What Problem?

[merjet]

Since by DEFINITION the swan has a long neck, we may DEDUCE that all things that are swans have long necks hence they have necks.

Brilliant! Done exactly like a medieval scholastic finding an answer in a book written by Aristotle. Next see if you can find a definition of swan with anus it to deduce 'all swans have an anus'.

Edited November 29, 2010 by Merlin Jetton

[BaalChatzaf]

Since by DEFINITION the swan has a long neck, we may DEDUCE that all things that are swans have long necks hence they have necks.

Brilliant! Done exactly like a medieval scholastic finding an answer in a book written by Aristotle. Next see if you can find a definition of swan with anus it to deduce 'all swans have an anus'.

No. I am simply observing that words like "swan" have definitions (sometimes).

I could easily imagine a bird who mouth is in its midsection (no neck there). But that bird would not be a swan.

In the real world, spiders have their mouths and eyes embedded in there bulky part of their body. They don't need necks apparently.

Another way of coming at this is to notice that vertibrates are essentially elongated cylinders with various organs attached to the sides through tubes. One end of the cylinder is the head. The other end is the arse. So to speak. Whatever else swans are they belong to the order of veribrates. They have spines. They also have lungs and guts layed out along the line of the spine (more or less). So they need an input end (call that the head if you wish) and the other end for dumping out waste. All of this follows from the fact that such critters are air-breather, water drinkers and food eaters.

Now there are living critters who don't breath air with specialized organs, or eat food and they also have no necks. We call them plants. (exclude odd balls like the Venus fly trap for this discussion).

Ba'al Chatzaf

[merjet]

Another way of coming at this is to notice that vertibrates are essentially elongated cylinders with various organs attached to the sides through tubes. One end of the cylinder is the head. The other end is the arse. So to speak. Whatever else swans are they belong to the order of veribrates. They have spines. They also have lungs and guts layed out along the line of the spine (more or less). So they need an input end (call that the head if you wish) and the other end for dumping out waste. All of this follows from the fact that such critters are air-breather, water drinkers and food eaters.

Congratulations. You tried to say why all swans have necks -- Why all S is P -- as opposed to 'all swans have necks because "neck" is in a dictionary definition of "swan", which reverses cause and effect.

[merjet]

For those of you who have read Harriman's book - The Logical Leap -, please offer an opinion.

First look at this presentation of an essay by Isaac Asimov:

It is about seven and a half minutes long.

Did Harriman say what needed to be said better than Assimov?

Thank you.

Ba'al Chatzaf

That's like asking me to compare bananas and camels, since Asimov's topic was not induction.

[BaalChatzaf]

For those of you who have read Harriman's book - The Logical Leap -, please offer an opinion.

First look at this presentation of an essay by Isaac Asimov:

It is about seven and a half minutes long.

Did Harriman say what needed to be said better than Assimov?

Thank you.

Ba'al Chatzaf

That's like asking me to compare bananas and camels, since Asimov's topic was not induction.

It was about scientific theories which are arrived at by induction (in part). All of physics starts with what comes through the senses.

Ba'al Chatzaf

[Ellen Stuttle]

Re-entering, starting with Ted's post #66

Well, that's a position you have come to by induction, isn't it? Some inductions fail, so all inductions are suspect?

If there's no method which guarantees reaching a true conclusion inductively, then, yes, all inductions are suspect.

That's either begging the question, or banal, or both. Bob went from saying that there exist specific invalid inductions (ones which I point out have obviously invalid methods) to saying that all induction is invalid. You chose an even easier path, the tautology that if no induction is guaranteed all are suspect. In any case, each of you is relying on the induced premise that there are inductions which fail. But people also make mistakes in their deductions. What of it?

Ted,

What I'm trying to find out from you is how you're defining the term "valid." I understand, and have tried to explain (and have myself been using), Ba'al's meaning. Best I can tell, what you mean (and what Merlin means) is simply "legitimate to use." Ba'al doesn't argue that induction isn't legitimate to use, only that there's no form of inductive reasoning which, if properly followed and proceeds from true premises, guarantees true results.

Are you disagreeing? If so, is it because you're using a different definition of "valid" than Ba'al is using? Or are you saying that there is some inductive form of argument from true premises which guarantees, if correctly followed, the truth of the conclusion?

