Below are a list of philosophical
terms and concepts that we will be using throughout the course. It is in chronological order according to
the reading schedule.
Note: this is a 'growing' list that will
be amended throughout the semester.
Possible Worlds
Think of all the ways in which the world could have been different from the way that it actually is: There could have one more tree in the quad than there actually is; there could have been a Taco Bell on Franklin Street; there could have been purple toads; you could have been a millionaire; Arnold Schwarzenegger could have been president; George W. Bush might not have ever been born; Dinosaurs might have ruled the world, never to be extinct, prohibiting humans from flourishing.
Now imagine that all of these different ways that the world could have been is a way that some world--some possible world--is. So, if it could have been that you are in the NBA, then there is a possible world where you are in the NBA. Now, true, in such a world, several things may have to be different--you may have to be several inches taller than you actually are now, or the rest of the population may have to be shorter than it actually is, or it may have to be that you have 'flubber' feet or an uncanny ability to always make a basket no matter how hard you try to miss, etc. But if it is true that you could have been in the NBA (no matter what else might have needed to be different about the world in order for this to be true), then let us say that there is a possible world where this IS the case.
If there is a possible world for every way the world could have been, then there will be (at least!) an infinite number of worlds (For there is a possible world where just 1 bunny hopped on the quad; another where 2 bunnies hopped on the quad; another where 3 bunnies hopped on the quad, etc.). But using these worlds will help us when we are trying to figure out what is possible and what is not.
For example, on of the second day of class I talked about deductive arguments and validity. I explained that a valid argument is one such that if the premises are true then the conclusion must be true. Is the following argument valid?
Premise 1: All monkeys are mischievous
Premise 2: George W. Bush is a monkey
Conclusion: George W. Bush is mischievous
One way to determine validity is to use possible worlds: Imagine all of the possible worlds where the 2 premises are true--i.e., imagine all of the worlds in which it is true that all monkeys are mischievous and that George W. Bush is a monkey. Among such worlds, is it ever false that George W. Bush is mischievous? No. In this way, we can use possible worlds as an imaginative tool to aid us in our intuitions about possibilia.
As we progress through the semester, you will see that we will use possible worlds often: to test for validity, to track our intuitions about material objects and identity, to create counterexamples to certain claims and arguments, etc.
For way too much information on Modal Realism, go here.
Qualitative vs. Numerical Identity
Numerical identity is the relation that each thing holds to itself--e.g., I am numerically identical to myself, you are numerically identical to yourself, Jon Stewart is identical to himself, etc. If x is numerically identical to y, then x and y are one in number; "they" are one.
Qualitative identity, on the other hand, is the relation that many things can have to many others, provided that they have the same properties in common. For example, in class I talked about how two markers could have many of the same properties--e.g., they could both be white on the outside, with a black felt tip, a black plastic cap, cylindrical in shape, so many inches long, kept in a cardboard box, etc.--yet since they are two markers they are not numerically identical. Rather, they merely share some of their properties, or qualities--they are qualitatively identical--but they are not one and the same, numerically identical, marker.
Necessary and Sufficient Conditions, and Bi-conditionals
n is a necessary condition for m just in case n must obtain in order for m to obtain. s is a sufficient condition for m just in case it is enough that s obtain in order for m to obtain, but m might obtain without s.
For example: drinking alcohol is a necessary, but not a sufficient condition, for being drunk; you must drink some sort of alcohol in order to be drunk. But drinking only some alcohol may not be enough to get drunk; you may need to drink a whole bunch of alcohol before you "feel warm inside." Drinking 2 bottles of tequila, on the other hand, is a sufficient, but not necessary, condition for being drunk. If you drink 2 bottles of tequila, you will get drunk. But drinking 2 bottles of tequila is not the only way to get sauced; drinking Gin would work just as well.
p is a necessary and sufficient condition for m just in case p must obtain and it is enough that p obtain in order for m to obtain.
