Notes on "Induction in Physics and Philosophy"

[Grames]

7 hours ago, P@NTH3ON said:

Is Peikoff basically saying that his inductive proof of causality that he goes over in a course called “An Inductive Approach to Philosophy” is wrong?

He is saying that it is no proof.  Causality is axiomatic, and axioms are not proven.

His  given motivation for this correction was to combat rationalism.  Rationalism is word-thinking rather than concept-thinking (my description).

Vertical integration is when one relates a higher level concept to a lower level concept, possibly through additional concepts in between them, by demonstrating the hierarchical dependency of one upon the other.

Horizontal integration is performed between two concepts that are not hierarchically dependent upon each other.  They can be related through some other concept(s) are are hierarchically prior to both, and they should not contradict each other directly or indirectly.

[StrictlyLogical]

2 hours ago, Grames said:

Vertical integration is when one relates a higher level concept to a lower level concept, possibly through additional concepts in between them, by demonstrating the hierarchical dependency of one upon the other.

Horizontal integration is performed between two concepts that are not hierarchically dependent upon each other.  They can be related through some other concept(s) are are hierarchically prior to both, and they should not contradict each other directly or indirectly.

Fascinating, from your description it would seem that performing a horizontal integration of A and B (with hierarchically prior C) is the same as performing two vertical integrations (A and C well as B and C).

Is this correct?

If not, could you describe how integrating A and B with use of hierarchically prior C, is the different from vertically integrating A and C as well as vertically integrating B and C?

[user16]

@Grames

Quote

Horizontal integration is performed between two concepts that are not hierarchically dependent upon each other.  They can be related through some other concept(s) are are hierarchically prior to both, and they should not contradict each other directly or indirectly.

If they are horizontally related through some other concepts that are hierarchically prior to both, how can causality and identity be horizontally relatable?  What concept is there that is “hierarchically prior” to identity?  I thought identity was the most fundamental concept anyone can form.  There shouldn’t be anything hierarchically prior to “identity” right?

[Grames]

6 hours ago, P@NTH3ON said:

@Grames

If they are horizontally related through some other concepts that are hierarchically prior to both, how can causality and identity be horizontally relatable?  

Remember that question you started with. the about Peikoff’s so-called (at the time) proof of induction?  It is no proof but it does serve as a nifty horizontal integration. 

Higher level concepts can be related and integrated with two vertical integrations to something in common, but that is not applicable to axioms and first level concepts.  Horizontal integration also refers to checking for noncontradiction.  Noncontradiction always applies and is the chief means by which we become suspicious of perceptual illusions.  

Technically existence comes before identity.  But the placement of existence as prior to identity (the “primacy of existence principle” is not derived or proven, because it too is part of the mechanics that make logic and proof possible.

[Grames]

10 hours ago, StrictlyLogical said:

Fascinating, from your description it would seem that performing a horizontal integration of A and B (with hierarchically prior C) is the same as performing two vertical integrations (A and C well as B and C).

Is this correct?

If not, could you describe how integrating A and B with use of hierarchically prior C, is the different from vertically integrating A and C as well as vertically integrating B and C?

Well, no.  The point of doing a horizontal integration is to make your knowledge a noncontradictory unity.  The two reductions don’t themselves rule out the possibility of a contradiction.  It is good to be able to reduce a concept, and is a requirement of a well formed concept, but it could still be in contradiction to some other concept.  

Consider the recent memewar entrant “Islam is right about women”.  This is an attempt to provoke horizontal integration in the reader.  It is quite possible for some feminist to able to identify Islam without actually knowing all of the attributes of the religion.  It is possible to have a concept but have it ordered around nonessentials.  To feminists, Islam and muslims are simply a non-white and non-christian ally in the fight against the white christian patriarchal power structure of America and the whole western tradition.  As one of the Abrahamic religions it is in fact patriarchal also, vehemently so when compared to Christianity.  The feminist concept of Islam is apparently no more than that group of people who claim to be muslims, and a feminist would reduce the concept to its referents and stop.  Horizontal integration is need to provoke the feminist into realizing this level of concept formation about Islam is inadequate.

[StrictlyLogical]

6 hours ago, Grames said:

The two reductions don’t themselves rule out the possibility of a contradiction.  It is good to be able to reduce a concept, and is a requirement of a well formed concept, but it could still be in contradiction to some other concept.

