Notice:  This log copyright 1995 by Pankaj Saxena and Tom Wright. 
Reproduction without prior permission is prohibited.

All statements starting with > were made by Tom Wright <Wright>

Session Start: Fri Oct 20 23:00:47 1995

<Subetai> Today's topic is Logic: Induction and Deduction. Briefly, 
<Subetai> this is what I would like to cover:
<Subetai> 1. Definition of Logic, Induction and Deduction.
<Subetai> 2. Basis of Logic - Law of Identity and its corollaries.
<Subetai> 3. Induction: How is induction justified? What is inductive
<Subetai> knowledge? What degree of certainty does this knowledge have?
<Subetai> What happens when this knowledge expands?
<Subetai> 4. Relationship between induction and integration.
<Subetai> 5. Deduction: differences between knowledge obtained through deduction and induction.
<Subetai> 6. Flaws in modern logic.
<Subetai>  
<Subetai> Before we begin, I'd like to present some definitions:
<Subetai> Logic: the art of non-contradictory identification (of some fact
<Subetai> of reality).
<Subetai> Induction: The process of reaching general conclusions from
<Subetai> specific facts.
<Subetai> Deduction: The process of deriving specific inference(s) from
<Subetai> general truths.
<Subetai> Now I'll open the discussion by asking the first question: why is
<Subetai> my definition of logic valid? What is the basis of logic?
<Subetai>  
<Will_P> The axiom of identity implies non-contradiction: metaphysically.
<Subetai> What are the corollaries of the law of identity?
<Will_P> And all questions can be re-cast into the form: "What is _____?"
<Will_P> I'm not sure what you mean.  You need more information to draw a 
corollary, right? 
<Subetai> Okay. So logic is based on the law of identity. The law of identity 
states that A is A. Logic identifies A. Correct?
<Subetai> Will: No. A corollary is a subsidiary truth. That is, if "X" is 
true, then "Y" must be true because it is implied by "X".
<Will_P> It is the method that is based on A=A, and only a method based on 
identity can identify.
<Subetai> The law of identity has as its corollaries the laws of 
non-contradiction, and the law of the excluded middle.
<Will_P> Aren't those both the same as Identity?
<Gilles-> What's the law of the excluded middle?
<Subetai> Will: right, they're corollaries.
<Will_P> Non-Contradiction: A cannot be non-A. Excluded middle:  either a 
thing is A or it is  non-A, never both A and non-A, or neither A nor non-A.
<Subetai> Okay. So the basis of logic is identity. Things have some 
identity, and the purpose of logic is identification.
<Will_P> A better way to state the law of excluded middle is:  either a 
proposition is true or it is false.  It can never be both true and false, and 
never can be neither true nor false.  (Given the 
context of non-arbitrary statements.)
<Subetai> Does anyone have any problems with my 
definitions of inductiona and deduction?
<Subetai> -a
<Will_P> Subetai, could you repeat them?
<Subetai> I can repeat the whole thing, not parts.
<Subetai> Before we begin, I'd like to present some 
definitions:
<Subetai> Logic: the art of non-contradictory 
identification (of some fact
<Subetai> of reality).
<Subetai> Induction: The process of reaching general 
conclusions from
<Subetai> specific facts.
<Subetai> Deduction: The process of deriving 
specific inference(s) from
<Subetai> general truths.
<Subetai> Now I'll open the discussion by asking the 
first question: why is
<Subetai> my definition of logic valid? What is the 
basis of logic?
<Gilles-> Subetai: I have a question about them: 
must one induce before he deduces?
<Subetai> Gilles: I don't think so. I think one can 
deduce from both general and specific facts.
<Will_P> Gilles, in what context?
<Subetai> Anyone?
<Subetai> And if one can deduce from specific facts, 
you didn't need induction there.
<Gilles-> Will: Subetai answered my question.  
<Subetai> Any problems with my definitions?
<Subetai> Okay, then I'll move on to induction.
<Gilles-> Subetai: in that case, why is deduction 
defined as "the process of deriving specific 
inferences from general truths?"
<Gilles-> Subetai: A specific fact isn't a general 
truth, is it?
<Subetai> Gilles: That's how it's defined in most 
logic books. We should add from "specific facts 
and/or general truths".
<Subetai> Would that be okay?