For example: Being an unmarried adult male is a necessary and sufficient condition for being a bachelor. If you are an unmarried adult male, then you are a bachelor, and you cannot be a bachelor without being an unmarried adult male.
A more fun example: Getting bit by the living dead is a necessary and sufficient condition for becoming a zombie. If you are bit by the living dead, then you will become a zombie; and you cannot become a zombie without being bitten by the living dead.**
Grrr. Arrrrg.
**Actually, I've been told by some of my more zombie lore informed friends that most zombie tales have some sort of cataclysmic event, like a nuclear blast from space or an unfortunate voodoo magic mishap or the rampant spread of a mutant virus, which causes the first zombies. In which case, it wouldn't be necessary condition of being a zombie that one is bitten by the living dead; one could become a zombie by being exposed to the freak explosion or voodoo magic or the mutant disease. I was thinking that zombies were a natural kind--like tigers or hippopotami--and that they have always just been here, being formed by one zombie biting another, forever back into eternity. But what do I know. I've only seen, like, 2 of the Resident Evil movies, where I was too busy ogling Milla Jovovich to pay much attention to the metaphysics of zombies. Besides, if you have been following this footnote so far, and if you agree with my friends about the details of zombie creationism, then you at least understand what a necessary and sufficient condition is, which means my pedagogical responsibilities have been carried out successfully. Go me.
Moving on.
We express th "necessary and sufficient condition" relation with the words "if and only if." So, for example, when we were discussing Leibniz's Law, I explained the principle as follows: An object a and an object b are identical if and only if a and b have all of the same properties. Because of the "if and only if", there are two parts to this statement, (i) and (ii):
(i) An object a and an object b are identical if a and b have all of the same properties.
(ii) a and b have all of the same properties if a and b are identical.
Another way to put the same point: a and b having all of the same properties is a necessary and sufficient condition for a being identical with b.
Paradox
In this class, we will have two ways of setting up a paradox.
Way 1: We will have a list of intuitive principles, each of which seems individually plausible, yet not all of them can be held consistently together. In other words, the individually plausible principles will yield a contradiction if we hold all of them together, and so we will be forced to jettison one of them.
Way 2: Seemingly acceptable premises will yield a seemingly unacceptable conclusion, via seemingly acceptable reasoning. Way 2 might not yield an outright contradiction as Way 1 might, but it will at the least demonstrate a tension in some principles that we ordinarily accept.
Paradox of the Heap
The Paradox of the Heap (also known as "Little by Little Arguments" and "The Bald Man Argument") can be formulated using a series of conditionals and using modus ponens (a valid inference that was discussed in class and on the logic handout here).
Imagine that we grant that a man with 1,000,000 hairs on his head is not bald. Call this the Hirsute Requirement. We may also grant that one hair more of less cannot make the difference between a bald man and a hirsute one. Call this the One-Hair-No-Diff Principle, or OHND. We can now generate the following argument:
The idea is that our tolerance for small changes can (such as the OHND Principle) eventually add up and yield an absurd conclusion such as that a man with no hair is not bald. Similar reasoning can be made to show that a heap can be made of 0 grains of hands, that a man with a million hairs on his head is bald, or even that you and I do not exist. We will be looking at several of these sort of "little by little" arguments as the semester proceeds.
Mereology, Mereological Sum, Simples, and Gunk
Mereology is the study of parts and wholes.
A mereological sum is the sum of any objects you please: your computer and the fried tofu I ate for breakfast; my left toe, your right ear, and the Statue of Liberty, etc. A mereological sum is considered an object (singular), even though the parts that make up the whole--e.g., my pink scooter, your backpack, and a couscous salad--may be far apart, not touching, and not even int he same country.
A mereological simple is an entity with no parts.
Gunk is an entity such that, for any one of its parts, its parts have parts. In other words, it has parts all the way down.
