allzermalmer

Truth suffers from too much analysis

Posts Tagged ‘Deduction’

Categorical Propositions aren’t Same as Conditional Propositions

Posted by allzermalmer on September 20, 2013

It is sometimes held that categorical propositions are equivalent to conditional proposition. However, at least with propositional logic, this isn’t necessarily true.

Categorical proposition: All X are Y.
Conditional proposition: If X then Y.

In other words, it is sometimes held that, All X are Y if and only if X implies Y.

This can be shown false by a very simple method that Categorical propositions aren’t equivalent to Conditional propositions. All we have to do is replace the variables X or Y with Truth Values, and see what the Truth of the proposition as a whole will come out to.

Suppose that X is True and Y is True. Now we replace those variables with their Truth Values in the Statements.

Categorical Proposition: All True are True= True.
Conditional Proposition: If True then True= True.

Suppose that X is False and Y is False.

Categorical Proposition: All False are False=True.
Conditional Proposition: If False then False=True.

Suppose that X is True and Y is False.

Categorical Proposition: All True are False= False.
Conditional Proposition: If True then False= False.

Here is where the Fallacy comes in of thinking Categorical Propositions are equivalent to Conditional Propositions.Suppose that X is False and Y is True.

Categorical Proposition: All False are True= False.
Conditional Proposition: If False then True=True.

We immediately notice that their truth value’s are not equivalent when each variable has the same truth value. This shows that categorical propositions necessarily say something different from conditional propositions.

The only way that Categorical Propositions will say the same thing as Conditional Propositions is if the Subject of the Categorical Proposition isn’t False & the Predicate isn’t True. In other words, the Subject of the Categorical Proposition must Exist.

All Mermaids are creatures that swim in the Ocean if and only if Mermaids implies creatures swim in the Ocean. Mermaids can’t not exist for this equivalency to hold with the Conditional, while the Conditional doesn’t need that Mermaids exist.

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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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The Logic of Discussions

Posted by allzermalmer on June 7, 2013

This blog will be based on a logical system developed by Polish logician Stanislaw Jakowski. It was published in the journal Studia Logica: An International Journal for Symbolic Logic, T. 24 (1969), pp. 143-1960

Implication (–> or C), Conjunction (& or K), Disjunction (v or A), Equivalence (<–> or E), Negation (~ or N, Possibility (<> or M), Necessity ([] or L),  and Variables (P or p, Q or q, R or r).

P = <>P or p = Mp
<>P = ~[]~P or Mp = NLNp

Discussive Implication (D): P–>Q = <>P–>Q or Dpq = CMpq
Discussive Equivalence (T): P<–>Q = (<>P–>Q) & (<>Q–><>P) or Tpq = KCMpqCMqMp

D1: P–>P = Dpp
D2: (P<–>Q) <–> (Q<–>P) = TTpqTqp
D3: (P–>Q) –> ((Q–>P)–>(P<–>Q)) = DDpqDDqpTpq
D4: ~(P&~P) = NKpNp [Law of Contradiction]
D5: (P&~P) –>Q = DKpNpq [Conjunction Law Overfilling]
D6: (P&Q) –>P = DKpqp
D7: P –> (P&Q) = DpKpq
D8: (P&Q) <–> (Q&P) = TKpqKqp
D9: (P&(Q&R)) <–> ((P&Q)&R) = TKpKqrKKpqr
D10: (P–>(Q–>R)) –> ((P&Q)–>R) = DDpDqrDKpqr [law importation]
D11: ((P–>Q)&(P–>R)) <–> (P–>(Q&R)) = TKDpqDprDpKqr
D12: ((P–>R)&(Q–>R)) <–> ((PvQ)–>R) = TKDprDqrDApqr
D13: P <–> ~~P = TpNNp
D14: (~P–>P) –> P = DDNppp
D15: (P–>~P) –>~P = DDpNpNp
D16: (P<–>~P) –> P = DTpNpp
D17: (P<–>~P) –>~P = DTpNpNp
D18: ((P–>Q)&~Q) –>~P = DKDpqNqNp

D19: ((P–>)&(P–>~Q)) –>~P = DKDpqDpNqNp
D20:  ((~P–>Q)&(~P–>~Q)) –> P = DKDNpqDNpNqp
D21:  (P–>(Q&~Q)) –>~P = DDpKqNqNp
D22:  (~P–>(Q&~Q)) –> P = DDNpKqNqp

D23: ~(P<–>~P) = NTpNp
D24: ~(P–>Q) –> P = DNDpqp
D25: ~(P–>Q) –> ~Q = DNDpqNq
D26: P–> (~Q–>~(P–>Q)) = DpDNqNDpq

A formulation of Aristotle’s Principle of Contradiction would be: “Two contradictory sentences are not both true in the same language” or “Two contradictory sentences are not both true, if the words occurring in those sentences have the same meanings”.

In Two Valued Logic, there is a Theorem known as the Law of Overfilling, or Implicational Law of Overfilling, or Dun Scotus Law, or L2 Theorem 1.

L2 Theorem 1: P—> (~P—>Q)

If an assertion implies its contradiction, then that assertion implies any and all statements.

“A deductive system…is called inconsistent, if its theses include two such which contradict one another, that is such that one is the negation of the other, e.g., (P) and (~ P) . If any inconsistent system is based on a two valued logic, then by the implicational law of overfilling one can obtain in it as a thesis any formula P which is meaningful in that system. It suffices…to apply the rule of modus ponens twice[ to P—> (~P—>Q)]. A system in which any meaningful formula is a thesis shall be termed overfilled.”

  1. Assume: P—> (~P—>Q)
  2. Modus Ponens: P
  3. Conclusion: ~P—>Q
  4. Modus Ponens: ~P
  5. Conclusion: Q

“[T]he problem of the logic of inconsistent systems is formulated here in the following manner: the task is to find a system of the sentential calculus which: (1) when applied to the inconsistent systems would not always entail overfilling, (2) would be rich enough to enable practical inference, (3) would have an intuitive justification. “

This means that Discussive Logic does not have the theorem of implicational law of overfilling. The theorem is not always true in Discussive Logic. Discussive Logic does not entail that a contradiction does not always entail any and all assertions. So Discussive Logic rejects the truth of the theorem P—> (~P—> Q), which is a theorem is two value logic, i.e. been proven true under conditions of two value logic.

Kolmogorov’s System

Here are Four axioms from Hilbert’s positive logic, and one axiom introduced by Kolmogorov.

K 1: P—> (Q—>P)
K 2: (P—> (P—>Q))—> (P—>Q)
K 3: (P—> (Q—>R))—> ((Q—> (P—>R))
K 4: (Q—>R)—> ((P—>Q)—> (P—>R))
K 5: (P—>Q)—> ((P—>~Q)—>~P)

Under these axioms, Two valued logic cannot be proved. Implicational Law of Overfilling not being provable in Discussive Logic implies that Two Valued logic cannot be proved in Discussive Logic. This entails that there might be overlap between Two Valued logic and Discussive Logic, but there is not a total overlap between Two Valued logic and Discussive Logic. Not all theorems of Two Valued logic will be theorems in Discussive logic (like law of overfilling), but some theorems of two valued logic are theorems in Discursive logic.

From these Axioms and the rule of inference known as Modus Ponens, there is one theorem which has some similarities to implicational law of overfilling.

K 9: P—> (~P—>~Q)

It is not the only Theorem that can be derived from the Axioms and Modus Ponens. Here is a list of some Theorems that can be derived by using  Modus Ponens on the Axioms.

K 6 : (P—>Q)—> ((Q—R)—> (P—>R))
K 7:  ((Q—>P)—>R)—> (P—>R)
K 8:  P—> ((Q—>~P)—> ~Q)
K 9:  P—> (~P—>~Q)

Proof of how K 6 – K 9 are derived are ignored for here. All that needs to be known is that K3 and applications of Modus Ponens is equal to If K4 then K 6. K 6 and applications of Modus Ponens is equal to If K 1 then K 7. K 7 and applications of Modus Ponens is equal to If K 5 then K 8. K 6 and applications of Modus Ponens is equal to If K 8 then K 7 implies K 9.

