Another way to express my doubt

Merleau-Ponty's analysis of cognition might suggest the following.

The cognitive process naturally ascribes " inter-actional extension" to every focal concept along a time or space dimension. E.g. the abstract noun "house" cognitively triggers a possible plethora of potential relationships of the conceiver with that class of objects we call "house" including possession, residence, possible destruction, existence before or after our own etc,etc, only some of which will have significance in real life contexts. But with the concept of "infinity", there are no "real life" boundary conditions operating to delimit cognitive speculation.

This implies that the concept of "infinity" is generally not a member of the set of functional or pragmatic cognitive concepts, except perhaps in the special case of the mathematics of numbers. In that sense, talking about "an infinity of objects" is a category mistake as defined by Gilbert Ryle. He might say questions about "an infinity of objects" is as meaningless as questions about " the location of the university" whilst wandering around the colleges and libraries of Oxford".

Now add to that angle the non-dualist thought that all concepts logically require a conceiver, then the concept of "infinity" only remains extant whilst conceivers do, therein you have another nail in the coffin.

And there also must be a Universe where you've won the Lottery. And there's another Universe where you've (coincidentally) won every lottery every played.

Now if you could only switch your consciousness to whichever Universe you chose, it would be like being able to recreate any aspect of "reality" you chose. You could pick and choose any Universe with any combination of attributes.

EDIT TIMED OUT

(Add the word precise) "......the precise location of the university......"

And at this precise moment are being nailed to a cross. Being boiled in oil. Are clinging to the north face of a mountain by your finger ends or going through a messy divorce which your counsel says will likely clean you out. Over and over again for ever and ever.

What's wrong with infinity if the earth is not a unique special case is that it drives us mad and that can only be avoided by using the word casually as a means of displaying intellectual chutzpah. Or not using it at all as some have found is the best bet.

There's a price to pay for thinking the earth is not the centre of the universe. The most intelligent sex would never dream of paying it.

Fres you might have to reword this post in language more suitable to the Average Clod (me). However your observation,



…...has a dualittic quality rife with possible contradictions and paradox in conflict with the general idea that nothing is entirely anything while everything is partly something else

In other words I don’t see anything special about numbers

My only poblem with 'infinity' is that it is a concept which is quite impossible for the human mind -- yours and mine included -- to visualize or otherwise conceive in a sensory way. (Much the same is true for the concept of 'nothing'.) However, it's quite easy to posit mathematically and, unless we're going to be very subjective about it, relying strictly on our senses for acceptable evidence, I see no reason to deny the reality of the condition.

The reasons numbers are a special case are

1.They have no cognitive extension in time or space. They are blank place markers for the concept of objects which do.

2. There are at least three different types of infinity regarding numbers. (google Paul Cohen), one of which depends on the choice of axioms for the foundations of mathematics.

The reasons numbers are a special case are

Ok but it’s hard for the Average Clod (me) to see that quality as restricted purely to numbers

Doubtless true but how does it impact upon the discussion

....because you said....


I am arguing that the mathematical concept(s) of infinity cannot be used as a model for what we call "physical objects", any more than the concept of "speed" say can be used to model what we call "countries".

Sorry Fres but this Average Clod doesn’t follow you. I’d assume an infinite Universe to have an infinite number of physical objects

No. On a non-dualistic basis all "physical objects"require an observer. The two are are co-existent and co-extensive. i.e, neither has meaningful ontological independence.And since observer's cannot actually "see"(in their mind's eye")an "infinity" of objects any more than they can "see" nothing (a point raised by Lustig above), such extremes are psychological sleights of hand. i,e, They require the vision of an observer "counting forever", or "seeing nothing". Only an immortal metaphysical god would qualify as such an observer.

Another way to express my doubt

i take comfort from the teachings of the most reverend p. heaton

"i was about to write a song
about the fear and the doubt
but my pen ran out"

Nah sorry Fres, you leave the Average Clod (me) out in the cold

Okay...so you are not familiar with non-dualism. If you consider just one well known fact that a frog in a tank will starve to death even though surrounded by what we call "dead flies", because the frog's perceptual apparatus cannot "recognize " them, then this might explain to you the idea that "existence" is relative to specific physiology, and that we are merely "selectively blind frogs" of another type. In simplistic terms "things require a thinger" and vice versa.

To the contrary I am its champion: “Nothing is entirely anything while everything is partly something else"

No sorry Fres you’ll have to restate that in terms of the Typical Dumbhead (me)

The point is that perception is active and limited by physiology and need. There is no"external object" impinging on our senses. We evoke such objectivity from the phenomena we experience from our side of our interaction with what is external to us. Segmentation of what we call "reality" is species specific and culture specific, i.e. we humans report the presence of "objects" through the culturally acquired spectacles of a common language.

Does a bird see "a tree" or merely experience "potential perchness"?.....
Does an ant see "a tree" or experience "its universe" ?.....
Do humans experience "the universe" or "the tree of another entity" ?......

Fres does that somehow detract from the reality of a rock

The general word/concept "rock" gives an expectation of a physical relationship, that is all....no specific picture, color, size etc. It is a particular interactive flow which identifies a particular rock. The word is just a an element in reporting that flow to ourself or others. Without observers/interactors/language users "rock" would be meaningless.