This paradox is fun to think about. Remember though that thinking of perception (like the threshold of hearing a noise) differs for people. SO defining what is out there in discrete terms will not result in the same answer for everyone. I think you are approaching this from a subjective angle for or less, which is how I see it — Gregory

Yes, to me it is fun to think about. I believe it's a good example of how our brain works in dealing with specifics (one grain of sand), and generalities (a pile of sand).

Try this approach: Start by imagining a single grain of sand. Now, add another grain of sand. We can easily imagine two grains of sand that are close together (not far apart). Add another grain - it's also easy to imagine three grains of sand that are close together. Now - when we try to add another grain - such that we would have four grains of sand - it gets harder to imagine. Do you visualize all four grains at the same time, or do you visualize two groups of two? The brain automatically tries to regroup numbers greater than three into new "visual" groups - hence; two groups of two. Adding more grains changes the image again, A group of five, or more, grains causes the brain to sub-divide the grains again into new distinct groups with a maximum of three grains each until one gets to three groups of three - or nine grains total. However, the brain simply can't visualize nine grains of sand in a group - only three groups of three. Try it yourself.

As a result of this simple "thought experiment" one could conclude that the maximum number of grains of sand (where one can visualize the individual grains) is nine. Any number of grains greater than nine results in an "image" of a pile - not individual grains. We have knowledge (math) that we can add more grains to the pile - or take grains away - but it's the image that will not change in our minds, not the actual number.

Ancient philosophers didn't have the knowledge of brain mechanics that we do today so they didn't think in terms of how the brain actually counts. However, they did understand the mechanics (math) of adding, or subtracting, grains of sand to a pile. They were just not able to "visualize" what was happening by adding or subtracting mentally. I believe the Sorites Paradox is a mental paradox - not a physical one.

Where does the paradox lie in the image of a pile of sand? — jkg20

https://www.bing.com/search?q=paradox%20definition&pc=cosp&ptag=G6C24A11441EEDE3&form=CONMHP&conlogo=CT3210127 . The paradox is not the first thing you see. However, it is there.

That generalised image must mean the smallest pile is 4 grains - three as a triangular base and one perched on top. Take that away an only have a clump or group of grains? Move the grains gradually apart and at some point they are not even a group? — apokrisis

There was a group of Germans that studied "visual grouping" back during the early 1900's. The study was called "Gestalt". https://en.wikipedia.org/wiki/Gestalt_psychology . How the mind groups information including visual information is very interesting.

The first question gets the sorites paradox going. The second question is nonsensical. — jkg20

The paradox is in the image - not in the actual number of grains of sand. There is no paradox in the actual number of grains of sand in the pile. The paradox happens when we try to visualize the "change" in the pile, in our mind, when the acual number of grains is changed physically. There are many things we do not see even though they may happen in plain sight. A classic example is" the "gorilla in the room". http://theinvisiblegorilla.com/gorilla_experiment.html .

Is the "shape" a paradox?

I suppose it boils down to having multiple images for a "pile" of sand and removing grains of sand one by one simply switches between one of these images of a pile and another image of a pile, the result being the pile remains a pile despite grains of sand being taken away. — TheMadFool

The problem, as stated in the sorites paradox, is not being able to determine at what point a group of grains of sand becomes a pile. Whatever number one may choose that constitutes an image of when a group of grains becomes a pile - then one grain added, or subtracted, should "change" that image. But, it doesn't. The "image" of the pile remains the same whether a grain is added, or subtracted. It's not the math - it's the way our brain works in creating the image.

Thanks for the response. It appears you are on the right track. There are many similar examples of the sorites paradox. They are easily missed though because our minds are occupied by the "single" groupings - as your example shows.

It's easy to understand the pile can be change by adding, or subtracting, grains of sand - but it's the "images" in our brain that doesn't change simply by adding or subtracting a single grain. We just don't have that many images of piles of sand such that we can visualize a "different" pile to account for every single grain. Sometimes the paradox can appear complex, but the principle of this solution is simple.

I believe you are correct..in philosophy. Philosophy is not bound by the regidity of "science" - so, yes I believe you could make a convincing argument in your favor.

Some interesting things happen when we think of a pile of sand. Example: "Sorites Paradox" - https://en.wikipedia.org/wiki/Sorites_paradox . A grain of sand has certain properties we recognize. A pile of sand also has certain properties we can recognize. But, we can't visualize the two groups of properties at the same time - resulting in a so-called paradox. In this example the "pile" of sand could also be called an emergent property. This example could also be listed a solution to the paradox.