This forms Kolmogorov’s System.

Lewis System of Strict Implication

Strict Implication is defined by modal operator of “it is possible that P” or <>P. So “P strictly implies Q” is equal to “It is not possible that both P and not Q”. But taking the conditional statement —> as strict implication means that the implicational law of overfilling is not a theorem.

Material Implication as a conditional is usually defined by the logical relationship of a conjunction.

Material Conditional: P—>Q = ~(P & ~Q)
“P implies Q” is equal to “Not both P and not Q”
Strict Conditional: P—» Q = ~<>(P & ~Q)
“P strictly implies Q” is equal to “It is not possible that both P and not Q”

Under Strict Implication, Law of Overfilling is not a theorem. Under Material Implication, Law of Overfilling is a theorem. And set of theorems which include only strict implication and not material implication is very limited.

Many Valued Logics

Based on a certain Three Value logical matrix, which shall be ignored, the Law of Overfilling is not a theorem. But there is another theorem in the Three Value logic which has some similarity to the Law of Overfilling.

L 1: P—> (~P—> (~~P—> Q))

Based on the theorem (stated above) of this specific three valued logic, it holds the overfilling of a system when it includes the inconsistent thesis of P, ~P, and ~~P. And the implicational theses of two valued calculus remains valued in the three valued logic. But the three valued logic also holds other theorems that are not in two valued logic, which are as follows.

L 2: P—> ~~P
L 3: ~~~P—> P
L 4: ~P—> ~(P—> P)

So in the three valued logic, which is ignoring the logical matrix of this three valued logic, we cannot obtain the Law of Overfilling. The Law of Overfilling will thus be a theorem in two valued logic but not a theorem in this three valued logic. But the three valued logic has a theorem that is similar to the Law of Overfilling but is not equivalent to the Law of Overfilling. This three value logic also has some theorems that are not theorems in two valued logic. Besides the Law of Overfilling not being a theorem in the three valued logic, the rest of implicational theorems in two valued logic are theorems in the three valued logic.

Calculus of Modal Sentences (M2)

The Modal Sentences of (M2) will assume that modal assertions are either true or false, or simply that the Modal sentences are two valued. But now suppose that there are factors that do not allow for the assertion P to be determined strictly to be either true or false.

For example: Suppose that you are flipping a coin. Suppose that you make the assertion that “During the game heads will turn up more times than tails will” and this is represented by the variable of P. There will be certain sequences that turn up so that P is true, and there will be certain sequences that turn up so that P is false. So P may take on both true and false.

“It is necessary that P” = []P

Taking the example above, we can say that “P occurs for all possible events”.

Q is any formula that includes (1) operators —>, V, &, <—>, ~ and [], (2) and variables p,q,r,s..etc. R is any formula that is already a Q formula and is replacements of variables in Q by interpreting them as P(x), Q(x), R(x), S(x)…etc, and interpreting [] by universal quantifiers “for every x”. Every Q satisfies (1) and (2) and every R satisfies (1) and (2), and additionally satisfying (3).

The operators are implication, disjunction, conjunction, equivalence, and necessity. These are applied to variables or connects variables. When those conditions are met, then it is a formula of Q. The replacement of the variables and [] are formula of R. (1) and (2) can be recognized as P–>Q, or []P—>Q, or []P—>P. We can replace those variables to formulas in R: P(x) —> Q(x), or For every x, P(x) —> Q(x), or For every x, P(x) —> P(x).

“It is possible that P” = <>P

<>P can be taken as “it is not necessary that not P”.

<>P = ~[]~P

Like we could change []P into “for every x”, we may also change <>P into “for some x”.

Definition of Discussive Implication and Discussive Equivalence

As is known, even sets of those inscriptions which have no intuitive meaning at all can be turned into a formalized deductive system. In spite of this theoretical possibility, logical researches so far have been taking into consideration such deductive systems which are symbolic interpretations of consistent theories, so that theses in each such system are theorems in a theory formulated in a single symbolic language free from terms whose meanings are vague.

But suppose that theses which do not satisfy those conditions are included into a deductive system. It suffices, for instance, to deduce consequences from several hypotheses that are inconsistent with one another in order to change the nature of the theses, which thus shall no longer reflect a uniform opinion. The same happens if the theses advanced by several participants in a discourse are combined into a single system, or if one person’s opinions are so pooled into one system although that person is not sure whether the terms occurring in his various theses are not slightly differentiated in their meanings. Let such a system which cannot be said to include theses that express opinions in agreement with one another, be termed a discussive system. (Italics is authors and Bold is mine)

Each the theses in discussive logic are preceded so that each thesis has the speaker has the reservation such that each assertion means  “in accordance with the opinion of one of the participants in the discussion” or “for a certain admissible meaning of the terms used”. So when you add an assertion to a discussive system, that assertion will have a different intuitive meaning. Discussive assertions have the implicit condition of the equivalence to <>P.

King Solomon having to decide between two harlots claiming to be the mother of a baby. Woman A claimed to be the mother of the baby and not the mother of the dead baby, and Woman B claimed to be the mother of the baby and not the mother of the dead baby. King Solomon being the arbitrator, under Discussive assertions, would have taken each Woman’s claim as having the prefix of possibility, or “it is possible that Woman A is the mother” or “it is possible that Woman A is not the mother”.

Discussive logic is not based on ordinary two valued logic. Discussive logic would not hold Modus Ponens in all cases if it did.

Take the statement P—>Q is asserted in a discussion. It would be understood to mean “It is possible that If P, then Q”. P is asserted in the same discussion. It would be understood to mean “It is possible that P”. Q would not follow from the two assertions in the discussion. For by Q would not follow in the discussion because Q stands for “It is possible that Q”. So it is invalid to infer from “It is possible that if P, then Q” and “It is possible P” that “It is possible that Q”. But people might assume the normal two value logic in which Modus Ponens holds in all cases.

For Discussive Logic, Discussive Implication is defined as such:

Definition of Discussive Implication: P—>Q = <>P—>Q

There is a theorem of M2 based on Discussive Implication.

M2 Theorem 1: <>(<>P—>Q) —> (<>P—><>Q)

So Modus Ponens may be used in Discussrive Logic when we understand that from (<>P—><>Q) and <>P, we may infer that <>Q by Modus Ponens.

For Discussive Logic, Discussive Equivalence is defined as such:

Definition of Discussive Equivalence: P <—> Q = (<>P—>Q) & (<>Q—><>P)

There is a theorem of M2 based on Discussive Implication.

M2 Theorem 2: <> (P<—>Q) —> (<>P—> <>Q)
M2 Theorem 3: <> (P <—> Q) —> (<>Q —> <>P)

Two valued Discussive System of Sentential Calculus: D2

The system of D2 (i.e. Discussive Logic) of two valued discussive sentential calculus is marked by the formula T, and are marked by the following properties: (1) Sentential variables and functors of Discussive Implication, Discussive Equivalence, Disjunction, Conjunction, and Negation. (2)  precedening T with the symbol of <> yields a theorem in two valued sentential calculus of modal sentences M2.

As the author says, “The system defined in this way is discussive, i.e., its theses are provided with discussive assertion which implicitly includes the functor <>/ This is an essential fact, since even such a simple law as P—>P, on replacement of —> with —-> (i.e. discussive implication leads) to a new theorem.”

D2 Theorem 1: P—>P

D2 is not a theorem in M2, specifically because M2 did not have discussive implication. But in order to make D2 theorem 1 into a theorem in M2, you have to add <> to D2 theorem 1 like this:

M2 Theorem 4: <>(P—>P)

System M2 is decidable, so the discussive sentential calculus D2, defined by an interpretation in M2 is decidable too.