(As I read Peikoff/Harriman, they're trying, though failing, to argue the latter in claiming that induction is "valid.")

Please state how you're defining "valid."

Ellen

[merjet]

valid (adj.)

1. having legal force; properly executed and binding under the law

2. well-grounded on principles or evidence; able to withstand criticism or objection, as an argument; sound

3. effective, effectual, cogent, etc.

4. Rare: robust; strong; healthy

5. Logic: correctly derived or inferred according to the rules of logic

http://www.yourdictionary.com/valid

It is proper in my view to describe an inductive argument as "valid" meaning #2 and #5. Note that #5 does not say "deductive logic". If somebody else like Ba'al or Ellen chooses to use the word "valid" and mean only #5 with "deductive" inserted, and use "invalid" to mean the contrary, then the result will simply be an argument over word meanings. If Ba'al or Ellen refuses to say that a inductive argument is "valid", then he/she should not say an inductive argument is "invalid" either. That an inductive argument is deductively invalid is banal.

What term would Ba'al or Ellen be willing to attribute to "all swans have necks"? Invoking the old "all swans are white" to imply that every inductive argument is invalid is self-refuting. Refuting an inductive generalization should require a relevant and specific counterexample.

[Guyau]

.

Ellen,

Your distinction in #81 between validity meaning “legitimate to use” and validity meaning an argument form in which it is impossible for the premises to be true and the conclusion false is important to keep track of.

Concerning #21 and #43: There is intimate connection between validation by experience and validation by deductive inference. (Similarly, with talk of proof, as when we say we have proven a coin is gold or that a defendant is guilty.) The principles of correct deduction, as well as the concepts of the logical constants and logical quantification must arise from experience of the world and language acquisition (language acquisition not isolated from successful operations in the world). Although it is fine in a logic course to simply stick to the elements of the discipline, and although it is fine to presume the common ground of logical principles between parties in a dispute over anything, the further question of where the logical principles and concepts come from is surely a sensible one. It was broached, for example, in Leonard Peikoff’s 1985 “Aristotle’s Intuitive Induction” in connection with the principle of non-contradiction.

Whether one wants to develop Aristotle’s form of induction called intuitive (also called abstractive)* or to look to some other cognitive process from experience to principles of (deductive) logic, it would seem that norms of logic must derive from wider norms of cognition.

Concerning Objectivist conception of validation:*

Take a look at Chapter 5, “The Theory of Meaning,” in Blanshard’s Reason and Analysis (1962). See especially his discussion of Peirce (5.5–5.6) and Schlick (5.20) and Ayer (5.36–5.37). Compare Blanshard’s treatment of verificationist theories of meaning with Peikoff’s treatment of them in his history of philosophy lectures (in the second series, modern philosophy).

Rand and Peikoff opposed verificationism and replaced it with validationism. An idea whose relationship to reality is established by perceptual evidence or by induction or deduction upon such evidence, they called validated. Naturally, validations of ideas can have various degrees of quality. Moreover, validationism can be posed in varieties of strength parallel its verificationist cousins. The variety validation-in-principle entails: an idea that in principle cannot have its relationship to reality established by perceptual evidence and logical inference is meaningless.

The parallel of the Rand-Peikoff validationism to verificationism holds only so far. There is no counterpart to the verificationist view that truth should be defined in terms of the verifiable. Truth is more primitive than validation for Rand and for Peikoff.

I have not traced the development internal to Objectivism of the specially defined validation idea (OPAR 8), but it fits well with Rand's 1967 definition of knowledge as "a mental grasp of the fact(s) of reality, reached either by perceptual observation or by a process of reason based on perceptual observation" (ITOE 35).

* I have not received the Harriman book yet; perhaps further elucidation is included there.

[BaalChatzaf]

valid (adj.)

1. having legal force; properly executed and binding under the law

2. well-grounded on principles or evidence; able to withstand criticism or objection, as an argument; sound

3. effective, effectual, cogent, etc.

4. Rare: robust; strong; healthy

5. Logic: correctly derived or inferred according to the rules of logic

http://www.yourdictionary.com/valid

It is proper in my view to describe an inductive argument as "valid" meaning #2 and #5. Note that #5 does not say "deductive logic". If somebody else like Ba'al or Ellen chooses to use the word "valid" and mean only #5 with "deductive" inserted, and use "invalid" to mean the contrary, then the result will simply be an argument over word meanings. If Ba'al or Ellen refuses to say that a inductive argument is "valid", then he/she should not say an inductive argument is "invalid" either. That an inductive argument is deductively invalid is banal.

