Oct 10, 2009
Originally posted on Half an Hour, October 10, 2009.
Tracy asks, in a DeRosa post, "Stephen Downes, I asked you before in a comment on one of Ken's posts if there is any evidence that could convince you that content knowledge is necessary for thinking."
OK, so we've dispensed with the idea that there is some particular 'core' set of knowledge which is required in order to learning reading, critical thinking, etc., which was the bulk of my argument.
I trust you'll take this point over to the "common core" people.
The question of what counts as content knowledge is trickier. Tracy says it is, "(a) and part of your (b)," which is to say, propositional in form and (in part) experiential.
Helpfully, she clarifies, "I don't mean 'or some set of appropriate dispositions to respond, or skill or habit of mind'."
And we get, again usefully, a concrete example: "How could we learn language without content knowledge? For example, how could a small child ask their mother for a biscuit without some awareness of what a biscuit is? This is a serious question and I would like to hear your answer."
Excellent response.
The requirement of "some awareness" of what a biscuit is, if it is 'content knowledge', is propositional and at least partially experiential in nature. It is, in other words, knowledge that can be expressed in a sentence, where the content of that sentence is based in part on experience (presumably, with biscuits).
I say, "can be expressed in a sentence." A strong version of this sort of knowledge is that it actually *is* a sentence in the brain. A weaker version allows that it might be stored in some alternative fashion, but that this fashion includes a one-to-one correspondence with the sentence. So (for example) it make be made up of constituent meanings of words, grammatical principles, etc., that are assembled in order to form the sentence.
I don't think there's anything to object to in this characterization, but I'm laying it out clearly so you can see what it is I believe I'm responding to.
Now, the question becomes, "could a small child ask their mother for a biscuit" without this sort of knowledge?
The quick answer is, of course she could. She could not ask _in language_ without knowing language -- in other words, trivially, a knowledge of language requires a knowledge of language -- but she could make her desire known without language, and therefore, her knowledge of what a biscuit is, whatever that may happen to be, is not propositional in form.
I know that it really sounds like I'm splitting hairs, but I'm not. We have two very clear alternatives here:
1. knowledge that is propositional (ie', "(a) and partly (b)", vs
2. knowledge that is "some set of appropriate dispositions to respond, or skill or habit of mind" - which, if I cash this out, ends up being non-propositional neural structures that are blended in with each other
When you - and Ken, I assume - say that 'content knowledge' is required in order to read or think critically, you mean, "the person most previously possess at least one instance of 1 in order to read or think critically."
Now - for me this seems a bit tricky, because it means you're saying, "the child must previously possess at least one instance of language in order to learn language."
But of course, it isn't that tricky - you just have them memorize it, by rote, so that they have the necessary building blocks (alternatively, you could say, following Chomsky and Fodor and the like, that these building blocks are innate, built in).
I argue, though, that these building blocks are in fact "some set of appropriate dispositions to respond, or skill or habit of mind" - that they perform the equivalent function of these memorized facts, but are not in fact memorized facts, in that they are not propositional in form, and are, in fact, complex neural dispositions to respond. Habits of mind. Webs of connections between neurons that do _not_ have a one-to-one correspondence with propositional expressions.
So I say: a child can ask for a muffin without having a single fact (of type 1) about muffins. And the evidence I offer is:
a. this could be a habitual behaviour, something copied from adult behaviour
b. 'reaching out', which is _interpreted_ as 'asking' could be a habitual or even innate behaviour
c. The child can express a desire for a muffin long before acquiring any linguistic knowledge whatsoever
d. animals, such as dogs, which _cannot_ have propositional knowledge of type 1. can nonetheless ask for a muffin
In other words, what I am saying, is that all the rest of this comes first, and propositional knowledge - knowledge of form 1 - only comes *after* skills like language and critical thinking are obtained.
They learn, in other words, the mechanics of of how to come up with and express facts, and only then do they learn the facts themselves.
So, now, we turn to the question, "is there is any evidence that could convince you that content knowledge is necessary for thinking."
So what would be required?
I would need to be shown that a person must know some proposition (of form 1), but not some particular proposition (of form 1), prior to learning language.
Let me express this formally.
For some language L, which contains constructions (sentences, functions, theorems, whatever) f, which in turn contain variables x,y,z and may be instantiated with constants a,b,c, where knowledge L requires knowledge of f(x), and where knowledge of f(x) requires knowledge of some instantiation f(a).
In other words, I need to know, that there is some constant instantiation in a language f(a) that must be known _prior_ to knowing f(x) and, by extension, L.
So what evidence would I need?
1. an example of f(a)
2. proof that f(x) cannot be understood without prior understanding of f(a)
3. proof that L cannot be understood without prior understanding of f(x)
And - this is important - 'proof' is more than just the assertion that (say) f(x) cannot be understood without prior understanding of f(a).
This is what DeRosa does all the time. He just says it, but he never proves. We're supposed to take it as self-evident. But it is not self-evident.
What would constitute a proof?
1. A set of statements, f(b) ... f(c) that can be supported through direct empirical evidence - we can see that they are true, they are experimentally shown to be true (where 'experimentally' means normal rigourous experiments, not some prof studying a dozen grad students).
2. An inference rule g (eg., a deductive inference, an inductive inference, an argument to the best explanation (aka abduction), a mathematical inference, or some other form of inference), such that
3. g(f(b)...f(c)) entails (L -> f(a)) (in other words, 1 and 2 entail some fact f(a) such that some language L cannot be learned without that fact f(a).
Or, to express the requirement as a whole less formally:
evidence which would prove that there is some fact without which a knowledge of some language is impossible.