There seems to be many ways to express objects, or actions, as emergent. Scientist seem to shy away from the study of emergence because it seems too much like magic. However, that criteria may be a draw to other people. Being familiar with emergence helps to eliminate some of the spookiness from the subject. I can imagine Neils Bohr must have had similar thoughts - when trying to convince Einstine about his thoughts on the structure of the atom.

Emergence is a lot like hunting and finding Easter Eggs. Sometimes, one can even find the so-called "prize egg". My opinion, (not even a theory), is: the "hidden-until-discovered" properties defining emergence is how the mind works (more neuroscience than physic). The brain is limited in the number of "properties" that can be assililated into what we define as an object, or idea. This limiting factor keeps us from seeing what would normally seem obvious - until it jumps-out-at-us (discovery). Then we try to explain why we didn't see it before by coining words like "emergence". If one really searches, they can discover all kinds of emergent properties in many fields of study. As a result, I believe "emergence" is a very interesting field of study in itself.

Absolutely. Math is more exact. But, I believe math separates science and philosophy. To me, philosophy is a better tool (than math) in trying to visualize wave-particle duality - (at this time). But, the foundations of philosophy need to change - especially in the light of quantum mechanics. That's what I'm attempting to do. We have a lot more information to work with now - than they did 2,000 years ago. Want to help?

It is not wrong to be confused by this. But that is the current model, Einstein called it wave particle duality. — Paul S

Thanks for the reply! The other comments over the past 24 hours are also interesting as well. Hopefully, you and the others will read this response.

One of the items missed by those that have looked at the "wave-particle duality" is how we define either one - that is: the particle, or the wave. The definition is acording to the "properties" (or actually a specific small group of properties. The brain uses electrochemical formation as inputs that define these properties. Each item, of our "focus", has these specific propties that have developed from habit over time.

When we "think" of different objects/items our brain visualizes a new set of properties that defines each new object. However, the brain can only focus on one set of properties at any specific time. We can easily change the focus, but our brain can still only focus on one set at a time. That creates the difficulty of trying to visualize a duality - such as the wave-particle duality. Another famous example is "The Rubin Vase": https://en.wikipedia.org/wiki/Rubin_vase . One can visualize the faces, or the vase, but not both at the same time.

https://www.researchgate.net/publication/330723666_Emergent_Quantum_Mechanics_David_Bohm_Centennial_Perspectives#:~:text=These%20properties%20are%20closely%20related%20to%20Emergent%20Quantum,zone%20between%20classical%20%28Hamiltonian%29%20mechanics%20and%20its%20quantization.

If we don't know the "who, or the how" - we may already be programmed by the machines.

"Existence" itself is an assumption. All existence, that we bieve we can prove, is based on assumptions. We assume things exist but threre's no way to prove it to the self - which is also created by the brain - which we can't prove. "I think, therefore I am", is bogus.

Can one emphathize with their own brain? First, the brain has to create the "self" that does the introspection. The self that the brain creates is an emergent property. There is nothing else there. It's like the forest, and trees. The forest does not exist - only the trees. The forest exists only in the mind - also as an emergent property. One must understand "Levels" to understand the reasoning. Levels is the hierarchy of property groupings. Properties are the brains creation of electrochemical impulses that fools the brain ito believing it has perceived.

Good take Paul. There is too great a difference between the technology we have to put man on the moon, and the technology needed to put man on mars. It's not just how long we can stay in space - we've done that for years at a time - but, not outside the Van Allen belts. Deep Space will kill humans within just a few months and our technology is not advanced enough to protect people over longer periods. It seems our scientist are overlooking that factor, but I don't know why.

Good question. Is there really a difference between man and what man programmed?

The "swamp" programmed it.

Maybe it is? The notion that something can "be" property only emerges with the subjective viewpoint. One object cannot "own" another object. So maybe the notion that an object can have a property is an anthropomophism. Is the property an aspect of the object, or is the object an instantiation of the property? — Pantagruel

A property in philosophy is defined as a description - not something that is owned: Property (philosophy)
From Wikipedia
In logic and philosophy (especially metaphysics), a property is a characteristic of an object; a red object is said to have the property of redness. The property may be considered a form of object in its own right, able to possess other properties.A property, however, differs from individual objects in that it may be instantiated, and often in more than one thing. It differs from the logical/mathematical concept of class by not having any concept of extensionality, and from the philosophical concept of class in that a property is considered to be distinct from the objects which possess it. Understanding how different individual entities (or particulars) can in some sense have some of the same properties is the basis of the problem of universals.