You might think that the world is a simple one: at rock bottom, the universe is made up of mereological simples--metaphysical atoms that cannot be sliced in half, even by an all-powerful being.
Or you might think that the universe is a gunky one: at rock bottom...well, there is no "rock bottom". The universe is made of objects which are made of parts, which are made of parts, which are made of parts, ad infinitum.
Or you might think that there universe is a hybrid of both gunk and simples: some things are gunky, others are simple, and only God knows which things are which.
Sortals
A sortal is a kind or type of thing that a particular object falls under. Take my cat, Nacho, for example. Nacho is big and gray and thinks he is mountain lion. But if someone were to ask me what kind of thing he is, I would say "a cat." He is part of a group of animals that satisfies certain criteria--e.g., has a certain genetic make-up, is decended from certain creatures, has particular physical characteristics, etc.
There are several different intuitive tests one might use to figure out whether some term, x, is a sortal term or not...(to be continued)
Wiggins' Tree and Cellulose Example
Imagine that there is a tree, T, that occupies a certain volume, v1, at a certain time, t1. However, at t1, v1 is also occupied by an aggregate of cellulose molecules, W. Thus, T and W are completely occupying the same place at the same time. Moreover, we know that T is not identical to because of Leibniz's Law. We could imagine that the tree is thrown into the wood chipper, but none of the cellulose molecules are destroyed. In this way, W has the property of being able to survive if thrown in a wood chipper, while T does not. Moreover, the tree could undergo a pruning, and have some of its branches removed, and yet still survive, whereas the aggregate of cellulose molecules would be destroyed. Thus, T has the property of being able to survive a pruning, while W does not. Thus, since there is at least one property that W and T don't share, by Leibniz's Law, W is not identical to T. But then this will violate principle Wiggins' principle S, or our commonsense principle (6).
Upside down "A" and Backwards "E"
(Sorry for the mere description; I couldn't get the actual symbols to post correctly.)
The upside down "A" and backwards "E" are quantifiers that range over variables that stand for objects.
The upside down "A" is read "for any" or "for all." We saw this in certain formulations of Leibniz's Law, and it is used in the Mark Johnston article "Constitution is Not Identity."
The backwards "E" stands for "there is" or "there exists." It is used in the Judith Jarvis Thompson article, "Parthood and Identity Across Time" (which was not assigned).
Plural Referring Expressions (vs. Singular Referring Expressions)
We often use singular referring expressions to talk about singular objects in the world. For example, "the dog", "the piece of chalk", "that beer over there", " my Material Constitution book", etc. These are all singular terms to refer to a single item in the world.
But notice that we also have plural referring expressions that seem to refer to many objects at once. For example, "the dogs", "the pieces of chalk", "those drinks over there", "those Material Constitution books on the shelves."
Accidental vs. Essential Properties
An accidental property is a property that an individual, x, might not have had. For example, you have the property of reading this handout right this very second. But intuitively you need not have had this property; you could have not been reading this handout right this very second and still be you.
An essential property, in contrast, is a property that an individual, x, has and must have in order for x to exist. So you, for example, have the property of having a certain genetic code. And you might think that it is necessary for you to have this genetic code--e.g., if "you" had a different genetic code, you wouldn't be you any more, you'd be someone else.
Another example: you might think that an essential property of a certain square, x, is that it is a closed figure with four right angles and four equilateral sides.
Modal Properties and Persistence Conditions
You have many properties. You have the property of reading this sentence right now. You have the property of being human. You have the property of being in my Phil330 class, of being a north carolina student, of being over 3 feet tall and under 8 feet tall, etc. In addition to these properties, however, you also have the following sorts of properties: could have been drinking a beer, could have been on a beach in Tahiti, could have chosen to go to a school other than UNC, could be a doctor, could jump out of an airplane on Valentine's Day 2008. All of these properties--what you could or might be--are called modal properties. They are what is possible, impossible and necessary for you.
