Continuous Properties of Identity



In this essay, I will prove that in order to couple our commonsense notion of identity with the strict philosophical notion of identity there must be a specific interpretation of the philosophical notion of identity.  The interpretation comes from a distinction between two kinds of properties of an individual- changeable and unchangeable.  A changeable property is anything that can be proven to be contingent to an individual.  An unchangeable property is anything that is necessary to an individual.  The latter will prove to be the correct interpretation of a property under the philosophical notion of identity so that it can be coupled with our commonsense notion of identity.

The Puzzle

In order for something to be identical to something else it must be uniquely identical to that other thing.  To clarify, if A is identical to B, then A is uniquely related to B; and only A and B share this relation.  It is important to separate the philosophical idea of identity from the broader, commonsensical idea of identity.  The philosophical idea would logically determine from the definition above that only one thing exists.  That is, A and B are the same thing.  The commonsensical idea may assume that A and B are still two completely separate things that happen to be identical.  An example of this would be identical twins.  A paradox, or puzzle, of identity does not arise from the commonsensical definition.  Therefore, the focus is primarily on the philosophical one.

The focus on identity in this paper will be taken from the principle of “the indiscernibility of the identical,” which states: If A is identical with B, then A and B have exactly the same properties (Perry, 784).  The problem that this particular definition poses to identity is that when the concept of linear time is taken as a property of an individual it follows that this property is ever changing.  More specifically, if it is assumed that time is in a constant state of progression, never stopping, then an individual thing can never be identical to itself from the previous instant.  For example, A exists at t1 and has the property of being at/in/of t1.  Time progresses and it is now t2.  A is now existing in t2 and no longer has the property of t1.  Thus, according to the principle of “the indiscernibility of the identical”, A is not the same individual as it was one t-moment ago.  It would then follow that a person is not the same person day to day, hour to hour, minute to minute and so on.  With the problem now clearly expressed, why is this a problem worth solving and to whom?  The answer is anyone who believes that they are the same individual thing that they were when they woke up this morning, were five years ago, or were when they read the previous sentence.  This “problem of identity” completely undercuts our commonsense notion of identity.  Therefore, the goal of this paper is to bridge the gap between the commonsense notion of identity with the principle of “the indiscernibility of the identical”, while not significantly changing the definitions of either.

Possible Solutions

The most apparent problem is in the conception of time as a property.  The principle of the indiscernibility of the identical, tacitly, forces an individual to individualize itself by its properties.  From this, most would agree that time is an important property of an individual.  After all, it is a property that we use to discern individuals from others in everyday life.  For example, when someone says, “I thought I saw you around the water fountain around lunch time.  Was that you?”, and you say, “No, it couldn’t have been me because I wasn’t at school around lunch time.”  This illustrates the application of time as a property.  But, time as a necessary property of an individual is an assumption made by the philosophical view.  Further examination will need to take place in order for this assumption to be taken seriously.  If time can prove to be a worthwhile property of an individual, or even a property that needs to hold in order to determine an individual, then there is some serious work that needs to be done in order to couple it with the philosophical view.  But, if it cannot, then the solution to the puzzle will just be a dismissal of time as a property that is necessary to an individual, because it has no effect on an individual’s identity.  The solution may be found through the application of time as a property.