<Gilles-> Subetai: Well, just to make sure, what 
would be an example of deducing from a specific 
fact?
<Subetai> Gilles: Okay. Lets say "Mary went to the 
mall this afternoon". Can you deduce from that 
that "Mary wasn't at school this afternoon"?
<Gilles-> Subetai: Yes.
<Will_P> Deduction is top-down.  Induction is 
bottom-up.
<Subetai> WillP: That's true in general.
<Subetai> Okay, moving on to the nature of 
induction:
<Subetai>  
<Subetai> Let's move on to the next question. 
Induction is the process of
<Subetai> reaching general conclusions from specific 
facts. To use a common
<Subetai> example, does the fact that the sun has 
risen in the east every
<Subetai> day of my life justify the belief that it 
will rise in the east
<Subetai> tomorrow? What do contextuality of 
knowledge and causality have
<Subetai> to do with induction?
<Subetai>  
<johnk> I need a definition of general truths. 
Specific facts when coalesced (via induction) 
form truths, right?
<Subetai> john: Yes, when integrated, they form a 
general truth.
<Subetai> Like the law of gravity.
<Subetai> Or any concept.
<Subetai>  
<johnk> So Mary's absense from school would also 
require knowledge of what constituted school's 
boundaries
<Will_P> Subetai, not until you find a causal 
mechanism.
<Subetai> john: It would require knowledge that 
school and the mall were two exclusive places.
<Subetai> mutually exclusive
<Subetai> Will: why? Were people wrong in believing 
that before gravity was discovered?
<johnk> more specific facts - aren't we building (by 
induction) general truths?
<Subetai> john: Mary's example was an example of 
deduction from a specific fact.
<Subetai> For building general truths, you do need 
induction.
<johnk> several facts
<Will_P> Subetai, I think you can say that an events 
constant recurrence is a kind of knowledge.  But 
before you can prove it is true that the sun will 
rise tomorrow, you need a causal mechanism.
<Will_P> Otherwise the argument rests on: "it has 
happened every other day".
<Gilles-> Subetai: are axioms exceptions to that?
<Subetai> Will: So you're saying that causality is 
required to prove the *necessity* of an event 
happening, while without it you are left with 
contingency?
<Subetai> Gilles: No, axioms are the broadest 
generalizations. They require induction.
<Will_P> Subetai, yes.  I think that's correct.
<Will_P> I don't think axioms even need induction.  
They are implicit in many forms of knowledge.
<Subetai> Will: Can you have no knowledge with just 
contingency? Isn't knowledge contextual?
<Ghaki> wouldn't it be arbitrary to assert that it 
might not?  you haven't seen it do otherwise.
<EricT> Will_P: But all knowledge needs induction, 
so underlying axioms are thereby induced.
<Will_P> Subetai, I'm not certain in this area.
<Subetai> Will: How can you form the concept 
"existence" without induction? Existence is an 
axiom.
<Subetai> Knowledge is contextual. Without knowing 
the cause for something, you can still have 
knowledge. This knowledge would be circumscribed:
<Subetai> (1) by the implied qualification "if no 
new fact is added".
<Subetai> (2) by the assumption that non man made 
reality has no choice. That "is is" is the same 
as "it has to be".
<Subetai> is is = it is
<Subetai> So you could say that the sun will rise in 
the east *unless* some new fact is added. The 
assumption is that reality continues to be what 
it is.
<Subetai> How's that?
<Subetai> That doesn't require knowing gravity 
(causes). Do you have knowledge there without it?
> Subetai: Of course
<Will_P> I've got an errand to run.  Brb.
<Gilles-> What do you mean by "knowing the cause for 
something"?  Because the ultimate cause for 
something is the nature of the something -- and 
the nature of the something is its attributes, 
right?  
<Subetai> Wright: So knowledge does not depend on 
knowing the cause. But without knowing the cause, 
you have contingency (i.e., contingent that 
things continue the way they have), while knowing 
causes gives you necessity.
<Subetai> sorry, that was for will, not wright
<Gilles-> Because in that case, it would be 
dangerous to try to distinguish between some 
pre-knowledge-of-cause knowledge and knowledge-of-
cause knowledge.  Am I explaining myself?