Persistence Conditions are those conditions under which something can or will continue to exist (or persist). Using the case of Goliath and Lumpl as an example: Goliath can survive having one of his arms removed, whereas Lumpl cannot; Lumpl can survive being squished, but Goliath cannot.
Law of Substitutivity of Co-referential Terms
The Law of Substitutivity of Co-Referential Terms claims that the following inference is valid (i.e., truth preserving), where "F" stands for any property whatsoever, and "x" and "y" are singular, co-referring terms:
What this means is that for any
statement such as "Superman wears blue tights", if an identity
statement such as "Superman = Clark Kent" is true, then we should be
able to substitute the co-referring term "Superman" with "Clark Kent"
and get the sentence "Clark Kent wears blue tights."
Notice that it is not always the case that the Law of Substitutivity of Co-referential Terms does not always hold. Take, for example, the sentence "Lois Lane believes the Superman wears blue tights." If we are considering a time prior to her discovery that Superman is identical to Clark Kent, then is will be false that "Lois Lane believed that Clark Kent wears blue tights." Yet if the Law of Substitutivity of Co-Referential Terms holds across the board, then this sentence will have to follow from "Lois Lane believes the Superman wears blue tights," since all we are doing is substituting "Superman" with the co-referential term "Clark Kent."
Cases, such as belief reports, and other intentional contexts are often called opaque (as opposed to transparent) contexts, since we cannot apply the Law of Substitution of Co-Referential Terms.
As we will see, some people think that there are other contexts that are opaque--e.g., modal contexts, which use locutions such as "it could have been" or "it is possible", etc. See the Johnston article, and his discussion of Lewis, for example.
"Qua" talk
Possible Worlds
Think of all the ways in which the world could have been different from the way that it actually is: There could have one more tree in the quad than there actually is; there could have been a Taco Bell on Franklin Street; there could have been purple toads; you could have been a millionaire; Arnold Schwarzenegger could have been president; George W. Bush might not have ever been born; Dinosaurs might have ruled the world, never to be extinct, prohibiting humans from flourishing.
Now imagine that all of these different ways that the world could have been is a way that some world--some possible world--is. So, if it could have been that you are in the NBA, then there is a possible world where you are in the NBA. Now, true, in such a world, several things may have to be different--you may have to be several inches taller than you actually are now, or the rest of the population may have to be shorter than it actually is, or it may have to be that you have 'flubber' feet or an uncanny ability to always make a basket no matter how hard you try to miss, etc. But if it is true that you could have been in the NBA (no matter what else might have needed to be different about the world in order for this to be true), then let us say that there is a possible world where this IS the case.
If there is a possible world for every way the world could have been, then there will be (at least!) an infinite number of worlds (For there is a possible world where just 1 bunny hopped on the quad; another where 2 bunnies hopped on the quad; another where 3 bunnies hopped on the quad, etc.). But using these worlds will help us when we are trying to figure out what is possible and what is not.
For example, on of the second day of class I talked about deductive arguments and validity. I explained that a valid argument is one such that if the premises are true then the conclusion must be true. Is the following argument valid?
Premise 1: All monkeys are mischievous
Premise 2: George W. Bush is a monkey
Conclusion: George W. Bush is mischievous
One way to determine validity is to use possible worlds: Imagine all of the possible worlds where the 2 premises are true--i.e., imagine all of the worlds in which it is true that all monkeys are mischievous and that George W. Bush is a monkey. Among such worlds, is it ever false that George W. Bush is mischievous? No. In this way, we can use possible worlds as an imaginative tool to aid us in our intuitions about possibilia.
As we progress through the semester, you will see that we will use possible worlds often: to test for validity, to track our intuitions about material objects and identity, to create counterexamples to certain claims and arguments, etc.
For way too much information on Modal Realism, go here.
