^Suppose you agree with Kant that we do have at least some a priori knowledge. Where does that knowledge come from? How do we know, for example, that all equilateral triangles are equiangular—
particularly because we can know that without physically examining any equilateral triangles?
^The point of introducing the synthetic a priori is to reject one way of answering that question. For the empiricist, one thing that would be acceptable would be to say that you can have a priori knowledge as long as it is knowledge derived from the meaning of words or concepts. So, as long as all a priori knowledge is analytic, then it would be okay for the empiricist.
^Once you introduce the synthetic a priori, however, it is no longer as easy for the empiricist to explain where that knowledge comes from—
the synthetic a priori knowledge that doesn’t ultimately come from knowledge of meaning.
^So, where does this knowledge come from? Let’s examine three answers.
^The first suggestion for where our a priori knowledge comes from is a form of rationalism. It’s less extreme than Descartes’s rationalism,
because it doesn’t claim that we learn everything through reason. Instead, these more modest rationalists just suggest that it is reason that explains how we learn the a priori synthetic truths of mathematics and philosophy. These modest rationalists suggest that we recognize those truths through the use of a rational faculty, or faculty of reason. There are two big problems with this idea.
] The first problem has to do with how the faculty of reason comes to know the things it knows. Modest rationalists like to suggest that reason “recognizes” or “perceives”
a priori synthetic truths. But this is just a metaphor, and it isn’t helpful.
Modest rationalists explicitly reject the notion that a brain-based explanation of how we come to know a priori synthetic truths is something we ought to seek. That’s just not a strategy that is worth pursuing.
] The second problem is that modest rationalists are very unclear about what a faculty of reason might be. The one thing that modest rationalists do seem to suggest is that the faculty of reason can’t just be a mechanism or collection of mechanisms in the brain. And rejecting an appeal to brain-based mechanisms for understanding human knowledge isn’t a promising
Theories of Knowledge LECTURE 12 do we have innate Knowledge?
not opposed in principle to explanations that ignore the role of the brain and brain mechanisms in knowledge, certainly you shouldn’t be satisfied with a name that stands for nothing. And unfortunately, in the case of modest rationalism, it seems that that’s all we have. Just a label—the faculty of reason—with no further detail about what such a thing might be.
^Modest rationalism doesn’t seem very plausible. Luckily, the other two explanatory strategies—the innate strategy and the language strategy—
are based on mechanisms in the brain. Furthermore, the strategies are compatible with each other, so
we can appeal to either one or both of the strategies to help explain our knowledge of a priori synthetic truths.
] The innate strategy involves innate brain mechanisms. Such mechanisms almost certainly play a role in our knowledge of basic facts about numbers.
] According to the language strategy, mathematical thinking is a result of our use of language.
^Both of these suggestions are plausible. The good news is that we don’t need to choose between them;
we can accept that both innate brain structures and language play a role in synthetic a priori knowledge.
T he evidence that innate mechanisms in the brain play a role in our knowledge of mathematics is strong. Beginning in the 1980s, developmental psychologists introduced what became known as the violation-of-expectation paradigm to investigate the innate cognitive abilities of preverbal children, even very young infants. Using that research technique, researchers have been able to establish that very young infants—as young as three or four days old—have a number of innate mental abilities that are relevant to our discussion of a priori synthetic knowledge.
Theories of Knowledge LECTURE 12 do we have innate Knowledge?
N ewborns have the ability to recognize when different collections of objects have differing numbers of objects. Psychologists refer to this as the ability to subitize, and developmental psychologists suggest that this ability is evidence that infants have an innate conception of number. In fact, by the age of a few months, babies behave as if they have an intuitive
understanding of very simple arithmetic operations, such as 1 + 1 = 2.
O ne of the pioneers of the suggestion that our ability to think abstractly is a result of our use of language was Soviet psychologist Alexander Luria. In a groundbreaking series of studies, he interviewed a number of Central Asian peasants and found that the ability to think and reason abstractly depended on the level of language learning that the peasants had attained.
Theories of Knowledge LECTURE 12 do we have innate Knowledge?
R esearch conducted by cognitive neuroscientist Stanislas Dehaene shows that there are at least two separate brain systems responsible for mathematical cognition: one involves approximate arithmetic and the other is employed when we compute exact arithmetic. Dehaene suggests that this second system is tied to the language that a person has learned.
This indicates that the best explanation of our a priori synthetic knowledge—such as our knowledge of mathematics—might involve both innate brain structures that provide us with the most fundamental concepts that we depend on for such knowledge and structures contained within our language that allow us to build on those fundamental concepts.
]Casullo, A Priori Justification.
Moser, ed., A Priori Knowledge.
]
reAdings
yTheories of Knowledge LECTURE 12 do we have innate Knowledge?
QUIZ
1 The fact that Nicholas Saunderson, the famous blind Lucasian professor of mathematics at Cambridge, could know facts about geometry would seem to provide some evidence against which of the following?
a Pure rationalism b Pure empiricism 2 Which of the following did
Immanuel Kant think involved claims that are true in virtue of logic and meaning alone?
a A priori b A posteriori c Analytic d Synthetic
3 Which of the following did Immanuel Kant think involved claims that were known independently of experience?
a A priori b A posteriori c Analytic d Synthetic
4 According to Kant, philosophical or mathematical truths are some of the few claims that can both be which of the following?
a Analytic a priori b Synthetic a priori c Synthetic a posteriori 5 Karen Wynn’s experiments on
the mathematical abilities of very young infants provide at least some evidence that some human mathematical knowledge is which of the following?
a The result of rational intuition b Due to innate mathematical
brain modules
c Due to linguistic knowledge 6 Soviet psychologist A. R. Luria’s
research suggests that at least some human mathematical knowledge is which of the following?
a The result of rational intuition b Due to innate mathematical
brain modules
c Due to linguistic knowledge Theories of Knowledge
LECTURE 12 QUIZ