19 votes
Accepted

Why is a set with one element distinct from the element itself?

In computing, there are data models (such as the XPath data model used for XML) in which an item and a singleton collection containing that item are treated as indistinguishable. You can build a ...
user avatar
18 votes

Why is a set with one element distinct from the element itself?

One reason why this is true is because there is such a thing as the empty set - the set with no elements at all. Consider a set X that contains only the empty set, and nothing else. How many elements ...
user avatar
8 votes

Why is a set with one element distinct from the element itself?

You may consider a collection as a container: Apparently a thing included in a container is different from the thing without container. Aside: Set theory provides operations to handle sets (= ...
user avatar
  • 20.5k
8 votes

Why is a set with one element distinct from the element itself?

Why do we need a zero when it's conceptually the same as nothing? Because zero, as a number, has very different properties from being nothing at all. The reasoning is similar about the empty set ...
user avatar
8 votes

How does one determine the boundary of an object?

It's a pragmatic thing more than a linguistic thing. If you want to go to the store, you think about your car If your car won't drive, you think about what part of it is at fault: engine, ...
user avatar
  • 13.5k
7 votes

What are the philosophical solutions to "ship of Theseus" problem of identity?

The Ship of Theseus is one of the more illuminating thought problems in philosophy, and it having been around for something like 2500 years indicates how insightful the early Greek philosophers were. ...
user avatar
  • 4,297
5 votes

Why is a set with one element distinct from the element itself?

They are distinct because a set is something different than most elements you can put into it. Sets and elements of sets usually are distinct categories or types of things (an element might be an ...
user avatar
  • 892
4 votes

Why are there no Computer Algebra Systems designed to import known mathematical identities/theorems?

What you're looking for is not a computer algebra system, but a proof assistant, such as Mizar, Coq, or Agda. Proof assistants are designed for the formalization of mathematical proofs in any field of ...
user avatar
  • 6,267
4 votes
Accepted

Can you think a teleporter kills the 'real' you, and also be a physicalist?

"Can you think a teleporter kills the 'real' you, and also be a physicalist?" If the description you provided of Parfit's thought experiment is accurate, then the answer is, 'Yes'. You said, ...
user avatar
4 votes

How does one determine the boundary of an object?

Disclaimer: concepts from my last book, I do Systems research. This is related to the Systems Theory. The object is the counterpart of the subject, being both the members of an interaction. An ...
user avatar
  • 4,377
4 votes

Why is a set with one element distinct from the element itself?

Try ordering water from a restaurant without a container. The container serves a purpose. In set theory, it introduces the notation of the set, and without sets, set theory wouldn't be very manageable;...
user avatar
  • 9,853
3 votes

When does something cease to exist?

In the example of the chair, the chair ceases to exist when its component parts no longer serve the human purpose for which the chair was made. Aristotle found four causes are necessary before change ...
user avatar
  • 4,640
3 votes

When does something cease to exist?

IMO this is nothing more than a question about how we define words. If we have a definition of ‘chair’ and something stops meeting that definition then it’s no longer a chair. If we named a group of ...
user avatar
  • 457
3 votes

How does one determine the boundary of an object?

I think it’s largely a linguistic thing, since the object/objects is/are what they are however we describe them. A more intriguing question (for me anyway) is that if you dismantle a Rubik cube into ...
user avatar
  • 457
3 votes

Personal Identity Dilemma

Punishment, as we see it, is a legal issue, and legality doesn't concern how one thinks and remembers, only what one has done, and the original Jack was the one to commit the crime, not Mark. So Jack ...
user avatar
2 votes

? as a logical connective

This was a misprint of the pdf. I checked other pdfs of the text and it the law of identity reads "it is necessary that a implies a" in the first case. If you've got the same rendering of ...
user avatar
2 votes
Accepted

Can an Inalienable Object be Possessed by two People?

TLDR: I don't think inalienable things can be owned at all. Inalienable means "incapable of being alienated, surrendered, or transferred" (source). This matches the legal concept of ...
user avatar
  • 2,872
2 votes

How does one determine the boundary of an object?

Short Answer It depends on your metaphysical presuppositions. Philosophers have wildly different ideas on how to determine what a thing is. Pragmatically, one can resort to picking something up and ...
user avatar
  • 9,853
2 votes

Can the copy or clone of something be a different, separate and independent entity?

At the point you copy something, the copy is an entity in its own right and while it may be identical to the original at that point, their paths will diverge from that point onwards. It is unwise to ...
user avatar
  • 457
2 votes

Why is a set with one element distinct from the element itself?

Plural quantification touches on the intuition you seem (in my opinion, so correct me if I'm wrong) to be having, here. E.g.: This is that the quantifier ∃R is a plural quantifier (and would thus be ...
user avatar
2 votes

When does something cease to exist?

Suppose to light the chair on fire, and it burns, and it turns into ashes. I think the easiest way to understand that philosophically is to not try to draw an infinitely precise line between existing ...
user avatar
  • 300
2 votes

What are the philosophical solutions to "ship of Theseus" problem of identity?

It comes down to definitions of words. If we say that the ship is the collection of atoms that it’s made of then replacing Aunty part of it means that the ship is divided into different parts that we ...
user avatar
  • 457
2 votes

How does one determine the boundary of an object?

The obvious thing is that there is no clear boundary. The case of living organisms in this discussion is particularly interesting. I am Peter, a material "object", in a broader sense. But ...
user avatar
2 votes

How does one determine the boundary of an object?

As a physicist, and from that perspective only, the question is arbitrary. Within a system, in physics, we often 'draw' imagined dotted lines around parts of that system and regard them as ...
user avatar
  • 21
2 votes

When does something cease to exist?

You can make it as complicated as you wish, but it simply depends on your definition of "exist" and of the object you are considering. Define that and you have your answer. Mind you event, ...
user avatar
2 votes

Why is a set with one element distinct from the element itself?

in the same vein as some answers above: Lets take a set theory, most set theories are endowed with an axiom of comprehension/ specification (1). Essentially, this axiom schema allows us to move ...
user avatar
1 vote

When does something cease to exist?

Simply speaking the move (from existence) to a non-existence state is happening when the object stops interacting with the environment. So in order to answer this question you have do define "...
user avatar
1 vote

Does the self change iff there is a change in knowledge?

When we sleep can our self sleep...?...sleep holding on to our ego tightly...? Can you say your self changes if there is a change in knowledge? The soul is usually called the Self. If you like ...
user avatar
  • 2,972
1 vote

What are the philosophical solutions to "ship of Theseus" problem of identity?

"No man ever steps in the same river twice, for it's not the same river and he's not the same man." Heraclitus (apparently) As @Frog suggests it is a matter of the meaning of words, and in ...
user avatar
1 vote

What are the philosophical solutions to "ship of Theseus" problem of identity?

Suppose Alfred owns a ship moored in the port of Honfleur in France. Suppose Alfred has enough money to pay for repairs to be carried out every day so that a bit of the ship is replaced every day and ...
user avatar
  • 3,525

Only top scored, non community-wiki answers of a minimum length are eligible