Qualitative vs. Numerical Identity
Numerical identity is the relation that each thing holds to itself--e.g., I am numerically identical to myself, you are numerically identical to yourself, Jon Stewart is identical to himself, etc. If x is numerically identical to y, then x and y are one in number; "they" are one.
Qualitative identity, on the other hand, is the relation that many things can have to many others, provided that they have the same properties in common. For example, in class I talked about how two markers could have many of the same properties--e.g., they could both be white on the outside, with a black felt tip, a black plastic cap, cylindrical in shape, so many inches long, kept in a cardboard box, etc.--yet since they are two markers they are not numerically identical. Rather, they merely share some of their properties, or qualities--they are qualitatively identical--but they are not one and the same, numerically identical, marker.
Necessary and Sufficient Conditions, and Bi-conditionals
n is a necessary condition for m just in case n must obtain in order for m to obtain. s is a sufficient condition for m just in case it is enough that s obtain in order for m to obtain, but m might obtain without s.
For example: drinking alcohol is a necessary, but not a sufficient condition, for being drunk; you must drink some sort of alcohol in order to be drunk. But drinking only some alcohol may not be enough to get drunk; you may need to drink a whole bunch of alcohol before you "feel warm inside." Drinking 2 bottles of tequila, on the other hand, is a sufficient, but not necessary, condition for being drunk. If you drink 2 bottles of tequila, you will get drunk. But drinking 2 bottles of tequila is not the only way to get sauced; drinking Gin would work just as well.
p is a necessary and sufficient condition for m just in case p must obtain and it is enough that p obtain in order for m to obtain.
For example: Being an unmarried adult male is a necessary and sufficient condition for being a bachelor. If you are an unmarried adult male, then you are a bachelor, and you cannot be a bachelor without being an unmarried adult male.
A more fun example: Getting bit by the living dead is a necessary and sufficient condition for becoming a zombie. If you are bit by the living dead, then you will become a zombie; and you cannot become a zombie without being bitten by the living dead.**
Grrr. Arrrrg.**Actually, I've been told by some of my more zombie lore informed friends that most zombie tales have some sort of cataclysmic event, like a nuclear blast from space or an unfortunate voodoo magic mishap or the rampant spread of a mutant virus, which causes the first zombies. In which case, it wouldn't be necessary condition of being a zombie that one is bitten by the living dead; one could become a zombie by being exposed to the freak explosion or voodoo magic or the mutant disease. I was thinking that zombies were a natural kind--like tigers or hippopotami--and that they have always just been here, being formed by one zombie biting another, forever back into eternity. But what do I know. I've only seen, like, 2 of the Resident Evil movies, where I was too busy ogling Milla Jovovich to pay much attention to the metaphysics of zombies. Besides, if you have been following this footnote so far, and if you agree with my friends about the details of zombie creationism, then you at least understand what a necessary and sufficient condition is, which means my pedagogical responsibilities have been carried out successfully. Go me.
Moving on.
We express th "necessary and sufficient condition" relation with the words "if and only if." So, for example, when we were discussing Leibniz's Law, I explained the principle as follows: An object a and an object b are identical if and only if a and b have all of the same properties. Because of the "if and only if", there are two parts to this statement, (i) and (ii):
(i) An object a and an object b are identical if a and b have all of the same properties.
(ii) a and b have all of the same properties if a and b are identical.
Another way to put the same point: a and b having all of the same properties is a necessary and sufficient condition for a being identical with b.
Paradox
In this class, we will have two ways of setting up a paradox.
Way 1: We will have a list of intuitive principles, each of which seems individually plausible, yet not all of them can be held consistently together. In other words, the individually plausible principles will yield a contradiction if we hold all of them together, and so we will be forced to jettison one of them.
Way 2: Seemingly acceptable premises will yield a seemingly unacceptable conclusion, via seemingly acceptable reasoning. Way 2 might not yield an outright contradiction as Way 1 might, but it will at the least demonstrate a tension in some principles that we ordinarily accept.