Methodological Theorem 1: “Every thesis T in two valued sentential calculus which does not include constant symbols of —>, <—>, V, becomes a thesis in T(d) in discusive sentential calculus D2 when in T the implication symbols is replaced by the [discurssive implication], and the equivalence symbols are replaced by [discusrive equivalence]. “

“Proof. Consider a formula T(d) constructed so as the theorem to be proved describes. It is to be demonstrated that <>T(d) is a thesis in M2. It is claimed that <>T(d) is equivalent to some other formulae; the equivalences will be proved gradually.”

Here are a couple more M2 Theorems.

M2 Theorem 5: <>(P—>Q) <—> (<>P—><>Q)
M2 Theorem 6: <>(P <—> Q) <—> (<>P <—> <>Q)
M2 Theorem 7: <>(P v Q) <—> (<>P v <>Q)

These theorems are about the distribution of <> over the variables. For example, M2 Theorem 5 distributes <> over implication, and M2 Theorem 6 distributes <> over equivalence, and M2 Theorem 7 distributes over Disjunction. M2 Theorem 5 and M2 Theorem 6 have Discussive Implication and Discussive Implication as the antecedents, respectively.

This shows how we can replace Discurssive Implication with regular implication and how we can replace Discurssive Equivalence with regular equivalence. So from <>(P—>Q), which contains Discurssive Implication, can be replaced with regular implication as <>P—><>Q. The form <>(P<—>Q), which contains Discurssive Equivalence, can be replaced with regular implication as <>P,—><>Q. Discurssive assertion like <>(PvQ) has the equivalence in M2, or Modal Logic, as <>P v <>Q.

The procedure yields the formula W, which is equivalent to <>T(d) and includes (1) only the symbols —>, <—>, and V, (2) variables, and (3) symbols <> in certain special positions, like each variable is directly preceded by <> and each symbol <> directly precedes a variable. Forming T(d) from the thesis T belonging to two value logic is possibly be seen that W can be obtained from T by preceding each variable by <>. For example, precede the variable P by <>P or precede the variable Q by <>Q. This procedure would yield the following theorems in M2.

(a) W is a result of the substitution in T
(b) <>T(d) is equivalent to W.
Hence T(d) is a thesis of D2

The theorems just listed above, immediately yields these theorems in Discussive Logic:

D2 Theorem 2: (P<—>Q) <—> (Q<—>P)
D2 Theorem 3: (P—>Q) —> ((Q—>P) —> (P<—>Q))

Each of the connectives in the D2 theorem just listed are Discurssive Equivalence for D2 Theorem 2 and Discurssive Implication for D2 Theorem 3.

Methodological Theorem 2: If T is a thesis in the two valued sentential calculus and includes variables and at the most the functors V, &, ~, then (1) T and (2) ~T —> q, are thesis in D2. The implication of (2) is Discurssive Implication.

Proof: The symbols V, &, and ~ retain respective meanings in M2 and D2, and that (3) []T is a thesis in M2. The symbols V, &, and ~ retain respective meanings in M2 and D2 and that (3) []T is a thesis in M2. Hence (1) by M2 Theorem 8 []P—><>P and (2) by M2 Theorem 9 []P—><>(<>~P—>Q).

M2 Theorem 8: []P—><>P
M2 Theorem 9: []P—> <>(<>~P—>Q)

We may apply the Methodological Theorem 2 to the Two Valued Logic Theorem of ~(Pv~P), i.e. Aristotle’s Principle of Contradiction.

L2 Theorem 3: ~(P&~P)

“Methodological Theorem 2 and Law of Contradiction in Two valued logic yieleds – in view of the law of double negation- the following theorem of Discussive logic.”

D2 Theorem 4: ~(P&~P) [Law of Contradiction]
D2 Theorem 5: (P&~P) —> Q [Conjunctional Law of Overfilling]

What these two theorems are basically stating is this: Suppose that we have an individual in a discussion, and this individual holds to the Discussive assertion of (P&~P), this individual would hold inconsistent opinions. And in Discussive logic, when an individual holds to inconsistent opinion, the persons opinion implies any and all discussive assertions. This basically forbids an individual from holding to discussive assertions that are contradictory to one another by D2 Theorem 4, and if we do hold to contradictory discussive assertions then any discussive assertion follows from the conjunction of contradictory discussive assertions. This is similar to Law of Overfilling in two value logic but not exactly the same.

We also have the following theorems in Discussive Logic.

D2 Theorem 6: (P&Q) —> P
D2 Theorem 7: P—> (P&P)
D2 Theorem 8: (P&Q) <—> (Q&P)
D2 Theorem 9: (P& (Q&R)) <—> ((P&Q) & R)
D2 Theorem 10: (P—> (Q—>R)) —> ((P&Q) —>R) [Law of Importation]
D2 Theorem 11:((P–>Q) & (P—>R)) <—> (P—>(Q & R))
D2 Theorem 12: ((P—>R) & (Q—>R)) <—> ((PvQ) —> R)
D2 Theorem 13:P <—> ~~P
D2 Theorem 14:(~P—>P) —>P
D2 Theorem 15:(P—>~P)>~P
D2 Theorem 16:(P<—>~P) —>P
D2 Theorem 17: (P<—>~P) —>~P
D2 Theorem 18: ((P—>Q) & ~Q) —> ~P

There are laws of inference by reductio ad absurdum that remain valid in Discurssive Logic.

D2 Theorem 19:((P—>Q) & (P—>~Q)) —> ~P
D2 Theorem 20:((~P—>Q) & (~P—>~Q)) > P
D2 Theorem 21:(P> (Q&~Q)) —> ~P
D2 Theorem 22: (~P —> (Q&~Q)) —>P

Here are some other theorems of Discurssive Logic.

D2 Theorem 23:~(P <—> ~P)
D2 Theorem 24:~(P—>Q) —>P
D2 Theorem 25: ~(P—>Q) —>~Q
D2 Theorem 26: P —> (~Q—>~(P—>Q))

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Logically Valid Arguments

Posted by allzermalmer on April 8, 2013

Categorically Valid Syllogisms

M stands for Middle Term; P stands for Major Term; S stands for Minor Term

Figure 1

(1) Barabara:If all M are P and all S are M, then all S are P
P. All M are P
P. All S are M
C. All S are P

(2) Celarent: If no M are P and all S are M, then no S are P
P. No M are P
P. All S are M
C. No S are P

(3) Darii: If all M are P and some S are M, then some S are P
P. All M are P
P. Some S are M
C. Some S are P

(4) Ferio: If no M are P and some S are M, then some S are not P
P. No M are P
P. Some S are M
C. Some S are not P

Figure 2

(1) Camestres: If all P are M and no S are M, then no S are P
P. All P are M
P. No S are M
C. No S are P

(2) Cesare: If no P are M and all S are M then no S are P
P. No P are M
P. All S are M
C. No S are P

(3) Baroko: If all P are M and some S are not M, then some S are not P
P. All P are M
P. Some S are not M
C. Some S are not P

(4) Festino: If no P are M and some S are M, then some S are not P
P. No P are M
P. Some S are M
C. Some S are not P

Figure 3

(1) Datisi: If all M are P and some M are S, then some S are P
P. All M are P
P. Some M are S
C. Some S are P

(2) Disamis: If some M are P and all M are S, then some S are P
P. Some M are P
P. Some M are S
C. Some S are P

(3) Ferison: if no M are P and some M are S, then some S are not P
P. No M are P
P. Some M are S
C. Some S are not P

(4) Bokardo: If some M are not P and all M are S, then some S are not P
P. Some M are not P
P. All M are S
C. Some S are not P

Figure 4

(1) Camenes: If all P are M and no M are S, then no S are P
P. All P are M
P. No M are S
C. No S are P

(2) Dimaris: If some P are M and all M are S, then Some S are P
P. Some P are M
P. All M are S
C. Some S are P

(3) Fresison: If no P are M and some M are S, then some S are not P
P. No P are M
P. Some M are S
C. Some S are not P

