Feb 27, 2011
(Note to philosophers: this represents only my take on the brakeless trains example, and is not intended to be a full and accurate depiction of Russell's argument (and does not even mention Strawson's response). I am concerned here not for exegetical accuracy, but rather, a clear tracing of my thinking on the subject.)
On 02/25/2011 2:26 PM, Savoie, Rod wrote, referring to:
http://halfanhour.blogspot.com/2011/02/connectivism-peirce-and-all-that.html
"there is the case where the object does not exist, and yet the word continues to have meaning. For example, 'brakeless trains are dangerous', to borrow from Russell. The whole area of counterfactuals in general. Which, if we follow the inferential trail, would have us believing with David K. Lewis that possible worlds are real. So *minimally* the meaning of the word, with respect to the object, must take place with respect to a theory or theoretical tradition."
Is there a word in that sentence ("brakeless trains are dangerous") that continues to have meaning whereas the object does not exist?
I replied:
Yeah - there's no such thing as a 'brakeless train' - all trains, and all; trains that have ever existed, have had brakes. So there is nothing that the noun phrase 'brakeless trains' refers to.
When you combine symbols (brakeless & trains), it is more a logic problem than a symbol/object problem.
The quick answer is to say we can just combine the terms. But when we are trying to understand the meaning of the sentence, combining terms is insufficient.
Let me explain (again, loosely following Russell):
When we say "brakeless trains are dangerous", are we saying "there exists an x such that x is a brakeless train and x is dangerous"? Well, no, because we are not saying "there exists an x such that x is a brakeless train."
So, how about, "there exists an x such that x is brakeless and x is a train and x is dangerous"? This is the 'combining terms' approach. But no, because we are not saying "there exists an x such that x is brakeless and x is a train."
Therefore, the statement "Brakeless trains are dangerous" cannot be rendered as an existential statement.
What we really mean by the statement is the counterfactual: "For all x, if x is a brakeless train, then x is dangerous." But what could we mean by such a statement? If meaning is what the sattement refers to, or what makes the statement true, then the statement is essentially meaningless, because
"For all x, if x is a brakeless train, then x is dangerous."
is equivalent to
"For all x, x is not a brakeless train or x is dangerous."
which means that our meaning is satisfied by reference to all things that are not brakeless trains, that is to say, everything in the world. Which means that our statement has exactly the same meaning as "The present king of France is dangerous," as the two sentences refer to exactly the same set of entities.
Perhaps, you might think, what we are talking about is not a union of the two sets, but an intersection. But the intersection of the set of 'brakeless trains' and the set of 'things that are dangerous' is empty, because there are no brakeless trains. Creating a three-set Venn diagram does not help either, because the intersection of 'things that are brakeless', 'things that are trains', and 'things that are dangerous' is also empty.
But what does it mean to combine symbols, if it does not mean to create the intersection of sets of objects denoted by the separate symbols? This is especially the case for a philosophy in which all statements depend on reference to experience for their truth. But even if you allow that some statements do not depend on reference to experience for their truth, the problem nonetheless remains, because there is no apparent way to create an inference to the conclusion 'brakeless trains are dangerous' that is not derived from the empty set, ie., derived from a contradiction.
Symbols are not limited to physical objects (because you seem to make that inference in your argument, but I do know that you don't necessarily think that).
Quite so. Symbols are not limited to physical objects. But for those symbols that are not limited to physical objects, where do they get their meaning? In semiotics generally, it must be something that is not the symbol itself; it must be from whatever the symbol signifies. Because it is the state of affairs in whatever the symbol signifies that will, for example, allow us to determine whether a statement containing the symbol is true or false.
You can make stuff up. You can give 'nothingness' a sense. (Sartre) Or 'time'. (Heidegger) Or 'history' (Marx). Or 'spirit'. (Hegel). Or space-time. (Kant) Or the self. (Descartes) But to philosophers who base their meaningfulness in experience, such as the positivists (and such as myself), the philosophies thus created are literally meaningless. What makes a statement involving one or the other of them true or false? The appeal is always to some necessity inherent in the concept. But necessities are tautologies, and from a tautology, nothing follows.
So what do symbols mean, if they do not refer to physical objects? This now becomes the basis for the issues modern philosophy. By far the primary contender is this: the symbols derive their meaning from a representation, where the representation may or may not have a direct grounding in the physical world.
For example, i - the square root of -1. It is clear that i does not refer to any number, because the square root of -1 does not exist. Nonetheless, the symbol i has a meaning - I just stated it - and this meaning is derived from the fact that it is postulated by, or embedded in, a representation of reality, ie., mathematics.