Paradox of the Heap
The Paradox of the Heap (also known as "Little by Little Arguments" and "The Bald Man Argument") can be formulated using a series of conditionals and using modus ponens (a valid inference that was discussed in class and on the logic handout here).
Imagine that we grant that a man with 1,000,000 hairs on his head is not bald. Call this the Hirsute Requirement. We may also grant that one hair more of less cannot make the difference between a bald man and a hirsute one. Call this the One-Hair-No-Diff Principle, or OHND. We can now generate the following argument:
(1) A man with 1,000,000 hairs on
his head is not bald.
(By the Hirsute Requirement)
(2) If a man with a 1,000,000 head-hairs is not bald, then a man with 999,999 head-hairs is not bald. (By OHND)
(3) If a man with 999,999 head-hairs is not bald, then a man with 999,998 head-hairs is not bald. (By OHND)
(4) If a man with 999,998 head-hairs is not bald, then a man with 999,997 head-hairs is not bald. (By OHND)
_______________________________________________________________________________________________
Therefore, a man with 0 head-hairs is not bald.
(2) If a man with a 1,000,000 head-hairs is not bald, then a man with 999,999 head-hairs is not bald. (By OHND)
(3) If a man with 999,999 head-hairs is not bald, then a man with 999,998 head-hairs is not bald. (By OHND)
(4) If a man with 999,998 head-hairs is not bald, then a man with 999,997 head-hairs is not bald. (By OHND)
_______________________________________________________________________________________________
Therefore, a man with 0 head-hairs is not bald.
The idea is that our tolerance for small changes can (such as the OHND Principle) eventually add up and yield an absurd conclusion such as that a man with no hair is not bald. Similar reasoning can be made to show that a heap can be made of 0 grains of hands, that a man with a million hairs on his head is bald, or even that you and I do not exist. We will be looking at several of these sort of "little by little" arguments as the semester proceeds.
Mereology, Mereological Sum, Simples, and Gunk
Mereology is the study of parts and wholes.
A mereological sum is the sum of any objects you please: your computer and the fried tofu I ate for breakfast; my left toe, your right ear, and the Statue of Liberty, etc. A mereological sum is considered an object (singular), even though the parts that make up the whole--e.g., my pink scooter, your backpack, and a couscous salad--may be far apart, not touching, and not even int he same country.
A mereological simple is an entity with no parts.
Gunk is an entity such that, for any one of its parts, its parts have parts. In other words, it has parts all the way down.
You might think that the world is a simple one: at rock bottom, the universe is made up of mereological simples--metaphysical atoms that cannot be sliced in half, even by an all-powerful being.
Or you might think that the universe is a gunky one: at rock bottom...well, there is no "rock bottom". The universe is made of objects which are made of parts, which are made of parts, which are made of parts, ad infinitum.
Or you might think that there universe is a hybrid of both gunk and simples: some things are gunky, others are simple, and only God knows which things are which.
Sortals
A sortal is a kind or type of thing that a particular object falls under. Take my cat, Nacho, for example. Nacho is big and gray and thinks he is mountain lion. But if someone were to ask me what kind of thing he is, I would say "a cat." He is part of a group of animals that satisfies certain criteria--e.g., has a certain genetic make-up, is decended from certain creatures, has particular physical characteristics, etc.
There are several different intuitive tests one might use to figure out whether some term, x, is a sortal term or not...(to be continued)
Wiggins' Tree and Cellulose Example
Imagine that there is a tree, T, that occupies a certain volume, v1, at a certain time, t1. However, at t1, v1 is also occupied by an aggregate of cellulose molecules, W. Thus, T and W are completely occupying the same place at the same time. Moreover, we know that T is not identical to because of Leibniz's Law. We could imagine that the tree is thrown into the wood chipper, but none of the cellulose molecules are destroyed. In this way, W has the property of being able to survive if thrown in a wood chipper, while T does not. Moreover, the tree could undergo a pruning, and have some of its branches removed, and yet still survive, whereas the aggregate of cellulose molecules would be destroyed. Thus, T has the property of being able to survive a pruning, while W does not. Thus, since there is at least one property that W and T don't share, by Leibniz's Law, W is not identical to T. But then this will violate principle Wiggins' principle S, or our commonsense principle (6).
