home

Peter Gärdenfors Department of Philosophy Lund University Sweden
 * Induction and the Evolution of Conceptual Spaces **

__**Peirce's Constraint on Inductive Inference:**__ A "hint" at an evolutionary explanation of why "The human intellect is peculiarly adapted to the comprehension of the laws and facts of nature." (pg. 1).

"Not man merely, but all animals derive by inheritance (presumably by natural selection) two classes of ideas which adapt them to their environment."

1. Notion (a general understanding) of force, matter, space and time. 2. Notion (a general understanding) of what sort of objects their fellow-beings are, and how they will act on given occasions.

__**Conceptual Spaces by Peter Gardenfors: **__

"An appropriate framework for **non-symbolic** models. Conceptual spaces consist of a number of ’quality dimensions’ that often are derived from perceptual mechanisms." [] **Symbolic vs. Non-symbolic:** Symbolic information is needed for cognitive tasks (i.e. spelling the word 'cup') Non-symbolic information is needed for motor tasks (picking up a 'cup') []

__Conceptual space is the geometry of thought.__ It is defined by axes representing qualities. __Concepts are regions in conceptual space.__ A natural property is a convex region of a conceptual space. A natural concept is represented as a set of regions in a number of domains together with an assignment of salience weights to the domains and information about how the regions in the different domains are correlated.

__Natural properties represent something exiting in reality, independent from human cognition.__ The author (Peirce) argues that to understand induction one must understand the cognitive analysis of natural properties.

<span style="font-family: Arial,Helvetica,sans-serif;">We use quality dimensions to classify kinds and judge similarities. Some of these dimensions are innate such as color, pitch and space, and are important to meet our basic survival needs. We also have learned quality dimensions such as “volume”. Some quality dimensions are culturally dependent such as the concept of time. Some cultures view time as circular while others see it as linear. Science can have an effect on quality dimensions such as the distinction between temperature and heat. (pg. 9)

<span style="font-family: 'Times New Roman','serif'; margin: 0in 0in 10pt;">Natural selection has made us develop conceptual spaces to correctly induce outcomes for the sake of survival. Though not all quality dimensions are innate a basic similarity can be seen in the perceptual categories of cultures around the world (e.g. distinction between species, colors, noises). Relativism emerges within the learned and culturally dependent quality dimensions. <span style="font-family: 'Times New Roman','serif'; margin: 0in 0in 10pt;">Today the problem with inductive inference lies within our past. Because conceptual systems evolved for the environmental conditions of our ancestors, in dissimilar environments (one founded on artificial objects and situations) our intuition about what properties are projectable is impaired.

__**<span style="font-family: Arial,Helvetica,sans-serif;">Logical Positivism: **__ <span style="font-family: Arial,Helvetica,sans-serif;">Logical positivism is a way of thinking popular in the mid-20th century which attempted to make philosophy more rigorous by creating criteria for evaluating the truth or falsity of certain philosophical statements. Its main criteria for any statement is verifiability, which comes from two different sources: //empirical statements,// which come from science, and //analytic truth//, statements which are true or false by definition. Logical positivism heavily influenced philosophy of science, logic, and philosophy of language, among other areas, though today it is largely viewed as an overly simplistic approach which has been displaced by newer philosophies. <span style="font-family: Arial,Helvetica,sans-serif;">[]

This is a paradox found which illustrates a problem where inductive logic violates intuition. It achieves this by presenting the idea that 1. Ravens are black (which via the law of implication) makes anything that is not black is not a raven. The paradox arises when we apply it to something unrelated to ravens such as seeing a green (not black) apple (not raven)
 * Hempel's "Paradox of confirmation**"

By the same reasoning, this statement is evidence that (2) //everything that is not black is not a raven.// But since (as above) this statement is logically equivalent to (1) //all ravens are black//, it follows that the sight of a green apple offers evidence that all ravens are black. This conclusion is contrary to common sense reasoning and seems paradoxical, as it implies that we have gained information about ravens by looking at an apple. [|Raven paradox]

Gandenfors uses this example as a way to support his conclusion that the use for inductive reasoning should be limited to situations which are "ecologically valid"


 * <span style="font-family: Arial,Helvetica,sans-serif;">DEFINITIONS **

<span style="font-family: Arial,Helvetica,sans-serif;">**INDUCTIVE INFERENCE** - Around 1960, Ray Solomonoff founded the theory of universal inductive inference, the theory of prediction based on observations; for example, predicting the next symbol based upon a given series of symbols. Solomonoff's theory attempts to be mathematically rigorous. <span style="font-family: Arial,Helvetica,sans-serif;">[]

<span style="font-family: Arial,Helvetica,sans-serif;">**PROJECTIBILITY** - A property of predicates (something affirmed or denied of the subject) measuring the degree to which past instances can be taken to be the guides of future ones. <span style="font-family: Arial,Helvetica,sans-serif;">[]

<span style="font-family: Arial,Helvetica,sans-serif;">**PROTOTYPE THEORY** - A mode of graded categorization in cognitive science where some members of a category are more central than others. For example, of the concept "furniture," //chair// is more frequently or commonly cited than //stool.// []

<span style="font-family: Arial,Helvetica,sans-serif;">__Prototype theory states that within a category there is one set of qualities that represent the category best.__ For example, while there are many different types of birds, we tend to view certain ones, such as robins, as more representational of the category.

<span style="font-family: Arial,Helvetica,sans-serif;">**Geometric Notion** is a part of mathematics concerned with questions of size, shape, relative position of figures, and the properties of space. <span style="font-family: Arial,Helvetica,sans-serif;">[]

<span style="font-family: Arial,Helvetica,sans-serif;">**Vector Notation** is useful for any quantity that has both an amount and a direction in space.

<span style="font-family: Arial,Helvetica,sans-serif;"> **Ecological Validity** is the degree to which the behaviors observed and recordied in a study reflect the behaviors that actually occur in natural settings.<span style="font-family: Arial,Helvetica,sans-serif;">