<Subetai> Gilles: I mean knowing that gravitation 
causes the earth to spin around the sun 
counterclockwise, and so the sun will rise in the 
east.
<Subetai> Gilles: I don't understand.
<Gilles-> Subetai: but that is just a wider, deeper 
knowledge -- it can't be put in a different 
category -- because you induced gravitation also.
<Subetai> Gilles: exactly. It's not a different 
category of knowledge at all.
<Subetai> Knowledge is always contextual, and you 
just have a wider context if you know about 
gravity.
<Gilles-> Subetai: The reason I brought it up was 
that Will said something about "not knowing the 
cause" of the sun rising.  Which leads me to 
believe that he would complain about not knowing 
the cause of gravity.
<Subetai> Gilles: okay. I think he was trying to 
differentiate between contingency and necessity, 
not imply that knowing about causality gives you 
a different *kind* of knowledge.
<Gilles-> Subetai: I think that type of comment 
implies some kind of desire for revelations.
<Subetai> Gilles: yes it does, if taken literally.
<Gilles-> Subetai: But what is the sense of 
differentiating between contingency and 
necessity?
<Gilles-> In this context?
<Subetai> Gilles: The sense is that with contingency 
you are ssaying: this will continue to happen if 
whatever is making it happen stays the same.
<Subetai> While with necessity you are saying that I 
know gravity makes this happen, and therefore it 
will happen because gravity is a universal law.
<Gilles-> Why wouldn't it stay the same?
<Subetai> Gilles: It would stay the same. That's 
because the assumption is that reality (non man 
made) has no choice to be other than what it is). 
That's why it's knowledge too.
<Subetai> I was arguing that you could have 
knowledge without knowing about gravity in this 
case. Will said you couldn't.
<Subetai> Can I take a break here to ask an 
unrealted question?
<Ghaki> Subetai: hey, it's your channel.  :^)
> Ghaki: Not exactly :)
<Subetai> I've noticed that many people are not 
participating. Perhaps it's because the subject 
matter is not interesting to them, but if there's 
another reason (such as the discussion's too 
technical, not technical enough, etc.), I'd like 
your comments on that later.
<Gilles-> Subetai: I'd really like to ask one more 
question.
<Subetai> Gilles: sure
<Gilles-> Subetai: what's the difference between 
knowing that the sun rises every day, and knowing 
that gravity is a universal law?  Other than the 
fact that the second is more fundamental than the 
first?
<TomR> Subetai:  I haven't done much thinking about 
logic, that's all.  I am following the discussion 
though.
<JohnGalt> Hello the channel!
<Subetai> Gilles: The difference is that in one case 
you've established the *why*.
<Subetai> Is that okay?
<Subetai> Well, while we're on induction, I'd like 
to discuss one more term: "integration".
<johnk> modelled the *why* - doesn't this make this 
knowledge also contingent?
<Subetai> What's integration?
<Subetai> john: it's contingent on reality staying 
the same, which is not the same as saying that 
whatever unknown facts cause the sun to rise in 
the east stay the same. In one case, the unknown 
fact might be a spring winding down.
<johnk> integration - the assembly of parts to form 
a whole?
> How about a definition to start out?
<Subetai> Okay. Integration is the collection of 
related facts into a unit.
<Subetai> This (as Rand says) implies more than a 
summation.
<johnk> the unit not being the aforementioned 
general truth, I presume?
<Subetai> The examples she uses are: (1) integration 
of sensations into a perception (2) The 
integration of entities into a concept.
> johnk: Integration is used in forming concepts.. 
for example
<Subetai> johnk: Could be. That's why I'm asking 
what the difference between integration and 
induction is.
<Subetai> Integration requires induction. What else?
> You integrate the many tables that you have seen 
into the concept "table"
<Will_P> re
> Welcome back, Will
<Subetai> Can the terms be substituted for each 
other?
<Ghaki> Induction is creating a new concept out of 
existing concepts (or perceived facts.)  
Integration is relating already existing concepts 
to each other.
<johnk> I guess that depends on whether general (as 
in general truth) is the same as objective
> Hmm..
<Subetai> Ghaki: What about the integration of 
specific entities into a concept? Rand used that 
term there.
> "The process of observing the facts of reality and 
of integrating them into concepts is, in essence, 
a process of induction." ITOE p. 36
<Subetai> Concept formation is induction, and that's 
a type of integration. But integration is also 
used to draw relationships among things in 
general, bot always with the purpose of forming 
concepts.