But what is the grounding for a representation? If we say "i has meaning in P', where does the representational system P obtain its meaning? It must have some, if only to distinguish it from being a 'castle in the air'. But more, if there is to be any commonality of representation, any communication between people using representational systems, then the representational system must in some way be externally grounded. Because, if i derives its meaning from its being embedded in the representational system, then, so does the symbol '1'. Because if you allow parts of your representation to have their meaning derived totally by reference to the physical world, you're right back where you've started, with essential elements of the system (like time, negation, self) without any external referent.
There are some options:
- picture (early Wittgenstein) - the representation is a picture or image of that which is represented
- coherence (Davidson) - it is the internal consistence of the representation itself that guarantees its truth
- cognitivism (Fodor) - the representation is innate
- possible worlds (Lewis) - the representation is grounded by reference to possible worlds
- pragmatism (James) - the representation is useful
- use, or pragmaticism (Peirce) - the effect of the meaning on action, or (later Wittgenstein) the use of the representation
In special cases, there are even more options. In probability theory, for example, there are three major interpretations:
- logical (Carnap) - the probability is the percent of the logical possibilities in which p is true
- frequency (Reichenbach) - the probability is the observed frequency in which p is true
- interpretive (Ramsey) - the percentage at which you would bet on p being true
As you can see, any of these could be applied to the statement that 'brakeless trains are dangerous' and we would have a story to tell, everything from the idea (from Davidson) that it is consistent and coherent with our understanding of trains, if not derived from it, that brakeless trains are dangerous, to (James) the usefulness of posting a sign to that effect in a train factory, to (Ramsey) how much an insurance company would be willing to cover you for were you to ride on a brakeless trains.
Which of these is true? They all are. Or to be more precise: none of them are. There is no external reality to which any of these 'representations' needs to set itself against in order to be true (or effective, or useful, etc). They are each, in their own way, a self-contained system. And each of our representations of the world is a combination of some, or all, of them. The meaning of any given term in a representation is distributed across the elements of that representation, and the meaning of the term consists in nothing over and above that.
The entities though so vital to the determination of truth in a representation - external objects, self, time, being, negation - are elements of the representation. The representation represents - no, is - the sum total of our mental contents.
So we come back to the initial question:
Is there a word in that sentence ("brakeless trains are dangerous") that continues to have meaning whereas the object does not exist?
And it follows that, if the phrase 'brakeless trains' does not refer to, or even represent, some external reality, none of the words in that sentence does. There are not special cases where some words refer and other words do not; all the words are, as it were, in the same boat. The case of 'brakeless trains' illustrates a case that applies to all words, even if it is only most evident in this particular example.
On 02/25/2011 2:26 PM, Savoie, Rod wrote, referring to:
http://halfanhour.blogspot.com/2011/02/connectivism-peirce-and-all-that.html
"there is the case where the object does not exist, and yet the word continues to have meaning. For example, 'brakeless trains are dangerous', to borrow from Russell. The whole area of counterfactuals in general. Which, if we follow the inferential trail, would have us believing with David K. Lewis that possible worlds are real. So *minimally* the meaning of the word, with respect to the object, must take place with respect to a theory or theoretical tradition."
Is there a word in that sentence ("brakeless trains are dangerous") that continues to have meaning whereas the object does not exist?
I replied:
Yeah - there's no such thing as a 'brakeless train' - all trains, and all; trains that have ever existed, have had brakes. So there is nothing that the noun phrase 'brakeless trains' refers to.
When you combine symbols (brakeless & trains), it is more a logic problem than a symbol/object problem.
The quick answer is to say we can just combine the terms. But when we are trying to understand the meaning of the sentence, combining terms is insufficient.
Let me explain (again, loosely following Russell):
When we say "brakeless trains are dangerous", are we saying "there exists an x such that x is a brakeless train and x is dangerous"? Well, no, because we are not saying "there exists an x such that x is a brakeless train."
So, how about, "there exists an x such that x is brakeless and x is a train and x is dangerous"? This is the 'combining terms' approach. But no, because we are not saying "there exists an x such that x is brakeless and x is a train."
Therefore, the statement "Brakeless trains are dangerous" cannot be rendered as an existential statement.
What we really mean by the statement is the counterfactual: "For all x, if x is a brakeless train, then x is dangerous." But what could we mean by such a statement? If meaning is what the sattement refers to, or what makes the statement true, then the statement is essentially meaningless, because
"For all x, if x is a brakeless train, then x is dangerous."
is equivalent to
"For all x, x is not a brakeless train or x is dangerous."
which means that our meaning is satisfied by reference to all things that are not brakeless trains, that is to say, everything in the world. Which means that our statement has exactly the same meaning as "The present king of France is dangerous," as the two sentences refer to exactly the same set of entities.