What term would Ba'al or Ellen be willing to attribute to "all swans have necks"? Invoking the old "all swans are white" to imply that every inductive argument is invalid is self-refuting. Refuting an inductive generalization should require a relevant and specific counterexample.

the word "valid" has a specific meaning with regard to first order predicate logic which is a deductive system. A proof (or deduction) is valid provided each step is taken according the one of the rules of natural deduction.

See: http://en.wikipedia.org/wiki/Natural_deduction

for the details.

All validity guarantees is that the conclusion followed from the premises according to the inference rules. Now we introduce the notion of soundness. IF the premises happen to be true AND the conclusion follows from the premises validly (according to the inference rules) THEN the conclusion is true. The degree of guarantee equals the truth of the principle of non-contradiction. If one starts with false premises then the conclusion might be true or might be false. It depends on the function which maps first order formulas into the set (TRUE, FALSE). Starting with false premises does not guarantee the true (or falsity) of the conclusion. All bets are off.

A word about non-contradiction. Why does the principle of non-contradiction have such a privileged place? Because in an inconsistent system EVERYTHING is TRUE, or put another way, the distinction between TRUE and FALSE is lost. That is why we absolutely insist that our mathematics and scientific systems be consistent. (Note: An inconsistent system is one which has a theorem of the form P & -P). One inconsistency ruins the system.

Validity is an adjective that applies to the form of the argument. Arguments are valid or invalid. True, False does not apply here.

In Aristotelian Categorical Logic there are 15 valid syllogistic argument forms (without existential import) or 19 valid syllogistic forms (with existential import). Any complex argument in Aristotelian Logic (called sorites) can be composed by chaining valid syllogisms together, the conclusion of a prior element is the premise of a later element.

In First Order Predicate Logic one uses the rules of Natural Deduction (referred to prior) or equivalent valid inference rules.

It turns out that First Order Predicate Logic is sufficient to ground the proof occurring in 99 percent of informal mathematical proofs in various subject areas. That is why First Order Logic is popular, because it covers nearly all the mathematical ground.

Anyway. To get to the nitty gritty. Validity is one thing. Truth is another and Soundness is Validity + Truth. In general we are interested in sound arguments to get us from where we are to where we ain't. Unsound derivations in formal logic are exercises in rule manipulation and have little or no practical use.

There are logical systems called paraconsistent logics which purport to handle contradictions. Such logical systems have no place in normal mathematical applications. See http://en.wikipedia.org/wiki/Paraconsistent_logic for some of the details.

Ba'al Chatzaf

[merjet]

http://rebirthofreason.com/Articles/Jetton/The_Problem_of_Induction.shtml

is an article by yours truly.

[peterdjones]

The "Problem" of Induction? What problem? Any valid inference scheme has the following characteristic: the truth value of the conclusion must be greater than or equal to the truth value of the premises. Assumption: true greater than false.

Induction is clearly not valid. Why? Because it is possible to start with true premises and end up with a false conclusion. The classical example as that of the white swans. A gazillion white swans seen and at some point non non-white swans seen. Inductive conclusion: all swans are white. But one fine day a dark swan is observed showing that the conclusion is false. Induction does not always produce true conclusion from true premises or more precisely, induction does not always produce true general statements from a true conjunction of particular statements.

As I asked: What problem?

Ba'al Chatzaf

y,

You seem to be saying the solution is to just abandon induction. But Rand can't, since many of her dearly held principles are

based on generalisations of observation. To put it another way, if you reject the apriori, as she does, and you reject

induction as well, you are not going to have much of an epistemology left.

[BaalChatzaf]

You seem to be saying the solution is to just abandon induction. But Rand can't, since many of her dearly held principles are

based on generalisations of observation. To put it another way, if you reject the apriori, as she does, and you reject

induction as well, you are not going to have much of an epistemology left.

We can't abandon induction. It is the only way to go from a limited set of particulars to an open ended generalization. What we have to abandon is the notion that induction guarantees correct inferences. Sometimes it produced correct inferences, sometimes not. But no guarantees like deduction.

Learning by trial and error is a form of induction. It is essential to our survival.

Ba'al Chatzaf