Propositional Logic

Modus Ponens: Given the conditional claim that the consequent is true if the antecedent is true, and given that the antecedent is true, we can infer the consequent.
P. If S then P
P. S
C. Q

Modus Tollens: 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.
P. If S then P
P. Not P
C. Not S

Hypothetical Syllogism: Given two conditional such that the antecedent of the second is the consequent of the first, we can infer a conditional such that its antecedent of the first premise and its consequent is the same as the consequent of the second premise.
P. If S then M
P. If M then P
C. If S then P

Constructive Dilemma: Given two conditionals, and given the disjunction of their antecedents, we can infer the disjunction of their consequents.
P. If S then P                 P. If S then P
P. If M then N               P. If M then P
P. S or M                        P. S or M
C. P or N                        C. P or P

Destructive Dilemma: Given two conditionals, and given the disjunction of the negation of their consequents, we can infer the disjunction of the negation of their antecedents.
P. If S then P                P. If S then P
P. If M then N              P. If S then N
P. Not P or Not N        P. Not P or Not N
C. No S or Not M        C. Not S or Not S

Biconditional Argument: Given a biconditional and given the truth value of one side is known, we can infer that the other side has exactly the same truth value.
P. S<–>P    P. S<–>P   P. S<–>P   P. S<–>P
P. S               P. P              P. Not S      P. Not P
C. P              C. S               C. Not P     C. Not S

Disjunctive Addition: Given that a statement is true, we can infer that a disjunct comprising it and any other statement is true, because only one disjunct needs to be true for the disjunctive compound to be true.
P. S
C. S or P

Disjunctive Syllogism: Because at least one disjunct must be true, by knowing one is false we can infer tat the other is true.
P. S or P   P. S or P
P. Not P   P. Not S
C. S          C. P

Simplification: Because both components of a conjunctive argument are true, it is permissible to infer that either of its conjuncts is true.
P. S & P   P. S & P
C. S          C. P

Adjunction: Because both premises are presumed true, we can infer their conjunction.
P. S
P. P
C. S & P

Conjunctive Argument: Because the first premise says that at least one of the conjuncts is false and the second premise identifies a true conjunct, we can infer that the other conjunct is false.
P. ~(S & P)   P. ~(S & P)
P. S                P. P
C. Not P        C. Not S

 

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Did Popper Solve The Problem of Induction?

Posted by allzermalmer on October 3, 2012

Karl Popper said that he believed he had solved the “Problem of Induction”, or what he called “Hume’s Problem”. But did Karl Popper really solve the Problem of Induction or Hume’s Problem? Maybe we should (1) take a look at what Popper considered to be Hume’s problem, and (2) see what Popper says his solution to the problem is. (Whether or not Popper did correctly identify Hume’s problem, is of no concern here).

Before we do this, I think we should start out with something basic, or part of basic, logic.

(A) Universal Quantifier Affirmative (All S are P): For each x, if x is S, then x is P
(E) Universal Quantifier Negation (No S are P) : For each x, if x is S, then x is not P
(I) Existential Quantifier Affirmative (Some S are P): There exists at least one x, such that x is S and x is P
(O) Existential Quantifier Negation (Some S are not P): There exists at least one x, such that x is S and x is not P

“All of the categorical propositions illustrated above can be expressed by using either the universal quantifier alone or the existential quantifier alone. Actually, what this amounts to is the definition of the universal quantification of propositions in terms of existential quantification and the definition of existential propositions in terms of universal quantification.” p. 349 Formal Logic: An Introductory Textbook by John Arthur Mourant

Now this means that the Universal Quantifier (UQ) can be expressed in a logically equivalent form to an Existential Quantifier (EQ), and the Existential Quantifier can be expressed in a logically equivalent form to Universal Quantifier. For something to be logically equivalent means they mean the same thing in a logical sense. Logically equivalent statements have the exact same truth. One can’t be true and the other false, for this would mean they are both necessarily false.

Universal Quantifiers to Existential Quantifiers

A: For each x, if x is S, then x is P    There does not exist at least one x, such that x is S and x is not P
E: For each x, if x is S, then x is not P    There does not exist at least one x, such that x is S and x is P
I: Not for each x, if x is S, then x is not P    There exists at least one x, such that x is S and x is P
O: Not for each x, if x is S, then x is P   There exists at least one x, such that x is S and x is not P

A: For each x, if x is Crow, then x is Black  ↔  There does not exist at least one x, such that x is Crow and x is not Black
E: For each x, if x is Crow, then x is not Black  ↔  There does not exist at least one x, such that x is Crow and x is Black
I: Not for each x, if x is Crow, then x is not Black  ↔  There exists at least on x, such that x is Crow and x is Black
O: Not for each x, if x is Crow, then x is Black  ↔  There exists at least on x, such that x is Crow and x is not Black

Existential Quantifiers to Universal Quantifiers

A: There does not exist at least one x, such that x is S and x is not P    For each x, if x is S, then x is P
E: There does not exist at least one x, such that x is S and x is P     For each x, if x is S, then x is not P
I: There exists at least one x, such that x is S and x is P   Not for each x, if x is S, then x is not P
O: There exists at least one x, such that x is S and x is not P    Not for each x, if x is S, then x is P

A: There does not exist at least one x, such that x is Crow and x is not Black  ↔  For each x, if x is Crow, then x is Black
E:
There does not exist at least one x, such that x is S and x is P  ↔  For each x, if x is Crow, then x is not Black 
I:
There exists at least one x, such that x is Crow and x is Black  ↔  Not for each x, if x is Crow, then x is not Black
O:
There exists at least one x, such that x is Crow and x is not Black  ↔  Not for each x, if x is Crow, then x is Black

It needs to be pointed out first that there are two types of statements.
(1)Necessary Truth: Statement whose denial is self-contradictory.
(2) Contingent Truth: One that logically (that is, without self-contradiction) could have been either true or false.

(1a) “All bachelors are unmarried males”
(2a) “Justin Bieber is an unmarried male”

A necessary truth is said to have no empirical content. A contingent truth is said to have empirical content.

Hume’s problem was that he found that he cannot justify induction by demonstrative argument, since he can always imagine a different conclusion.

What Popper takes to be “Hume’s Problem”

“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.” pg. 3-4 Logic of Scientific Discovery

“The root of this problem [of induction] is the apparent contradiction between what may be called ‘the fundamental thesis of empiricism’- the thesis that experience alone can decide upon the truth or falsity of scientific statements- and Hume’s realization of the inadmissibility of inductive arguments.” pg. 20 Logic of Scientific Discovery

Here’s an Inductive argument

Singular: (P1) There exists at least one x, such that x is Crow and x is Black
Singular: (P2) There exists at least one x, such that x is Crow and x is Black

Universal: (C) For each x, if x is Crow, then x is Black

Popper’s Solution to “Hume’s Problem”

“Consequently it is possible by means of purely deductive inferences (with the help of the modus tollens of classical logic) to argue from the truth of singular statements to the falsity of universal statements. Such an argument to the falsity of universal statements is the only strictly deductive kind of inference that proceeds, as it were, in the ‘inductive direction’ that is, from singular to universal statements.”pg. 21 Logic of Scientific Discovery

Here’s Popper’s solution

Universal: (P1) For each x, if x is Crow, then x is not Black
Singular: (P2) There exists at least one x, such that x is Crow and x is Black
Universal: (C) Not for each x, if x is Crow, then x is not Black

Singular statement leads to a universal statement. From there exists at least one x, such that x is Crow and x is Black, the conclusion is reached that not for each x, if x is Crow, then x is not Black.

Here’s Poppers understanding of Induction: “It…passes from singular statements…to universal statements…”

Here’s Poppers solution to the ‘Problem of Induction: “Such an argument to the falsity of universal statements is… from singular to universal statements.”

So going from singular statement to universal statement can be justified by  going from singular statements to universal statements. This falls for the problem of induction again, because this is a circular argument that is used to defend induction.

