geoff

"You still have yet to establish that abstract entities exist independently of human cognitive activity."

This quote, taken from Wizardry's response, seems to be a common request (objection?) from other respondents to my OP. I shall try to answer it.

I cannot prove that the laws of logic are necessary. I can only offer a few thoughts about why I believe they are so, and why the opposite idea (that they are contingent) is absurd. Let me note at the outset that I do think the laws of logic (and other abstract objects) are contingent upon intellectual activity, but not human intellectual activity. They have the character of necessity, which would make it plausible to believe they depend upon an unlimited mind (which the human mind is not). So, now the "few thoughts." If we deny the necessity of the laws of identity, excluded middle, and contradiction, our conversation (thoughts, actions) reduce to meaninglessness. Why? Because all meaningful interaction is based upon these laws (whether spider, human, or AI). In short, if we hold that the laws of logic are contingent upon human intellectual activity, then they become contingent and, because of this status, potentially changeable. (I don't think I need to hold to the strong version of the argument I advocated before that included the idea that abstract objects exist in a Platonic sense.)

I am very concerned with Vorkosigan's wrangling over my choice of the word "necessary" and his insistence that "'necessary' is a subjective term." How can that which has to be in all possible worlds be subjective? How can the laws of identity, exluded middle and contradiction be subjective? If Vorkosigan is saying that we cannot (at least at our present station in life) tease out all that these laws mean, fine. If he is saying that the laws of logic do not yield knowledge that borders on certainty, no disagreement there. But if what he says is to be taken to mean that the laws of logic could be different than what they are, that is absurd (I am trying to be charitable in my interpretation of his statement but this is the only interpretation I think that jibes with it).

Some of you noted that "logic" is, essentially, a means by which we symbolically represent the necessary relationships between certain ideas (e.g., if it is raining outside, the ground will be wet.). Who would disagree with that? I certainly don't. As I stated above, I am not going to insist on the Platonic existence of abstract objects. My argument doesn't stand or fall on that assertion. But I do stand by the notion that abstract objects are necessary (i.e., couldn't be any other way)and depend upon intellectual activity of the sort that could only be done by an unlimited, necessary mind. Put another way, it is more plausible that theism can account for abstract objects than N&E. Finally, I am not arguing that evolution is untrue. I am arguing that it is implausible for N&E to account for abstract objects.

[ May 28, 2002: Message edited by: geoff ]

[ May 28, 2002: Message edited by: geoff ]</p>

Synaesthesia

It is important to note that naturalistic theories do not have to account for abstract 'objects' as such. What must be explained is the human conception of abstract objects and the nature of functional relationships. Notice that I seperate the human conception of abstract objects, and the objective properties of relations in general.

An unlimited mind clearly is overkill. All that is required to form a conception of an abstract object is a representational system capable of distinguishing between an instatation and a general pattern. In otherwords, we ourselves are more than capable of creating abstractions. Evolutionary accounts (memetic and genetic) provide an explanation of where our capabilities come from and have significantly more explanatory surplus than theories requiring infinite complexity.

Kyle Smyth

Basically you are saying that the human mind cannot create the laws of logic, and the laws of logic are vital, so there must be a god? If that is a proper summation then I am still confused as to where you get the idea that the human mind cannot think of the laws of logic. We know the laws of logic, otherwise we could not think logically. So either we were given the laws of logic as a gift form our creator, or we created them. Deducing that the laws of logic are necessary for logical thought does not prove either scenario. You have to prove that logical thought and abstracts are necessary components of the universe. An abstract is NOTHING more then a thought. The laws of logic are nothing more then collected thoughts. Absent the concept of the number 4 the universe would not 'pfffffft---pop' into non-existence. Nothing about abstracts and logical thought are necessary to anything other then our perception of the universe. I agree totally that the idea of a universe viewed without the aid of abstracts and logic to be utterly mind boggling, but the idea of a universe without cognitive thought is not so hard to fathom. Logic does not require observation to be logical; the logic of the universe does not need to be seen to function. You need to prove that absent cognitive thought there would be no universe, no creation, no possible evolution. Simply stating that logic is vital and thus requires an unlimited mind is not sufficient. I can (and will) counter claim that logic is not vital to the universe, and thus it does not require an unlimited mind, and in fact is nothing more then a byproduct of social evolution, which is in turn nothing more then a byproduct of natural evolution.