Not sure if I was clear… the point of my question was to determine whether any additional “logic” was happening in a horizontal integration, i.e. something which could uniquely be identified as part of a horizontal integration and not a vertical one.  Finding a contradiction while engaging in a “horizontal integration” or a two connected “vertical integrations” seem also to be the same exercise.

I am missing something about the difference between the following

1)   H(A,B)

and

2)   V(A,C) AND V(B,C)

 

6 hours ago, Grames said:

Consider the recent memewar entrant “Islam is right about women”.  This is an attempt to provoke horizontal integration in the reader.  It is quite possible for some feminist to able to identify Islam without actually knowing all of the attributes of the religion.  It is possible to have a concept but have it ordered around nonessentials.  To feminists, Islam and muslims are simply a non-white and non-christian ally in the fight against the white christian patriarchal power structure of America and the whole western tradition.  As one of the Abrahamic religions it is in fact patriarchal also, vehemently so when compared to Christianity.  The feminist concept of Islam is apparently no more than that group of people who claim to be muslims, and a feminist would reduce the concept to its referents and stop.  Horizontal integration is need to provoke the feminist into realizing this level of concept formation about Islam is inadequate.

This seems to describe a simple failure of any kind of rational integration, 1) or 2), by butchering the concepts as you describe.  I’m interested in the techniques of integration on properly well formed concepts, and in particular the “vertical” and “horizontal” aspects.

Your description of horizontal integration is:

19 hours ago, Grames said:

Horizontal integration is performed between two concepts that are not hierarchically dependent upon each other.  They can be related through some other concept(s) are are hierarchically prior to both, and they should not contradict each other directly or indirectly.

It seems that the crux of horizontal integration is finding the x1…xn which are related to and hierarchically prior to both.  It appears as though H(A,B) is a combination of V(A, x1)…AND V(A,xn) AND V(B, x1)…AND V(B, xn) where x1…xn are all the facts which are related to both A and B and are hierarchically prior to both.

So I guess to be more succinct, is it true that:

H(A,B) =  V(A,x1)… AND V(A, xn) AND V(B,x1)… AND V(B, xn)

or is H something more than this?

[Grames]

11 hours ago, StrictlyLogical said:

or is H something more than this?

Horizontal integration should be performed with more than just one other concept.  Ideally it would be done with every other concept one held.  But who has time for that?  So this is a task that is never fully completed, it can only be partially completed.  Still, some of those pairwise selections H(A,B) would be better than others, better in being not trivial and potentially revealing obscured contradictions.

Possibly some heuristic could be invented for selecting two different concepts (or given one, find another)  that would have the most potentially fruitful result.  I would think something about the concepts being “far apart” would be one good metric to employ.

11 hours ago, StrictlyLogical said:

I am missing something about the difference between the following

1)   H(A,B)

and

2)   V(A,C) AND V(B,C)

 

Your 2) V(A,C) AND V(B,C) is merely one way to go about performing H(A,B). I don’t know of other methods and don’t want to commit to ruling out the possibility of there being others.  So I can’t actually answer this question.

[user16]

@Grames

Quote

Remember that question you started with. the about Peikoff’s so-called (at the time) proof of induction?  It is no proof but it does serve as a nifty horizontal integration. 

Higher level concepts can be related and integrated with two vertical integrations to something in common, but that is not applicable to axioms and first level concepts. 

I think I get what you’re saying I just want to affirm a couple things.  I noticed you stated “proof of induction.”  I think you might have made a typo here.  What I was referring to was Peikoff’s “inductive proof of causality.”  My understanding is (or was) that Peikoff was not “proving induction,” he was using induction to induce (prove) causality.  This was my previous understanding of what was happening.  And now from you I’m understanding that it was not a proof of causality but a nifty horizontal integration of “identity” and “causality.”  Is this an accurate understanding of what you are saying?

And one more thing, you mentioned “not applicable to axioms and first level concepts.”  So that’s exactly what I was wondering about horizontally integrating “identity” with “causality.”  If the way that you horizontally integrate concepts is by vertically integrating to something in common, I was just saying you can’t do that with “identity” and “causality” because you can’t get beneath them.  So I was thinking that there is no way to horizontally integrate “causality” and “identity” but again you’re saying that in that older lecture I referred to about induction, peikoff presents another way to horizontally integrate “causality” and “identity,” that doesnt involve vertical integration to something in common, right?