<Subetai> bot = not
<Subetai> So integration is a wider term than 
induction.
<Ghaki> ok, so induction is a subset of integration.
<Subetai> Anyone have anything to add there?
<Subetai> Okay, we're winding up our discussion. 
Let's talk about
<Subetai> deduction. Deduction is the process of 
deriving specific
<Subetai> inference(s) from general truths. Anybody 
like to add something
<Subetai> to that?
<Subetai> Gilles already pointed out that we can 
deduce from specific facts to other specific 
facts.
<Subetai> I don't know if we're on a time limit 
here. I planned the discussion for an hour. It's 
almost over, so I'll finish with some comments on 
modern logic.
<Subetai>  
<Subetai> Last item on the agenda: modern logic. 
Here's a textbook
<Subetai> definition of logic: "The major task of 
logic is to establish a
<Subetai> systematic way of deducing the logical 
consequences of a set of
<Subetai> sentences". What's wrong with this 
definition?
<Subetai>  
<Subetai> That's from _Brittanica_.
<Ghaki> it doesn't mention reality at all.
<Will_P> Subetai, it is completely disconnected from 
reality- from percepts or facts.
<Subetai> As I see it, they're reduced logic to a 
word game. The essential element of identifying 
the facts of reality is missing.
<Subetai> Will, Ghaki: Right
<Subetai>  
> Rationalism, in other words
<Subetai> Here's another item from the same book: 
"Inductive logic, as it
<Subetai> applies to logic in systems of the 20th 
century [..] is obsolete.
<Subetai> The problems earlier subsumed under 
induction are considered to
<Subetai> be concerns of the methodology of the 
natural sciences, and logic
<Subetai> is generally taken to mean deductive 
logic." This is what Rand
<Subetai> meant when she said "... if reason is to 
be destroyed, it is
<Subetai> man's integrating capacity that has to be 
destroyed." Any 
<Subetai> comments?
<Subetai> Well, that's pretty obvious. I thought I'd 
include that to show what the status quo is on 
that at schools.
<Subetai>  
<Subetai> Okay. We're at the end of tonight's 
discussion. Here's something
<Subetai> to finish with: I've seen a couple of 
discussions on Godel's
<Subetai> theorem on #AynRand recently. People have 
come on the channel
<Subetai> claiming, in essence, that logic is 
incapable of adequately
<Subetai> dealing with reality. Godel said so.
<Subetai> This is what Godel's theorem says: "Within 
any rigidly logical
<Subetai> mathematical system there are propositions 
(or questions) that
<Subetai> cannot be proved or disproved on the basis 
of the axioms within
<Subetai> that system and that, therefore, it is 
uncertain that the basic
<Subetai> axioms of arithmetic will not give rise to 
contradictions."
<Subetai> What's the problem with that?
<Subetai>  
<Will_P> Logic is nothing like that!
<Subetai> Will: why not?
<Ghaki> If I understand it correctly, that would be 
like saying you can't prove gravity by just 
saying "A is A".
<Will_P> Godel spoke of systems that were 
self-contained: disconnected from reality.
<Will_P> Logic is based on facts/axioms of reality 
and as such, a proposition which is not provable 
is arbitrary and implies no contradiction.
<Will_P> provable/disprovable.
<Subetai> Will: You mean that his criterion of a 
logical statement was whatever could be put in 
the form of a "categorical proposition", with no 
reference to whether that statement was connected 
to reality?
<Subetai> of a = for a
<Will_P> Subetai, precisely.
<Subetai> Okay, so what about the comment that the 
basic axioms of arithmetic could end up 
contradicting themselves?
<Will_P> If you apply his argument to Logic, he's 
saying that because there are arbitrary 
statements, you can know nothing.
<Will_P> They won't.  I can say that.
<Subetai> Okay. So what keeps logic non-contradictory
 is reality. There is nothing inherent in the 
methodology of logic that can create a 
non-contradictory system.
<Will_P> He'd be saying contradictions exist 
metaphysically.
<gk> Okay. So we had no argument on that. :(
*<Will_P> :)
* Wright turns the channel log off
Session Close: Sat Oct 21 00:04:44 1995