I think that's clear enough.
Tracy asks, in a DeRosa post, "Stephen Downes, I asked you before in a comment on one of Ken's posts if there is any evidence that could convince you that content knowledge is necessary for thinking."
OK, so we've dispensed with the idea that there is some particular 'core' set of knowledge which is required in order to learning reading, critical thinking, etc., which was the bulk of my argument.
I trust you'll take this point over to the "common core" people.
The question of what counts as content knowledge is trickier. Tracy says it is, "(a) and part of your (b)," which is to say, propositional in form and (in part) experiential.
Helpfully, she clarifies, "I don't mean 'or some set of appropriate dispositions to respond, or skill or habit of mind'."
And we get, again usefully, a concrete example: "How could we learn language without content knowledge? For example, how could a small child ask their mother for a biscuit without some awareness of what a biscuit is? This is a serious question and I would like to hear your answer."
Excellent response.
The requirement of "some awareness" of what a biscuit is, if it is 'content knowledge', is propositional and at least partially experiential in nature. It is, in other words, knowledge that can be expressed in a sentence, where the content of that sentence is based in part on experience (presumably, with biscuits).
I say, "can be expressed in a sentence." A strong version of this sort of knowledge is that it actually *is* a sentence in the brain. A weaker version allows that it might be stored in some alternative fashion, but that this fashion includes a one-to-one correspondence with the sentence. So (for example) it make be made up of constituent meanings of words, grammatical principles, etc., that are assembled in order to form the sentence.
I don't think there's anything to object to in this characterization, but I'm laying it out clearly so you can see what it is I believe I'm responding to.
Now, the question becomes, "could a small child ask their mother for a biscuit" without this sort of knowledge?
The quick answer is, of course she could. She could not ask _in language_ without knowing language -- in other words, trivially, a knowledge of language requires a knowledge of language -- but she could make her desire known without language, and therefore, her knowledge of what a biscuit is, whatever that may happen to be, is not propositional in form.
I know that it really sounds like I'm splitting hairs, but I'm not. We have two very clear alternatives here:
1. knowledge that is propositional (ie', "(a) and partly (b)", vs
2. knowledge that is "some set of appropriate dispositions to respond, or skill or habit of mind" - which, if I cash this out, ends up being non-propositional neural structures that are blended in with each other
When you - and Ken, I assume - say that 'content knowledge' is required in order to read or think critically, you mean, "the person most previously possess at least one instance of 1 in order to read or think critically."
Now - for me this seems a bit tricky, because it means you're saying, "the child must previously possess at least one instance of language in order to learn language."
But of course, it isn't that tricky - you just have them memorize it, by rote, so that they have the necessary building blocks (alternatively, you could say, following Chomsky and Fodor and the like, that these building blocks are innate, built in).
I argue, though, that these building blocks are in fact "some set of appropriate dispositions to respond, or skill or habit of mind" - that they perform the equivalent function of these memorized facts, but are not in fact memorized facts, in that they are not propositional in form, and are, in fact, complex neural dispositions to respond. Habits of mind. Webs of connections between neurons that do _not_ have a one-to-one correspondence with propositional expressions.
So I say: a child can ask for a muffin without having a single fact (of type 1) about muffins. And the evidence I offer is:
a. this could be a habitual behaviour, something copied from adult behaviour
b. 'reaching out', which is _interpreted_ as 'asking' could be a habitual or even innate behaviour
c. The child can express a desire for a muffin long before acquiring any linguistic knowledge whatsoever
d. animals, such as dogs, which _cannot_ have propositional knowledge of type 1. can nonetheless ask for a muffin
In other words, what I am saying, is that all the rest of this comes first, and propositional knowledge - knowledge of form 1 - only comes *after* skills like language and critical thinking are obtained.
They learn, in other words, the mechanics of of how to come up with and express facts, and only then do they learn the facts themselves.
So, now, we turn to the question, "is there is any evidence that could convince you that content knowledge is necessary for thinking."
So what would be required?
I would need to be shown that a person must know some proposition (of form 1), but not some particular proposition (of form 1), prior to learning language.
Let me express this formally.
For some language L, which contains constructions (sentences, functions, theorems, whatever) f, which in turn contain variables x,y,z and may be instantiated with constants a,b,c, where knowledge L requires knowledge of f(x), and where knowledge of f(x) requires knowledge of some instantiation f(a).
In other words, I need to know, that there is some constant instantiation in a language f(a) that must be known _prior_ to knowing f(x) and, by extension, L.
So what evidence would I need?
1. an example of f(a)
2. proof that f(x) cannot be understood without prior understanding of f(a)
3. proof that L cannot be understood without prior understanding of f(x)
And - this is important - 'proof' is more than just the assertion that (say) f(x) cannot be understood without prior understanding of f(a).
This is what DeRosa does all the time. He just says it, but he never proves. We're supposed to take it as self-evident. But it is not self-evident.
What would constitute a proof?
1. A set of statements, f(b) ... f(c) that can be supported through direct empirical evidence - we can see that they are true, they are experimentally shown to be true (where 'experimentally' means normal rigourous experiments, not some prof studying a dozen grad students).
2. An inference rule g (eg., a deductive inference, an inductive inference, an argument to the best explanation (aka abduction), a mathematical inference, or some other form of inference), such that
3. g(f(b)...f(c)) entails (L -> f(a)) (in other words, 1 and 2 entail some fact f(a) such that some language L cannot be learned without that fact f(a).
Or, to express the requirement as a whole less formally:
evidence which would prove that there is some fact without which a knowledge of some language is impossible.
I think that's clear enough.