[Grames]

22 hours ago, P@NTH3ON said:

I think I get what you’re saying I just want to affirm a couple things.  I noticed you stated “proof of induction.”  I think you might have made a typo here.  What I was referring to was Peikoff’s “inductive proof of causality.”  My understanding is (or was) that Peikoff was not “proving induction,” he was using induction to induce (prove) causality.  This was my previous understanding of what was happening.  And now from you I’m understanding that it was not a proof of causality but a nifty horizontal integration of “identity” and “causality.”  Is this an accurate understanding of what you are saying?

Yes, that was a kind of typo.  Peikoff’s “inductive proof of causality” is the subject under discussion.  Yes, and by the way proof is also a method of integration because what is proved is related to other knowledge.

 

22 hours ago, P@NTH3ON said:

And one more thing, you mentioned “not applicable to axioms and first level concepts.”  So that’s exactly what I was wondering about horizontally integrating “identity” with “causality.”  If the way that you horizontally integrate concepts is by vertically integrating to something in common, I was just saying you can’t do that with “identity” and “causality” because you can’t get beneath them.  So I was thinking that there is no way to horizontally integrate “causality” and “identity” but again you’re saying that in that older lecture I referred to about induction, peikoff presents another way to horizontally integrate “causality” and “identity,” that doesnt involve vertical integration to something in common, right?

Yes, the fact that you can contemplate the axioms and relate them to each other is a form of integration even though Peikoff would deny there is proof or derivation or deduction happening.   The order of Existence, Identity, and Consciousness has methodological (epistemological) significance in order to affirm Primacy of Existence and deny Primacy of Consciousness, but each is a mentally abstracted facet of existence which exhibits all three simultaneously. 

Causality merely appears to come “after” Identity in that it is easier to understand or imagine some object as static and then add the dynamics but in reality everything that exists is always acting (even if slowly).  Understanding Identity as static omits the greater part of an existent’s Identity, how it acts.

[ReasonFirst]

@Grames

I have question about what exactly you mean when you state “hierarchically prior?”  If you vertically integrate the concept “cat” to the concept “animal” and the concept “dog” to the concept “animal,” is this an example of horizontally integrating the concept “cat” with the concept “dog?”  I wasn’t sure if the term “hierarchically prior” is interchangeable with “higher level.”  In the example I just gave, the concept “animal” is a higher level concept than “dog” or “cat”  but I don’t know if it is “hierarchically prior.” I think if “animal” was a “hierarchically prior” concept to “dog” and “cat,” the mental process I verbally described above would be an example of horizontal integration, but I just wanted to ask you be sure?

[Boydstun]

Grames was posting steadily through last February. Then there was a three-week gap before his most recent post, which was last March. I don’t know his actual name. Perhaps he has deceased. Does anyone know him or anything about him beyond what he shared publicly (that he was male and lived in PA)?

[dream_weaver]

He last visited on October 4, available via his profile page. 

There is not a mechanism in place for what you ask, @Boydstun. 

[Grames]

On 12/19/2020 at 4:44 PM, ReasonFirst said:

@Grames

I have question about what exactly you mean when you state “hierarchically prior?”  If you vertically integrate the concept “cat” to the concept “animal” and the concept “dog” to the concept “animal,” is this an example of horizontally integrating the concept “cat” with the concept “dog?”  I wasn’t sure if the term “hierarchically prior” is interchangeable with “higher level.”  In the example I just gave, the concept “animal” is a higher level concept than “dog” or “cat”  but I don’t know if it is “hierarchically prior.” I think if “animal” was a “hierarchically prior” concept to “dog” and “cat,” the mental process I verbally described above would be an example of horizontal integration, but I just wanted to ask you be sure?

 

'Hierarchically prior" is used to draw attention to the ‘level’ or degree of abstraction in a concept.

Lower level concepts are hierarchically prior to higher level concepts because they must exist before they are integrated into the higher level concept.  But given the concepts of cat, dog, bird, and fish, the concept animal could be formed from any two of them, the others being added later.  So ‘must exist’ or ‘logical necessity’ is inaccurate, and ‘chronologically prior’ would also be wrong. “Hierarchically prior” establishes the relationship between two concepts without claiming too much: that one concept is lower level than and a referent of the higher level concept.

Your cat and dog example is one way of horizontally integrating them.  Any general statement relating cats and dogs would also be a horizontal integration such as “Dogs like to chase cats.”