knowledge. The chemist would have had to experience that water is made up of two hydrogen atoms and one oxygen atom. This is problematic, since atoms are, by definition, something that we cannot experience with our senses. Thus, under the Yoruba theory of epistemology, that would not be considered knowledge. That would be considered belief, or Igbagbo.

Imo is based on someone having a direct experience. For example, say that you see a friend drive down the street in a red mustang. You have Imo that your friend Dave drove down the street in a red mustang. This is knowledge, and this is based on a 1st person experience. But now say that you tell other friend Rick that you saw Dave  drive down the street in a red mustang. For Rick, this would be Igbagbo, or belief. This is 2nd hand knowledge. All Rick knows is what he heard you say, and this is not first person experience. This is not knowledge.

Igbagbo is based on secondhand knowledge. This means that you have no experience about what is being talked about, but it is something that is told you. Thus, going back with the chemistry teacher, they are telling you something that they have Imo on, that they have knowledge on. Now, since they tell you, and you do not have knowledge on it, you only have Igbagbo. You take it that you have knowledge, but it is a belief so long as you do not have first hand experience on it.

Imo=First hand experience=See friend drove a red mustang
Igbagbo= Second hand experience=Told friend drove a red mustang

In order to have Imo, you need to have a sensory experience and cognition (comprehend what you are experiencing). I can walk down an aisle at the library, and have all sorts of experiences, but I am not cognitively aware of the books that I am walking by. Thus, I do not know, as I walk down the aisle of the library with the books on each side of me, what books they are. I am not cognitively aware of if it is Moby Dick or Crime and Punishment. This would not count as Imo.

Nothing that we experience first hand would go under Igbagbo. So if I learn something in science class, and I have no personal experience of it, I do not know it. I only know that my teachers told me something. This is just a belief that I can hold on what the teacher told me. Thus, I do not know that two hydrogen atoms and one oxygen atoms make up water. I believe that they do because my teacher told me. Those of us that are not scientists, and more importantly experimentalist in science, do not know anything that scientists tell us. We only believe what they tell us, or what they tell us that they experience.

Now a question could come up for knowledge about mathematics or logic. How do I know, in geometry, that “In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle.” I do not know this. My geometry teacher tells me this. I do not know it until I work out the proof myself. Once I work out the proof myself, then I know that “In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle”. So I can be taught this proposition, and I can only have Igbagbo about it. It is not until I do the actual proof myself do I have Imo about it. The same holds with logic.

Let us say that I have Imo that if I drop a feather and a bowling ball on the moon, that they both land at the same time. I tell Rick this, but Rick does not believe me. We can settle this issue by testing what I said. Rick could go to the moon and drop a bowling ball and a feather at the same time, and see if they land at the same time. From this, Rick would come to have Imo himself. He would than have knowledge.

Now imagine that I make a claim, and it is one that cannot be tested. Just imagine that I say, “I saw a white crow catch a white squirrel.” Rick might not believe me, and there is no way to test this. There is no way for Rick to come to have Imo on this. Thus, we can settle this by asking someone else. Now imagine that Dave was with me, and Steve as well, when this happened. We all saw it happen. Thus, Rick can ask Steve and Dave. They all tell Rick the same thing I said, and so he might come to believe what I said. Thus, he would come to have Igbagbo.

Now imagine the same situation above, about white crow getting white squirrel. But let us change things a bit. I was the only person there, and no one else was there. Thus, I was the only person that saw it happen, and thus the only one to have Imo. Rick cannot test this himself, and he cannot ask anyone else. So this question is open if Rick will believe me or not.

From these three examples, we find that there are three levels with the Yoruba epistemology. (I.) 1st hand experience, (II.) Igbagbo open to testing & transform into Imo, (III.) Igbagbo never open to verification (or can be), but testimony, or explanation.

Now moving with (III.), there is one important thing that comes into play. This is the character of the speaker. If I am someone who makes the claim about the white crow and white squirrel, and I am known as a liar, no one is going to believe what I say. However, if I am known as an honest person, then that leads credence to believe what I say. Thus, with the science teacher, I come to believe them because I am taught that scientist have good character, and should be believed, even if I cannot experience what they talk about. Character is very important in judging whether to believe what someone says. Character is important in whether or not to have Igbagbo on someone’s Imo.

We can conclude that since Imo is based on 1st hand experience, that the Yoruba works with what we call methodological solipsism. This is the position “that knowledge about the existence & non-existence of everything outside of self origin in immediate experience, or “the given”, which is not strictly shared (with other selves” (Rollins). In other words, knowledge about what is the case and what is not the case, comes from my personal experience. That is the only thing that I can know to be the case or not. I can only know what you say, and I cannot know what you experience. Thus, I will either come to believe you or not, or withhold judgement on what you say. Everything else outside of one’s personal experience is just a belief. It is not based on the testimony of your senses. This does not mean one holds that only one’s self alone exists. It is only in method that one works with such a position.

Now there is something else that is important about the Yoruba epistemology, and it involves tradition. Let us say, hypothetically, that my tradition says that “If a black cat crosses your path, then you will break your leg that day.” Now, the Yoruba will not automatically have igbagbo on this, unless it comes from someone of good character. However, they will accept this tradition if they find, through their own personal experience, that they find it to be true or happen. Thus, they will have Imo on the subject. This means, if my father and my fathers father held to something as Imo, it does not mean I will follow it unless I find it to be true myself. Thus, if I am told there is a certain way to farm my crops, I will not do it unless I find it to be true myself. This means that traditions will not be held unless they are personally found to be true, and thus continue on with the tradition.

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