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Sherlock-Holmesian Reasoning

Posted by allzermalmer on September 22, 2012

Sherlock Holmes is the “[t]he only unofficial consulting detective”, and he had a certain method of reasoning in his “detecting”. This is laid out in the “The Sign of Four” by Sir Arthur Conan Doyle. One chapter is called “The Science of Deduction“, which goes over Holmes basic outline of reasoning. I have altered the format of The Science of Deduction reproduced here by trying to put it more into a Dialectical format.

Those portions that are italicized are not done so in the story itself. I have italicized them myself in order to show important features of Sherlock Holmes method of detection, or method of reasoning. These help to form the basic outlines, or characteristics, of his method propounded here. These are what I shall call Holmesian Reasoning, or Holmesian Thinking.

“Sherlock Holmes took his bottle from the corner of the mantel piece, and his hypodermic syringe from its neat morocco case. With his long, white, nervous fingers he adjusted the delicate needle and rolled back his left shirtcuff. For some little time his eyes rested thoughtfully upon the sinewy forearm and wrist, all dotted and scarred with innumerable puncture marks. Finally, he thrust the sharp point home, pressed down the tiny piston, and sank back into the velvet lined armchair with a long sigh of satisfaction.

Three times a day for many months Watson had witnessed this performance, but custom had not reconciled his mind to it. On the contrary, from day to day he had become more irritable at the sight, and his conscience swelled nightly within him at the thought that he had lacked the courage to protest. Again and again he had registered a vow that he should deliver his soul upon the subject; but there was that in the cool, nonchalant air of his companion which made him the last man with whom one would care to take anything approaching to a liberty. Sherlock Holmes great powers, his masterly manner, and the experience which Watson had had of his many extraordinary qualities, all made Watson diffident and backward in crossing him.

Yet upon that afternoon, whether it was the Beaune which Watson had taken with his lunch or the additional exasperation produced by the extreme deliberation of his manner, he suddenly felt that he could hold out no longer.

Watson: “Which is it today? Morphine or cocaine?”

Holes raised his eyes languidly from the old black letter volume which he had opened.

Holmes: “It is cocaine, a seven-per-cent solution. Would you care to try it?”

Watson : “No, indeed. My constitution has not got over the Afghan campaign yet. I cannot afford to throw any extra strain upon it.”

Holes smiled at Watson’s vehemence.

Holmes: “Perhaps you are right, Watson, I suppose that its influence is physically a bad one. I find it, however, so transcendently stimulating and clarifying to the mind that its secondary action is a matter of small moment.”

Watson: “But consider! Count the cost! Your brain may, as you say, be roused and excited, but it is a pathological and morbid process which involves increased tissue change and may at least leave a permanent weakness. You know, too, what a black reaction comes upon you. Surely the game is hardly worth the candle. Why should you, for a mere passing pleasure, risk the loss of those great powers with which you have been endowed? Remember that I speak not only as one comrade to another but as a medical man to one for whose constitution he is to some extent answerable.”

Holmes’s did not seem offended. On the contrary, he put his fingertips together, and leaned his elbows on the arms of his chair, like one who has a relish for conversation.

Holmes: “My mind rebels at stagnation. Give me problems, give me work, give me the most abstruse cryptogram, or the most intricate analysis, and I am in my own proper atmosphere. I can dispense then with artificial stimulants. But I abhor the dull routine of existence. I crave for mental exaltation. That is why I have chosen my own particular profession, or rather created it, for I am the only one in the world.”

Watson: “The only unofficial detective?”  said while raising his eyebrows.

Holmes: “The only unofficial consulting detective, I am the last and highest court of appeal in detection. When Gregson, or Lestrade, or Athelney Jones are out of their depths–which, by the way, is their normal state–the matter is laid before me. I examine the data, as an expert, and pronounce a specialist’s opinion. I claim no credit in such cases. My name figures in no newspaper. The work itself, the pleasure of finding a field for my peculiar powers, is my highest reward. But you have yourself had some experience of my methods of work in the Jefferson Hope case.”

Watson: “Yes, indeed, I was never so struck by anything in my life. I even embodied it in a small brochure, with the somewhat fantastic title of ‘A Study in Scarlet.’ ”

Holmes shook his head sadly.

Holmes: “I glanced over it. Honestly, I cannot congratulate you upon it. Detection is, or ought to be, an exact science and should be treated in the same cold and unemotional manner. You have attempted to tinge it with romanticism, which produces much the same effect as if you worked a love story or an elopement into the fifth proposition of Euclid.”

Watson: “But the romance was there. I could not tamper with the facts.”

Holmes: “Some facts should be suppressed, or, at least, a just sense of proportion should be observed in treating them. The only point in the case which deserved mention was the curious analytical reasoning from effects to causes, by which I succeeded in unravelling it.

Watson  was annoyed at Holmes criticism of a work which had been specially designed to please him. Watson confess, too, that he was irritated by the egotism which seemed to demand that every line of his pamphlet should be devoted to Holmes own special doings. More than once during the years that Watson had lived with Holmes in Baker Street Watson had observed that a small vanity underlay his companion’s quiet and didactic manner. He made no remark however, but sat nursing his wounded leg. Watson had had a Jezaii bullet through it some time before, and though it did not prevent him from walking it ached wearily at every change of the weather.

Holmes: “My practice has extended recently to the Continent,” said Holmes after a while, filling up his old brier-root pipe. “I was consulted last week by Francois le Villard, who, as you probably know, has come rather to the front lately in the French detective service. He has all the Celtic power of quick intuition but he is deficient in the wide range of exact knowledge which is essential to the higher developments of his art. The case was concerned with a will and possessed some features of interest. I was able to refer him to two parallel cases, the one at Riga in 1857, and the other at St. Louis in 1871, which have suggested to him the true solution. Here is the letter which I had this morning acknowledging my assistance.”

Holmes tossed over, as he spoke, a crumpled sheet of foreign notepaper. Watson glanced his eyes down it, catching a profusion of notes of admiration, with stray magnifiques, coup-de-maitres and tours-de-force, all testifying to the ardent admiration of the Frenchman.

Watson: “He speaks as a pupil to his master.”

Holmes: “Oh, he rates my assistance too highly. He has considerable gifts himself. He possesses two out of the three qualities necessary for the ideal detective. He has the power of observation and that of deduction. He is only wanting in knowledge, and that may come in time. He is now translating my small works into French.”

Watson: “Your works?”

Holmes: “Oh, didn’t you know?” he cried, laughing. “Yes, I have been guilty of several monographs. They are all upon technical subjects. Here, for example, is one ‘Upon the Distinction between the Ashes of the Various Tobaccos.’ In it I enumerate a hundred and forty forms of cigar, cigarette, and pipe tobacco, with coloured plates illustrating the difference in the ash. It is a point which is continually turning up in criminal trials, and which is sometimes of supreme importance as a clue. If you can say definitely, for example, that some murder had been done by a man who was smoking an Indian lunkah, it obviously narrows your field of search. To the trained eye there is as much difference between the black ash of a Trichinopoly and the white fluff of bird’s-eye as there is between a cabbage and a potato.

Watson: “You have an extraordinary genius for minutiae.”

Holmes: “I appreciate their importance. Here is my monograph upon the tracing of footsteps, with some remarks upon the uses of plaster of Paris as a preserver of impresses. Here, too, is a curious little work upon the influence of a trade upon the form of the hand, with lithotypes of the hands of slaters, sailors, cork cutters, compositors, weavers, and diamond-polishers. That is a matter of great practical

interest to the scientific detective–especially in cases of unclaimed bodies, or in discovering the antecedents of criminals. But I weary you with my hobby.”

Watson: “Not at all. It is of the greatest interest to me, especially since I have had the opportunity of observing your practical application of it. But you spoke just now of observation and deduction. Surely the one to some extent implies the other.”