Is it possible to imagine a world in which no time exists?  The answer is yes and there are two solutions to what that world is.  This world can either be a constant or steady universe in which the “idea” of time just simply exists.  It is what theoretical physicist would call a B-theory of time.  An easy way to imagine it is as the entire universe is a block or chunk that exists while everything “spins” about inside of it.  There is no temporal movement within it.  No temporal movement should be understood as time does not move as our commonsense would tell us it does.  That is, in a linear, or number line like motion with no ability to regress, only the ability to progress.  This world could have a god outside of it which gave it being, but that is irrelevant to the topic at hand.  The second theory of time would be that the only world that exists is in the present.  That means that we cannot ever refer to a previous instant because it does not exist anymore.  More specifically, the present-state theory would only allow for us, strictly speaking, to talk about “right now”, but we could never to this.  By the time we got done talking about “now”, “now” would have already passed out of existence.  The implausibility of the second idea is obviously apparent.  The former may be able to disprove time as existing necessarily.  Let us parallel it with ours that we are presently in.  It holds all the same scientific laws and is exactly similar in all ways, except no intelligent life exists.  This assertion is important because it could be possible that time is only a property that exists when you assume that humans live in the world.  To clarify, take a circle, square, triangle, or any geometric shape.  They all have certain necessary properties that distinguish them from other individual shapes and keep them identical to themselves.  Humans do not ascribe these properties to them they just inherently have them.  We may give the properties names such as: “four-sided”, “four right-angles”, and “180 degrees”, but we cannot say that we ascribe these inherent properties.  Furthermore, we ascribe time as a property of our world as we ascribe hot or cold to something.  A fire is not hot to itself it is only hot to us or anything else that is not as hot as it.  The property of hot or cold would not exist if humans did not ascribe it to help us better understand our world. Time is just that.  As Hume thought, we say something came before something else in cause and effect relationships to help us better understand what is taking place in front of us.  Time should be thought of just as Hume and Kant believed that we as humans bring these properties into existence through the way in which we perceive the world.  Therefore, in a steady universe, time would not apply if humans were taken out of it.  The universe would simply be in that everlasting state with everything “spinning” about inside of it.  To clarify, if one is logically permitted to assert that time is just a property that we ascribe, and the universe would be the same without the ascription of it, then we could still uphold the principle of “the indiscernibility of the identical” by dismissing the property of time.  Time is just a misrepresentation of what the principle is speaking to when it says, “property”.  The interpretation of the word “property” in the definition of the principle of “the indiscernibility of the identical” should be interpreted as necessary properties of an individual i.e. properties that hold in all possible worlds/universes, for example, the aforementioned right-angle of a square.

Therefore, the only properties that should be taken into account when discussing “the indiscernibility of the individual” are the necessary ones not the contingent ones.  If contingent properties are considered when assessing if an individual is the same individual, then it is possible to constantly be changing a contingent property of an individual and, thus, constantly be changing that individual.  Surely, though, a reliable principle would not be guilty of this.  Thus, “property” should be interpreted as only those properties that are necessary to an individual when using this principle in assessment of an individual.

Although this solution solves the problem of time and the principle of “the indiscernibility of the identical”, it is unable to solve the problem that time poses to the commonsense notion of identity.  The reason for this is because our commonsense notion of time is that it is linear and something that necessarily exists even without us.  This conception would be completely opposite from the potentially acceptable idea of time that is needed in order to avoid the problems in the philosophical view of the individual that was previously stated.  More specifically, if we uphold commonsense and trust it, then we cannot say that it is wrong and our view of the world needs to change.  Commonsense tells us that we do not need to do that.  It is commonsense for a reason i.e. we have some sort of internally trust in it.  Therefore, the solution of re-evaluating time as a property of an individual would go against what it means to have commonsense, and that is not the goal of the paper.  A unification of the philosophical view and the commonsensical view is the only solution the paradox.

The Next Solution

A successful solution may be found in what kind of distinction can be made by analyzing what types of properties exist.  There are all sorts of properties that exist in our world.  Person-hood, hot, green, round, and big are examples of what we think are all different properties from each other.  However, it is possible to show that there is really only one distinction that needs to be made when categorizing properties.  That is, there are properties that are unchangeable and there are properties that are changeable.

A changeable property should be thought of as any property that is contingent on something else.  This has a very broad scope.  This “something” could be another property, human, world, law of science, or an individual.  Let us take an easy idea of a changeable property to help grasp this move.  For example, hair on an individual is an easily changed property.  It is often cut by people every three to four weeks.  This “cutting” is a changing of a previous property of that individual.  Painting one’s house is also an example of a changing of a “changeable” property.  Changeable properties are ones that are contingent to something else.  In these examples the hair is contingent on there being a person and the paint is contingent to the house.  It is important to note also that the hair is not contingent to the hair being there because this is a necessary and quite trivial truth.