Perhaps, you might think, what we are talking about is not a union of the two sets, but an intersection. But the intersection of the set of 'brakeless trains' and the set of 'things that are dangerous' is empty, because there are no brakeless trains. Creating a three-set Venn diagram does not help either, because the intersection of 'things that are brakeless', 'things that are trains', and 'things that are dangerous' is also empty.
But what does it mean to combine symbols, if it does not mean to create the intersection of sets of objects denoted by the separate symbols? This is especially the case for a philosophy in which all statements depend on reference to experience for their truth. But even if you allow that some statements do not depend on reference to experience for their truth, the problem nonetheless remains, because there is no apparent way to create an inference to the conclusion 'brakeless trains are dangerous' that is not derived from the empty set, ie., derived from a contradiction.
Symbols are not limited to physical objects (because you seem to make that inference in your argument, but I do know that you don't necessarily think that).
Quite so. Symbols are not limited to physical objects. But for those symbols that are not limited to physical objects, where do they get their meaning? In semiotics generally, it must be something that is not the symbol itself; it must be from whatever the symbol signifies. Because it is the state of affairs in whatever the symbol signifies that will, for example, allow us to determine whether a statement containing the symbol is true or false.
You can make stuff up. You can give 'nothingness' a sense. (Sartre) Or 'time'. (Heidegger) Or 'history' (Marx). Or 'spirit'. (Hegel). Or space-time. (Kant) Or the self. (Descartes) But to philosophers who base their meaningfulness in experience, such as the positivists (and such as myself), the philosophies thus created are literally meaningless. What makes a statement involving one or the other of them true or false? The appeal is always to some necessity inherent in the concept. But necessities are tautologies, and from a tautology, nothing follows.
So what do symbols mean, if they do not refer to physical objects? This now becomes the basis for the issues modern philosophy. By far the primary contender is this: the symbols derive their meaning from a representation, where the representation may or may not have a direct grounding in the physical world.
For example, i - the square root of -1. It is clear that i does not refer to any number, because the square root of -1 does not exist. Nonetheless, the symbol i has a meaning - I just stated it - and this meaning is derived from the fact that it is postulated by, or embedded in, a representation of reality, ie., mathematics.
But what is the grounding for a representation? If we say "i has meaning in P', where does the representational system P obtain its meaning? It must have some, if only to distinguish it from being a 'castle in the air'. But more, if there is to be any commonality of representation, any communication between people using representational systems, then the representational system must in some way be externally grounded. Because, if i derives its meaning from its being embedded in the representational system, then, so does the symbol '1'. Because if you allow parts of your representation to have their meaning derived totally by reference to the physical world, you're right back where you've started, with essential elements of the system (like time, negation, self) without any external referent.
There are some options:
- picture (early Wittgenstein) - the representation is a picture or image of that which is represented
- coherence (Davidson) - it is the internal consistence of the representation itself that guarantees its truth
- cognitivism (Fodor) - the representation is innate
- possible worlds (Lewis) - the representation is grounded by reference to possible worlds
- pragmatism (James) - the representation is useful
- use, or pragmaticism (Peirce) - the effect of the meaning on action, or (later Wittgenstein) the use of the representation
In special cases, there are even more options. In probability theory, for example, there are three major interpretations:
- logical (Carnap) - the probability is the percent of the logical possibilities in which p is true
- frequency (Reichenbach) - the probability is the observed frequency in which p is true
- interpretive (Ramsey) - the percentage at which you would bet on p being true
As you can see, any of these could be applied to the statement that 'brakeless trains are dangerous' and we would have a story to tell, everything from the idea (from Davidson) that it is consistent and coherent with our understanding of trains, if not derived from it, that brakeless trains are dangerous, to (James) the usefulness of posting a sign to that effect in a train factory, to (Ramsey) how much an insurance company would be willing to cover you for were you to ride on a brakeless trains.
Which of these is true? They all are. Or to be more precise: none of them are. There is no external reality to which any of these 'representations' needs to set itself against in order to be true (or effective, or useful, etc). They are each, in their own way, a self-contained system. And each of our representations of the world is a combination of some, or all, of them. The meaning of any given term in a representation is distributed across the elements of that representation, and the meaning of the term consists in nothing over and above that.
The entities though so vital to the determination of truth in a representation - external objects, self, time, being, negation - are elements of the representation. The representation represents - no, is - the sum total of our mental contents.
So we come back to the initial question:
Is there a word in that sentence ("brakeless trains are dangerous") that continues to have meaning whereas the object does not exist?
And it follows that, if the phrase 'brakeless trains' does not refer to, or even represent, some external reality, none of the words in that sentence does. There are not special cases where some words refer and other words do not; all the words are, as it were, in the same boat. The case of 'brakeless trains' illustrates a case that applies to all words, even if it is only most evident in this particular example.