Holmes: “Why, hardly,” he answered, leaning back luxuriously in his armchair and sending up thick blue wreaths from his pipe. “For example, observation shows me that you have been to the Wigmore Street Post Office this morning, but deduction lets me know that when there you dispatched a telegram.”

Watson: “Right! Right on both points! But I confess that I don’t see how you arrived at it. It was a sudden impulse upon my part, and I have mentioned it to no one.”

Holmes: “It is simplicity itself,” he remarked, chuckling at my surprise–“so absurdly simple that an explanation is superfluous; and yet it may serve to define the limits of observation and of deduction. Observation tells me that you have a little reddish mould adhering to your instep. Just opposite the Wigmore Street Office they have taken up the pavement and thrown up some earth, which lies in such a way that it is difficult to avoid treading in it in entering. The earth is of this peculiar reddish tint which is found, as far as I know, nowhere else in the neighbourhood. So much is observation. The rest is deduction.”

Watson: “How, then, did you deduce the telegram?”

Holmes: “Why, of course I knew that you had not written a letter, since I sat opposite to you all morning. I see also in your open desk there that you have a sheet of stamps and a thick bundle of postcards. What could you go into the post office for, then, but to send a wire? Eliminate all other factors, and the one which remains must be the truth.

Watson: “In this case it certainly is so,” he replied after a little thought. “The thing, however, is, as you say, of the simplest. Would you think me impertinent if I were to put your theories to a more severe test?”

Holmes: “On the contrary,” he answered, “it would prevent me from taking a second dose of cocaine. I should be delighted to look into any problem which you might submit to me.”

Watson: “I have heard you say it is difficult for a man to have any object in daily use without leaving the impress of his individuality upon it in such a way that a trained observer might read it. Now, I have here a watch which has recently come into my possession. Would you have the kindness to let me have an opinion upon the character or habits of the late owner?”

Watson handed Holmes over the watch with some slight feeling of amusement in his heart, for the test was, as he thought, an impossible one, and he intended it as a lesson against the somewhat dogmatic tone which Holmes occasionally assumed. Holmes balanced the watch in his hand, gazed hard at the dial, opened the back, and examined the works, first with his naked eyes and then with a powerful convex lens. Watson could hardly keep from smiling at Holmes crestfallen face when he finally snapped the case to and handed it back.

Holmes: “There are hardly any data,” he remarked. “The watch has been recently cleaned, which robs me of my most suggestive facts.”

Watson: “You are right,” he answered. “It was cleaned before being sent to me.”

In Holmes heart he accused his companion of putting forward a most lame and impotent excuse to cover Watson’ s failure. What data could he expect from an uncleaned watch?

Holmes: “Though unsatisfactory, my research has not been entirely barren,” he observed, staring up at the ceiling with dreamy, lacklustre eyes. “Subject to your correction, I should judge that the watch belonged to your elder brother, who inherited it from your father.”

Watson: “That you gather, no doubt, from the H. W. upon the back?”

Holmes: “Quite so. The W. suggests your own name. The date of the watch is nearly fifty years back, and the initials are as old as the watch: so it was made for the last generation. Jewellery usually descends to the eldest son, and he is most likely to have the same name as the father. Your father has, if I remember right, been dead many years. It has, therefore, been in the hands of your eldest brother.”

Watson: “Right, so far,” said I. “Anything else?”

Holmes: “He was a man of untidy habits–very untidy and careless. He was left with good prospects, but he threw away his chances, lived for some time in poverty with occasional short intervals of prosperity, and finally, taking to drink, he died. That is all I can gather.”

Watson sprang from his chair and limped impatiently about the room with considerable bitterness in his heart.

Watson:  “This is unworthy of you, Holmes,” he said. “I could not have believed that you would have descended to this. You have made inquiries into the history of my unhappy brother, and you now pretend to deduce this knowledge in some fanciful way. You cannot expect me to believe that you have read all this from his old watch! It is unkind and, to speak plainly, has a touch of charlatanism in it.

Holmes: “My dear doctor,” said he kindly, “pray accept my apologies. Viewing the matter as an abstract problem, I had forgotten how personal and painful a thing it might be to you. I assure you, however, that I never even knew that you had a brother until you handed me the watch.”

Watson: “Then how in the name of all that is wonderful did you get these facts? They are absolutely correct in every particular.”

Holmes: “Ah, that is good luck. I could only say what was the balance of probability. I did not at all expect to be so accurate.”

Watsons: “But it was not mere guesswork?”

Holmes: “No, no: I never guess. It is a shocking habit–destructive to the logical faculty. What seems strange to you is only so because you do not follow my train of thought or observe the small facts upon which large inferences may depend. For example, I began by stating that your brother was careless. When you observe the lower part of that watch case you notice that it is not only dinted in two places but it is cut and marked all over from the habit of keeping other hard objects, such as coins or keys, in the same pocket. Surely it is no great feat to assume that a man who treats a fifty-guinea watch so cavalierly must be a careless man. Neither is it a very far fetched inference that a man who inherits one article of such value is pretty well provided for in other respects.

Watson nodded to show that he followed his reasoning.

Holmes: “It is very customary for pawnbrokers in England, when they take a watch, to scratch the numbers of the ticket with a pinpoint upon the inside of the case. It is more handy than a label as there is no risk of the number being lost or transposed. There are no less than four such numbers visible to my lens on the inside of this case. Inference–that your brother was often at low water. Secondary inference–that he had occasional bursts of prosperity, or he could not have redeemed the pledge. Finally, I ask you to look at the inner plate, which contains the keyhole. Look at the thousands of scratches all round the hole–marks where the key has slipped. What sober man’s key could have scored those grooves? But you will never see a drunkard’s watch without them. He winds it at night, and he leaves these traces of his unsteady hand. Where is the mystery in all this?”

Watson: “It is as clear as daylight,” he answered. “I regret the injustice which I did you. I should have had more faith in your marvellous faculty. May I ask whether you have any professional inquiry on foot at present?”

Holmes: “None. Hence the cocaine. I cannot live without brainwork. What else is there to live for? Stand at the window here. Was ever such a dreary, dismal, unprofitable world? See how the yellow fog swirls down the street and drifts across the dun coloured houses. What could be more hopelessly prosaic and material? What is the use of having powers, Doctor, when one has no field upon which to exert them? Crime is commonplacc, existence is commonplace, and no qualities save those which are commonplace have any function upon earth.

Watson had opened his mouth to reply to this tirade when, with a crisp knock, our landlady entered, bearing a card upon the brass salver.

Landlady Mrs. Hudson: “A young lady for you, sir,” she said, addressing Watson’s companion.

Holmes: “Miss Mary Morstan,” he read. “Hum! I have no recollection of the name. Ask the young lady to step up, Mrs. Hudson. Don’t go, Doctor Watson. I should prefer that you remain.”

1. Detection is, or ought to be, an exact science and should be treated in the same cold and unemotional manner.

Sherlock Holmes does not allow for emotions to come into his method of detection, or his method of reasoning. He tries to keep feelings and emotions outside of he considers to be how detection is actually done or how detection actually ought to be done. Now Holmes is either guided by what detection actually is or what detection ought to be, or both what detection is and what detection ought to be. This appears to be open to being derived from  Is v. Ought and Descriptive v. Normative, or Is and Ought are one and the same and Descriptive and Normative are one and the same. As Joe Friday use to say, “Just the facts, ma’am.”. The Facts, for Holmes, are, or ought to be, treated in a cold and unemotional manner.

2.  Analytical reasoning from effects to causes, by which succeeded in unravelling a fact.

Sherlock will argue from an observation to a cause of that observation. From a single fact, Holmes argues to another, which is what produced the fact before him, what is the facts cause. From the fact that there is smoke, by analytical reasoning, Holmes concludes that there is fire. From the fact that there is red mud on Dr. Watson’s pants, he argues to a cause of the red mud on Dr. Watson’s pants. This fact was noticed by observation. From the facts of scratches and writing, and a certain functional characteristic on the watch that he observed, Holmes reaches a certain cause of those scratches and writing, and certain functional characteristics of the watch.