Upside down "A" and Backwards "E"
(Sorry for the mere description; I couldn't get the actual symbols to post correctly.)
The upside down "A" and backwards "E" are quantifiers that range over variables that stand for objects.
The upside down "A" is read "for any" or "for all." We saw this in certain formulations of Leibniz's Law, and it is used in the Mark Johnston article "Constitution is Not Identity."
The backwards "E" stands for "there is" or "there exists." It is used in the Judith Jarvis Thompson article, "Parthood and Identity Across Time" (which was not assigned).
Plural Referring Expressions (vs. Singular Referring Expressions)
We often use singular referring expressions to talk about singular objects in the world. For example, "the dog", "the piece of chalk", "that beer over there", " my Material Constitution book", etc. These are all singular terms to refer to a single item in the world.
But notice that we also have plural referring expressions that seem to refer to many objects at once. For example, "the dogs", "the pieces of chalk", "those drinks over there", "those Material Constitution books on the shelves."
Accidental vs. Essential Properties
An accidental property is a property that an individual, x, might not have had. For example, you have the property of reading this handout right this very second. But intuitively you need not have had this property; you could have not been reading this handout right this very second and still be you.
An essential property, in contrast, is a property that an individual, x, has and must have in order for x to exist. So you, for example, have the property of having a certain genetic code. And you might think that it is necessary for you to have this genetic code--e.g., if "you" had a different genetic code, you wouldn't be you any more, you'd be someone else.
Another example: you might think that an essential property of a certain square, x, is that it is a closed figure with four right angles and four equilateral sides.
Modal Properties and Persistence Conditions
You have many properties. You have the property of reading this sentence right now. You have the property of being human. You have the property of being in my Phil330 class, of being a north carolina student, of being over 3 feet tall and under 8 feet tall, etc. In addition to these properties, however, you also have the following sorts of properties: could have been drinking a beer, could have been on a beach in Tahiti, could have chosen to go to a school other than UNC, could be a doctor, could jump out of an airplane on Valentine's Day 2008. All of these properties--what you could or might be--are called modal properties. They are what is possible, impossible and necessary for you.
Persistence Conditions are those conditions under which something can or will continue to exist (or persist). Using the case of Goliath and Lumpl as an example: Goliath can survive having one of his arms removed, whereas Lumpl cannot; Lumpl can survive being squished, but Goliath cannot.
Law of Substitutivity of Co-referential Terms
The Law of Substitutivity of Co-Referential Terms claims that the following inference is valid (i.e., truth preserving), where "F" stands for any property whatsoever, and "x" and "y" are singular, co-referring terms:
Fx
x = y
______
Fy
Notice that it is not always the case that the Law of Substitutivity of Co-referential Terms does not always hold. Take, for example, the sentence "Lois Lane believes the Superman wears blue tights." If we are considering a time prior to her discovery that Superman is identical to Clark Kent, then is will be false that "Lois Lane believed that Clark Kent wears blue tights." Yet if the Law of Substitutivity of Co-Referential Terms holds across the board, then this sentence will have to follow from "Lois Lane believes the Superman wears blue tights," since all we are doing is substituting "Superman" with the co-referential term "Clark Kent."
Cases, such as belief reports, and other intentional contexts are often called opaque (as opposed to transparent) contexts, since we cannot apply the Law of Substitution of Co-Referential Terms.
As we will see, some people think that there are other contexts that are opaque--e.g., modal contexts, which use locutions such as "it could have been" or "it is possible", etc. See the Johnston article, and his discussion of Lewis, for example.
"Qua" talk