[ May 28, 2002: Message edited by: Kyle Smyth ]</p>

geoff

Again, if we hold that the laws of logic depend upon human intellectual activity, then they become contingent and, because of this status, potentially changeable. This contradicts the notion that the laws of logic are necessary (i.e., could not be any other way).

geoff

From Kyle Smith:

"You have to prove that logical thought and abstracts are necessary components of the universe. An abstract is NOTHING more then a thought. Absent the concept of the number 4 the universe would not 'pfffffft---pop' into non-existence. Nothing about abstracts and logical thought are necessary to anything other then our perception of the universe. "

My reply:

I am not saying that the existence of the universe depends upon the existence of abstract entities, specifically the laws of logic. How can this be construed from what I've written? To set the record straight, I am saying that the laws of logic are necessary (i.e., true in all possible worlds, could not be any other way) and thus cannot depend upon that which is contingent. N&E affirms the existence of only that which is physical or supervenient upon the physical. The universe then is contingent (i.e., might not have existed). But the laws of logic are the result of intellectual activity. How can N&E reconcile these two contradictory ideas?

From Synaesthesia:

"We ourselves are more than capable of creating abstractions."

My reply:

Contingent (i.e., unnecessary) beings cannot create that which is necessary (if you take issue with the idea that the laws of logic, e.g., are necessary, please refer to my previous posts which show the absurdity of believing otherwise.). Cognitive sciences can show us how our minds grasp, appropriate, and use laws of logic and other abstract objects but it cannot show how the necessary laws of logic depend upon human (i.e., contingent) thought.

[ May 29, 2002: Message edited by: geoff ]

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Vorkosigan

The contradiction you identify is not a problem for us. I can't recall you demonstrating that the laws of logic could not be any other way.

Vorkosigan

Jack the Bodiless

What is "materialism" in this context?

Since Einstein, there has been no "materialism" in the sense commonly used. Matter and energy are interchangeable. Ultimately, there is only energy in different forms, and a framework of natural laws governing the flow and interactions of energies. Doesn't a natural law fit the definition of an "abstract entity"? We can point to phenomena acting in accordance with a natural law, but not to the law itself.

It is because of this framework of "abstract" natural laws, already included in the "materialist" Universe (therefore no need to separately derive or "account" for them), that the Universe behaves in a predictable pattern, and logic is our description of those aspects of reality that we have evolved to perceive and deal with.

For instance, according to quantum mechanics, there is no universal "Law of the Excluded Middle". A particle can simultaneously BE and BE NOT, or exist in a superposition of states. We have problems grasping this because these phenomena are not significant at the macroscopic level which our perceptions and reason evolved to cope with. Therefore logic fails us.

Kyle Smyth

The point I was trying to make was that the laws of logic are nothing more then prerequisites for human perception. The only way that the laws of logic could be 'necessary' or 'vital' is if they extended past human perception. I was under the impression that was the argument you were making.

'I am saying that the laws of logic are necessary (i.e., true in all possible worlds, could not be any other way) and thus cannot depend upon that which is contingent.'

Which gets to the point I was trying to make, that the laws of logic are determined by human thought. The logic of the universe as they appear to our senses without augmentation are simple, cause and effect (as you said, it is raining, therefore the ground will be wet), A leads to B. Of course you get more complicated systems as well, its raining (A), so the ground will be wet (B), and when the ground is wet plants grow (B=C) so when it rains plants will grow (If A=B and B=C then A=C). All that represents is a human interpretation of a system, and that's all logic is. If we are geared to think in a different manner our logic would be different, but like I said it may be unfathomable to us but it is not impossible. I have a feeling that any being that derived its system of logic form the quantum universe might have a slightly different outlook then we do. Even to the extent that I agree that it is unlikely that any other logic paradigm will be discovered that is not because the laws of logic are all that special. It just means that the universe acts consistently. The laws of logic are contingent upon the characteristic of human perception, and to that extent they are not vital. Finally it is imperative to understand that most of the laws of logic are self-referential to abstract ideas. The laws of logic describe the rules for thinking within a preset system. If you were to change the fundamental premises of that system of thinking (as I am sure would happen in the case of the aforementioned quantum being) then you would get a far different logical system with different rules. All you are arguing is that I can not perceive it, therefore it is not possible.

[ May 29, 2002: Message edited by: Kyle Smyth ]</p>

NumberTenOx

In agreement with the many posts above, I don't understand the difficulty. I always thought Plato was a little whacked.

• We perceive the ordered workings of the universe.
• We create ideal constructs to understand these workings (numbers, logic, etc.)

These constructs do have an "ideal" reality, the very place that inspired them, the material universe. You might as well ask "why are the laws of physics universal?" In a sense these constructs do have an independent reality, because they exist unchanging in the workings of the world around us.

And that, of course, is the central question of all. Why is the universe like it is, full of matter/energy and governed by the unchanging laws of physics? To assert that the human conception of these laws is ideal, and therefore has a separate reality from the universe, is orthogonal to that question.

NumberTenOx

I'm new at this, I want to try again, I'm still trying to understand Geoff's point.

The reason we perceive logical constructs to be "abstract" is because they work more than once, i.e. they work in Berlin and they work in Chicago. That seems to give them an independent existence. But really, it's the laws of physics that are universal, that work in both Berlin and Chicago, our logical constructs are just the description of that fact.