In the examples that are given in the dialogue, inductive reasoning is being used. Holmes moves from what is known to what is unknown. Holmes moves from the known to the unknown. Holmes moves from the effect, from the known, to the unknown cause. Holmes knows there is red mud on Watson’s pants, but Holmes did does not know where Watson went when Holmes was not with Watson. Holmes, also, did not see Watson walk into any red mud in the time that they were together.

3. The power of observation,  deduction, and a wide range of exact knowledge, (and intuition(?)).

You must be able to use your senses. You must be able to observe in order to notice things. You must have a wide base of exact knowledge. The example of Watson’s clock is one. Holmes notices some scratches on it, and he notices some writing on it, and he also knows the type of watch. The type of watch is based on Holmes wide range of exact knowledge. This wide range of exact knowledge also includes Holmes notices some scratches on it, and he notices some writing on it,  feels the watch in his hand, he focuses his attention to the dials of the clock, he opens the back of the watch and looks at the internal functionings of the watch with his naked eye and than with a magnifying instrument in front of his naked eye. These are the facts of observation that is shown to Holmes by observation.

Holmes have a wide range of exact knowledge, which either comes from his personal experience or from those that he has read in books or other people have said. He knows that jewelry is passed down to the eldest son, the eldest son usually has the same first name as the father, and he knows what  50 years old watches look like. From this exact knowledge he could deduce that the watch is Watson’s brothers. From that wide range of exact knowledge is previous knowledge brought to the situation when make the observations, which is how certain things can stand out to garner ones attention.

Holmes has a wide range of knowledge that is known to be true, and he has these particular observation, data, before him, and these together allow him to deduce something that is not known by the observations, or  data, itself or the wide range of knowledge itself. He does not know that the watch was owned by Watson’s brother and that Watson cleaned the watch before showing it to Holmes. But he knows a certain general principle that was established by enumeration of particular observations by himself or others, and the observations before Holmes now are consistent with those general principles themselves, and so it is another enumeration of that general principle.

All men are mortal (part of Holmes wide range of knowledge). Socrates is a man (observation made by Holmes). So Holems concludes that Socrates is mortal, even though Holmes has not made the observation itself that Socrates is mortal. Holmes concludes this through logical deduction from these known things. But the conclusion that Holmes draws is one that is not known itself by observation. He has not observed that Socrates has died, and so does not know that Socrates is mortal.

4. Eliminate all other factors, and the one which remains must be the truth.

Holmes will eliminate other factors that can lead to different conclusions of the observations before him. Take the example of the ash that comes from different cigars. Holmes had enumerated many experiments with a hundred and forty forms of cigar, cigarette, and pipe tobacco. He noticed that each type of cigar, cigarette, and pipe tobacco, left their own distinct ash. This became a wide range of exact knowledge he obtained.If Holmes did not know all these different possible cigars, cigarettes, and pipe tobacco, and the ash they leave behind, then he would not know what else would be consistent with the ash that Holmes observes. But knowing these things, he can eliminate certain possible types of cigars, cigarettes, and pipe tobacco, because the observation eliminates those causes of the ash. The observation is not consistent with those possible causes, or source, of the ash that is left behind.

Knowing all the possible factors involved in the situation, would allow Holmes to eliminate certain possible causes for what is being observed. Holmes would eliminate what is impossible, because the observation contradicts a cause that is possible in and of itself. Like eliminating that the ash belongs to cigar type x because cigar type x ash is not similar to the ash observed. So whatever else is left would be the truth if it is the only factor left, like cigar y is the only source consistent with the observed ash, and if it is not the only factor left then at least know what is not the possible source of the ash. Cigar types a,b, and c have been eliminated. It narrows the search down further to the cigar, cigarette, and pipe tobacco to be the source, the cause, of the ash observed.

Holmes eliminates possible causes of the effect that is observed, and only one possible cause is correct. The murder smoked a particular type of tobacco product, and that particular tobacco product left behind a certain kind of ash. He eliminated particular tobacco products as the cause of the ash because those causes product different effects than the one observed. So the murder did not smoke those tobacco products. But Holmes himself did not observe what particular tobacco product itself that the murder smoked. He is eliminating a possible unknown cause by a known effect, and how the possible unknown cause is not consistent with the known effect.

5. Some facts ought be suppressed, or not given much attention.

Some observations ought not to be taken attention or pay much attention to. This appears to follow from Holmes saying that emotions that are found to go along with observations ought to be ignored. This is because emotions are not cold and unemotional. There are also other factors that do not play into a possible cause for the observation, which appears to come from ones wide range of exact knowledge, or intuition. The shoes that Watson has on appear to have no causal relation with the watch the Watson presented for Holmes to observe. So Holmes ought to suppress the observation of what shoes Watson has on, or Holmes emotional state in making the observation of the watch.

(This blog post will go through alteration and addition at a later date.)

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Refutation of Realism

Posted by allzermalmer on June 28, 2011

This blog is going to be based off an article done by W.T. Stace. The name of the paper is The Refutation of Realism, and it appears in the philosophical journal Mind, Vol. 43, No. 170 (Apr., 1934), pp. 145-155. This article is a play off of G.E. Moore’s article The Refutation of Idealism.

Now, the obvious question would be “What is meant by realist?”. Stace goes on to say, by realist, he means someone who agrees to the assertion that “some entities sometimes exist without being experienced by any finite mind.” Now, this might not be what all realist would agree to, but it is close enough to the very basic idea.

So let us take a look at what a realist might believe. Before me is a book, and I know this because I am seeing it, I am touching it, and I hear it when I slam my hand against it, I am smelling it, and taste it. Now, a realist would believe that the book continues to exist when I put it in a drawer, and I no longer have those experiences of it, and there is no other finite mind experiencing it. Thus, a realist will at least believe that it continues to exist when no one is experiencing it.

Now, there would also seem to be no point in asserting that entities might exist unexperienced, unless they do, as a matter of fact, sometimes exist unexperienced. Now, imagine that the universe has a property, which we call X, as a matter of fact, the universe has no such property, would be useless, and has no contribution to truth. Now, some realist might think that such a belief of the relation between knowledge and object as such, helps them in someway of helping with the belief in things that exist unexperienced by some mind.

Now, it should be stated as clearly as possible, and which is very important. That statement is,  One cannot prove that no entities exist without being experienced by minds. For, it is always possible that they do exist unperceived. However, it is also possible that they do not exist unperceived. Thus, we find that both are equal in their possibility. But, the main point is this: We have not the slightest reason for believing that they do exist unexperienced. And it is from this that the realistic position is groundless, and one that ought not to be believed. And the realistic position is like that of “there is a unicorn on the planet Mars”. We cannot prove that there is not a unicorn on Mars. However, since there is not the slightest reason to suppose that there is one, it is a proposition which we ought not to believe.

Now it will not be held that objects of experience, like a color patch that is green, are “mental”. And so when it comes to the question of if what we experience is only mental, it will be held that this question is meaningless, and this is a form of neutral monism. Now, the position will be as follows: “There is absolutely no reason for assertion that these non-mental, or physical, entities ever exist except when they are being experienced, and the proposition that they do so exist is utterly groundless and gratuitous, and one which ought not to be believed.”

It will be attempted to show that we do not know that any single entity exists unexperienced. It will be inquired how we could possibly know that unexperienced entities exist, even if they do exist unexperienced.

Let us get back to a previous example. Now, at this moment, I am experiencing this book in front of me. But how can I know that it existed last nigh in my drawer, when, as far as I know, no other finite mind was experiencing it? How can I know that it will continue to exist tonight when there is no one in the room? A realist knows, or at least believes, that they continue to exist. Now a question comes up: How could such knowledge, or belief, be obtained and justified?

