The representational theory of cognition gives rise to a natural theory of intentional states such as believing, desire and intending. According to this theory, intentional stares factor into two aspects, a functional aspect that distinguishes believing from desiring and so on, and a content aspect that distinguishes beliefs from each other, desires from each other, and so on. A belief that 'p' might be realized as a representation with the content that 'p' and the function of serving as a premise in inference. A desire that 'p' might be realized as a representation with the content that 'p' and the function of initiating processing designed to bring about that of 'p' and terminating such processing when a belief that 'p' is formed.
Zeno of Elea's argument against motion precipitated a crisis in Greek thought. They are presented as four arguments in the form of paradoxes, such are to follow:
(1) suppose a runner needs to travel from a start 'S' to a finish 'F', and hence to 'F', but if 'N' is the midpoint of 'SM', he has first to first travel to 'N'. And so on ad infinitum (Zeno 'what has been said once can always be repeated). But it is impossible to accomplish an infinite number of tasks in a finite time. Therefore, the runner cannot complete (or start) his journey.
(2) Achilles runs a race with tortoise, who has a start of 'n' metres. Suppose the tortoise runs one-tenth as fast as Achilles. Then by the time Achilles had reached the tortoise's starting-point. The tortoise is n/10 metres ahead. By te time Achilles has reached that point, the tortoise is n/100 metres ahead, and so on, ad infinitum. So Achilles cannot catch the tortoise.
(3) an arrow cannot move at a place at which it is not. But neither can it move at a place at which it is. That is, at any instant it is at rest. But if at no instant is it moving, then it is always at rest.
(4) suppose three equal blocks, 'A', 'B', 'C' of width 1, with 'A' and 'C' moving past 'B' at the same speed in opposite directions. Then 'A' takes one time, 't', to traverse the width of 'B', but half the time, ½, to traverse the width of 'C'. But these are the same length, so 'A' takes both 't' and t/2 to traverse the distance 1.
These are the barest forms of the arguments, and different suggestions have been =made as to how Zeno might have supported them. A modern approach might be inclined to dismiss them as superficial, since we are familiar with the mathematical ideas, as (a) that an infinite series can have a finite sum, which may appear ti dispose of (1) and (2) and (b) that there may appear to no such thing s velocity a point or instant, for velocity is defined only over intervals of time and distance, which may seem to dispose of (3) the fourth paradox seems merely amusing, unless Zeno had in mind that the length 1 is thought of as a smallest unit of distance (a quantum of space) and that each 'A' and 'C, are travelling so that they traverse the smallest space in the smallest time. On these assumptions there is a contradiction, for 'A' passes 'C' in half the proposed smallest time.
Zeno of Elea's argument against motion precipitated a crisis in Greek thought. They are presented as four arguments in the form of paradoxes, such are to follow:
(1) suppose a runner needs to travel from a start 'S' to a finish 'F', and hence to 'F', but if 'N' is the midpoint of 'SM', he has first to first travel to 'N'. And so on ad infinitum (Zeno 'what has been said once can always be repeated). But it is impossible to accomplish an infinite number of tasks in a finite time. Therefore, the runner cannot complete (or start) his journey.
(2) Achilles runs a race with tortoise, who has a start of 'n' metres. Suppose the tortoise runs one-tenth as fast as Achilles. Then by the time Achilles had reached the tortoise's starting-point. The tortoise is n/10 metres ahead. By te time Achilles has reached that point, the tortoise is n/100 metres ahead, and so on, ad infinitum. So Achilles cannot catch the tortoise.
(3) an arrow cannot move at a place at which it is not. But neither can it move at a place at which it is. That is, at any instant it is at rest. But if at no instant is it moving, then it is always at rest.
(4) suppose three equal blocks, 'A', 'B', 'C' of width 1, with 'A' and 'C' moving past 'B' at the same speed in opposite directions. Then 'A' takes one time, 't', to traverse the width of 'B', but half the time, ½, to traverse the width of 'C'. But these are the same length, so 'A' takes both 't' and t/2 to traverse the distance 1.
These are the barest forms of the arguments, and different suggestions have been =made as to how Zeno might have supported them. A modern approach might be inclined to dismiss them as superficial, since we are familiar with the mathematical ideas, as (a) that an infinite series can have a finite sum, which may appear ti dispose of (1) and (2) and (b) that there may appear to no such thing s velocity a point or instant, for velocity is defined only over intervals of time and distance, which may seem to dispose of (3) the fourth paradox seems merely amusing, unless Zeno had in mind that the length 1 is thought of as a smallest unit of distance (a quantum of space) and that each 'A' and 'C, are travelling so that they traverse the smallest space in the smallest time. On these assumptions there is a contradiction, for 'A' passes 'C' in half the proposed smallest time.
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