Guess it depends on how one wishes to classify property. — Mww

Yes. Classifying Properties is difficult. The philosopher David Hume defined some of those problems in his writings. Generally, properties is defined as a piece of land - but that's not what we are defining here. I do believe the subject is worthy of study/discussion though.

There is a paradoxical line of thought here though in my view. We emerge from the beginning of the universe and yet we define emergence from our very own admittedly? emergent nature. In essence, emergence is a very human concept, because we can perceive what we call emergence, and that the universe itself could appear that way to us.

What is also interesting is that as we go further back to the origin, we see that our emergence is essentially a fluke. Our reality as we perceive it is more akin to rare once off mutation spawned from something possibly beyond time itself. — Paul S

Good thinking Paul! You may also want to consider how we perceive anything (visual) to even be able to ask the question of emergence. Even our thoughts about an object are "emergent" within the brain. That kind of thinking can go all the way back to Plato's Cave. Personally, I don't think we've spent enough time in science on the subject of emergence. It still seems too vague for science to have a real interest - which leaves it up to philosophers.

I have a problem trying to understand "all" of anything.

How do you determine what something is from all angles?

Bcause of perspective, a truth can be false.

"Maybe this is a cheap way out, but I'd say that whatever fits your intuitions best is the most reliable "starting point" for "normal life" questions." I agree. It seems we don't have enough information to go deeper in the rabbit hole.

When the apple is envisioned, the seeds are not included in the vision, and when the seeds are envisioned, the apple is not a part of the vision. The mind does not envision both at the same time. That is why we can conclude no two objects can occupy the same space at the same time. We envision either the seed, or the apple, but not both at the same time. A famous example is: the Rubin Vase. One can visualize the faces, or the vase, but not at the same time: https://en.wikipedia.org/wiki/Rubin_vase .

It is still a part of the apple, and occupies some of the same space.

I guess some folks see philosophy itself as being rdiculous nonsense.

"It's starting to sound like this little intraversable [newly minted] rabbit hole is going to require a fair bit of camouflage to disguise the nature of its many contradictions." Contradictions may be illusions in our mind. Example: "Sorites Paradox": https://en.wikipedia.org/wiki/Sorites_paradox . The mind does not envision the concept that the pile of sand is made up of grains of sand because we think in property-groups. The group of properties that define the grain of sand is not the same properties that define a pile of sand - therefore the mind does not recognize both at the same time. Take another example: The "Rubin Vase":https://www.bing.com/search?q=Rubin%20Vase&pc=cosp&ptag=G6C9A11441EEDE3&form=CONBDF&conlogo=CT3210127 . The mind cannot reconize the face, and the vases, at the same time. Our minds tell us what is "real", and what isn't. I believe we just need to understand more of how our minds work - not just accept what we believe to be true.

"What point of logic are we attempting to advance here?" Thank you! That is exactly what I was attempting to advance. Typically, our vision is very myopic - which has led us up to making statements such as; "no two objects can occupy the same space at the same time". You've just demonstrated there are many such instances where different objects occupy the same space at the same time. I define that phenomenon as "Levels". Stated simply, levels is the "hierarchy" of property groupings. The brain can only deal with a few (limited) properties at the same time, so the "objects" created by our brains are also very limited. We can visualize the apple; but we cannot visualize the apple, (and the seed), at the same time. The apple, and the seed, are two different property groupings.The brain cannot visualize two property-groupings at the same time, so it will attempt to group them toether such as we have learned in Gestalt. The rules of Gestalt then governs what we "see".

"So it's really a matter of how you define the boundaries of an object." Speaking in generalities, I don't believe the boundaries of objects influenced what science has said about two objects occupying the same space at the same time. In some circumstances what you said is correct but, generally I don't believe boundaries are part of how we generally define objects.

Me too!

I really like this post Jack. It gives a short summary of how our "knowledge" is aligned to our emotion - not just our senses.

It was quoted from the article.

Thanks for the note.

You're right. Perception of reality is often just spoken of as reality, but thinking about it I believe you're closer to being right.

Vaugueness and Lazyness are both properties that can support philosopher.

Is a vague philosopher a lazy philosopher?