There are two ways in which it could be asserted that the existence of any sense-objects can be established. They are by sense-perception, and the other is inference from sense-perception. I know of the existence of the book now because I see it. It is part of my sense experience. Now, I am supposed to know of the other side of the moon, which has never been seen, by inference from all the various actual astronomical observations, and so I make an inference from things actually experienced. And, it is also a possible experience. I could fly out to the moon, and go around to the dark side to have a sense experience.

1. It should be obvious that we cannot have sense-perception of things that are not sense-perceptions. For, to have a sense-perception of something that is not a sense-perception would be a contradiction. Both sense-perception and not sense-perception. And, if we were to have a sense-perception, it would be experienced by some finite mind, and so it would not be existing without some finite mind experiencing it.

2. Now inference seems like the most likely candidate for coming to the belief of things existing unexperienced by some finite mind. So how can I pass, by inference, from a particular fact of experiencing the book now, when it is being experienced, to the different particular fact of the existence of the book yesterday or tomorrow, when no finite mind is experiencing it? Now the onus of proof is on those that say things somethings exist when some finite mind is not experiencing. It would be up to them to show how they passed from what is sense-perception to something that is not a sense-perception. So one may sit back and wait for them to show how they came to such a proposition, which means to support their proposition.And Bertrand Russell had something to say about this, “Belief in the existence of things outside of my own biography must, from the standpoint of theoretical logic, be regarded as a prejudice, not as a well-grounded theory.”

Now, such an inference to things existing when some finite mind is not experiencing it cannot be done by an inductive inference. Induction works from what has been observed, what we have experienced, to what will be experienced, but which is currently unexperienced. For example, every morning I have found that the sun rises in the east. This I have experienced. From this, based on an inductive inference, I come to the conclusion that tomorrow morning, which is unexperienced, that I will experience the sun rising in the east.

Now inductive reasoning cannot help me here, since I have never experienced something existing unexperienced, since that is just a contradiction, and not possible. In other words, there is no case where it has been observed to be true that an experienced object continues to exist when is not being experienced. It is, by hypothesis, its existence when not being experienced, cannot be observed. And induction is also about generalization from observed facts, but there is not one single case of an unexperineced existence, since that is a contradiction, which can be the basis of the generalization that entities continue to exist when one is experiencing them.

Now, since induction is ruled out, we are left with deductive inferences. Deduction depends on consistency. Thus, when given P→Q, we can only prove Q if P is admitted. From P→Q , all that can be admitted is that P and not Q are inconsistent with each other, and we cannot hold both propositions, P and not Q, together, though we can hold to P and not Q as separate propositions. Thus, to assert that the book exists now when I am experiencing it, to the existence of the book when no one is experiencing it, together is an internally inconsistent proposition. But, there is no inconsistency when these two propositions are asserted separately. In other words, deductive inferences do not allow us to reach that because things exist when some finite mind is experiencing them, to things existing when no finite mind is experiencing them, is deductively invalid.

Thus we find that we have no sense-perception to support the realist position, and that we cannot use inferences to the realist position, since deduction and induction do not help us.

Now it is not proved that because we cannot make an inference to the existence of things existing unexperienced by some finite mind, that they do not exist unexperienced. For such a way of reasoning would be fallacious. However, because it has not been proved there does not exist things unexperienced, that it shows that they do exist unperceived. For to argue either way would be an argument from ignorance. An argument from ignorance carries these two forms, which is both, respectively, positive and negative.

Positive:If a proposition has not been disproven, then it cannot be considered false and must therefore be considered true.
Negative:If a proposition has not been proven, then it cannot be considered true and must therefore be considered false.

Now that we have no sense-perception that can allow us to assert such a proposition, and we cannot make an inference to such a proposition, we ought not to believe it. For we ought not to believe that there is a unicorn on Mars because we have no sense-perception of it, and we have no inference to reach such a conclusion. It does not mean that it does exist or does not exist, but that we ought not to believe it. Thus, the unicorn are like the existence of things existing unperceived by some mind. And from a logical point of view, the onus of proof is on the realist that asserts that things exist unperceived by some finite mind, and until they keep to their burden, we ought not to believe what they say.

Now some might come to use the causal processes to make an inference to things existing when not experienced. The whole argument of causal sequences continuing on when not perceived is  begging the question. For you are still assuming that things that happen when perceived continue on when not perceived, and that is the thing in question.  If  someone, say, John stays in the room as he builds a fire and keeps it going till it is done, which takes about an hour, he observes a certain sequences of the phenomena. The sequence follows like this, m, n, o, p, q, r,  s, t, u. Now if John leaves the room after it starts, and returns half an hour, he will see it at sequence q. If John leaves the room after that sequences and returns to it in a quarter-hour, he will get the sense experience of s. And on this goes. John will thus ‘infer’ that m,n,o, & p have occurred in his absence and that of any other mind. However, the only way this inference can be made is with the belief that things go on in his absence, or as if he were there. John cannot infer the conclusion of things going on unperceived as they do when perceived, because of his belief in uniform causal sequences rests on belief in the general belief in continuity of nature, i.e. continued occurrence of events when he is not perceiving them. He has to first come to the belief in continued existence when no one is perceiving things before he can believe in uniform causal sequence when not being perceived. Thus, he cannot logically make the inference that he does.

So, like we cannot perceived unexperienced things, so too we cannot perceive unexperienced processes and laws. Also, like we cannot infer from anything which we experience to the existence of unexperienced things, so we cannot infer from any processes and laws we experience the existence of unexperienced processes and laws. And our belief in the processes of causality that happens when we experience it, to it going on when we do not experience it, is based on the belief in the continued existence of things when we are not experiencing it, and so begs the question.

Now some have made some distinction between sense-data and our awareness of sense-data. It is said that Green is not the same as awareness of Green. This is said because of us comparing different sense-data. Say that I experience a green sense-datum and a blue sense-datum. We find that there is some common element between them, and this is awareness. Thus, awareness must be different from green, since awareness also exists in the case of blue, and that awareness is not green. Thus, it is thought that Green exists when we are not aware of Green. But this is not the case.

Whenever we come across green, we find that we have awareness of green, but we also find that green and awareness of green are not the same thing. Thus, there is a difference between X and Y. Yet when we find X, we also find Y. Thus, to say that X goes on existing when Y is not there, is not supported by sense-perception, and now we are stuck with inference, and we come to the same problems. We do not find sense-perception to show that green exists when there is no awareness of green, and we cannot make an inference to it either. Thus, such a distinction between green and awareness of green does not allow us to believe that things exist when unexperienced by some finite mind.

Now, since experience and inferences cannot lead us to the realist position, and all the arguments to such a conclusion are fallacious, we ought not to believe it. However, some would say that it is probably true, and thus we ought to believe it. However, all such reasoning would have to be based on the same types of arguments, and they all come to rely on fallacious reasoning. Also, since both options are possible, we find that they have an equal probability, and one does not have a greater probability than another. Heads and tails both have the same probability. Also, we cannot present an argument to support the realist position, and if we could then we could just as well use the critique presented her to show that it could be even more probable that they do not exist when not experienced by some finite mind.

Now some mind resort to it being an animal faith a primitive belief, or an instinctive belief. To invoke such things to support the realist proposition is to throw up ones hands in defeat, and to admit that one has no rational reasons to support their beliefs. It becomes an unreasoned belief, and has nothing to rely on by fiat. It is to be one who files for bankruptcy, and gets ride of rational grounds for their belief.

So, throughout, we find that the logically correct position is this. We cannot have any reason whatsoever to believe that unexperienced entities exist. We cannot prove that they do not exist. The onus of proof is on those who assert that they do exist unexperienced. We have found that experience does not attest to the existence of unexperienced things, and we have no way of inference to reach it (without fallacious reasoning), and thus we find that it is impossible to reach such a conclusion. Thus, we ought not to believe it, if we are to be rational, like we do not believe in a unicorn on Mars.

But, the way around this is to be explained as it being a mental construction, or a fiction. It is a pure assumption which we invent to simplify our view of the world.

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