Now that we have a clear idea of what a “changeable” property is, we should see if it can satisfy our criteria of identity.  With respect to commonsense, it can be done.  When a changeable property of an individual is changed we would never say that that person is a new individual.  If Bobby got a hair cut and I see him previous to that and then after, I would not say Bobby is a different individual.  That is, Bobby is a different Bobby.  I would say that he is still the same individual just with a different property of hair.  Therefore, this distinction of “changeable” would give no problems to our commonsense idea of identity.  In fact, it basically plays right into the notion of commonsense, and it is probably a foundational idea for where this commonsense idea of identity comes from.

The second criterion, upholding the principle of “the indiscernibility of the identical”, does not fare too well.  The principle states that an individual must “have exactly the same properties” if it is to be the same individual.  If we take “changeable” properties to apply to this, we find that the individual is not the same as the previous one, even if that individual actually is the same person—as in the “hair cut” example.  Therefore, interpreting “property” as being “changeable” fails to satisfy the second criterion.

Although the notion of “changeable properties” does not satisfy the second criterion an enlightening point can be drawn from this.  To interpret a “property” as “changeable” under this criterion would prove to be inherently flawed.  The individual must keep “exactly the same properties” in order for it to be the same individual.  And, if that is the case they cannot be allowed to change if we are to satisfy it.  The properties under the interpretation of the principle of “the indiscernibility of the identical” must be “unchangeable”.  If they are, then it will satisfy the second criterion very easily.  If an example of an “unchangeable” property can be given and supported and it can satisfy the criteria, then it can be shown how it is possible to solve the puzzle of identity.

Solving the Puzzle

A property must be shown to be “unchangeable” if it is to have any foundation for its application to the two criteria.  An “unchangeable” property should be thought of as one that is necessary to an individual and cannot be shown to be contingent at all to anything other than itself.  There are some properties that often come to mind when we are talking about them as “necessary to an individual”.  Properties such as: personhood to a person, extension to a physical object, or the efficacious property of a cause.  These would all seem like plausible properties that, if were changed, would change the individual into another individual.  Moreover, if they were changed, then that individual would not be itself anymore.  For example, to say that a cause is still a cause if it lost its efficacious property would prove that it cannot be a cause anymore.   It could still be something, though.  This something, whatever it is would still “be”; and that something/individual could be shown to be the same individual even if it lost all its properties except one.  That property is existence.  Existence is the only unchangeable property of an individual which keeps it from changing into a different individual.  If you were to change an individual’s existence, then it would cease to exist; and no longer be capable of being a different individual.  Therefore, existence is the only “unchangeable” property of an individual.


The problem, or paradox, of identity is now solved by showing how the criteria can be satisfied by applying our new notion of existence as a foundation for why we know we are the same person that woke up this morning to who is reading this sentence right now.  We understand that we existed then and we exist now.  Therefore, we are the same individuals.  A possible objection to this point would be to object to how we know we exist.  But, as Descartes showed “I think, therefore I am” is an a priori truth about existence.  Thus, it would follow that if an individual is capable of affirming its existence at any time, then it can affirm itself to be the same individual that exists at the present moment.  A possible objection to this point would be that an individual that does not think would never be able to affirm its existence.  To this, I would agree, because it is irrelevant for a non-thinking thing to be able to affirm its existence.  This is true because “being able to affirm” is only an attribute of a thing which holds the capacity to affirm, i.e. a thinking thing.  I would ask for the person to show me proof of a thinking thing that can “affirm” without being able to think.  From this, it might follow that artificial intelligence could be possible proof of that type of thing, but much work would need to be done in order to show that it is an intelligible view worth holding.

The second criterion is solved by showing that if the principle of “the indiscernibility of the identical” is correctly interpreted as only applying to “unchangeable” properties, then it too is satisfied.  More specifically, the principle, as previously discussed, should only be interpreted in this way if it is to be coupled with our commonsense idea of identity.  If the principle is not interpreted in this way, then I will never be able to escape the paradox of being a different individual from the moment I started this paper to the moment I ended it.

Works Cited

Perry, John.,  ed.  Introduction to Philosophy Classical and Contemporary Readings.  4th Edition.  New York:  Oxford, 2007.

Douglas Jason Keffler (’09) is a Philosophy major at Arizona State University.


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