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Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.

Molyneux's problem is a thought experiment in philosophy concerning immediate recovery from blindness. It was first formulated by William Molyneux, and notably referenced in John Locke's An Essay Concerning Human Understanding (1689). The problem can be stated in brief, "if a man born blind can feel the differences between shapes such as spheres and cubes, could he, if given the ability to see (but now without recourse to touch), distinguish those objects by sight (alone), in reference to the tactile schemata he already possessed?"

The question was originally posed to Locke by philosopher William Molyneux, whose wife was blind:

Suppose a man born blind, and now adult, and taught by his touch to distinguish between a cube and a sphere of the same metal, and nighly of the same bigness, so as to tell, when he felt one and the other, which is the cube, which is the sphere. Suppose then the cube and the sphere placed on a table, and the blind man made to see: query, Whether by his sight, before he touched them, he could now distinguish and tell which is the globe, which the cube? To which the acute and judicious proposer answers: 'Not. For though he has obtained the experience of how a globe, and how a cube, affects his touch; yet he has not yet attained the experience, that what affects his touch so or so, must affect his sight so or so…'

To which Locke responds in An Essay Concerning Human Understanding:

I agree with this thinking gentleman, whom I am proud to call my friend, in his answer to this problem; and am of opinion that the blind man, at first sight, would not be able with certainty to say which was the globe, which the cube, whilst he only saw them; though he could unerringly name them by his touch, and certainly distinguish them by the difference of their figures felt.

In 1709, in A New Theory of Vision, George Berkeley also concluded that there was no necessary connection between a tactile world and a sight world—that a connection between them could be established only on the basis of experience. He speculated:

the objects to which he had hitherto used to apply the terms up and down, high and low, were such as only affected or were in some way perceived by touch; but the proper objects of vision make a new set of ideas, perfectly distinct and different from the former, and which can in no sort make themselves perceived by touch

— (sect. 95).
In 1749, Denis Diderot wrote Letter on the blind for the benefit of those who see as a criticism of our knowledge of ultimate reality.

A similar problem was also addressed earlier in the 12th century by Ibn Tufail (Abubacer), in his philosophical novel, Hayy ibn Yaqdhan (Philosophus Autodidactus). His version of the problem, however, dealt mainly with colors rather than shapes.

Regarding Molyneux's problem, the authors Asif A. Ghazanfar & Hjalmar K. Turesson (2008) have recently noted:

Production of speech is seen as a pure motor act, involving muscles and the neurons controlling them, while perception of speech is seen as purely sensory, involving the ear and the auditory pathway. This parcellation of the systems appear intuitive and clear, but recent studies … suggest that such divisions may be fundamentally wrong. Rather than separate processes for motor outputs and individual sensory modalities, adaptive action seems to use all the available context-specific information. That is, neural representations across the brain may be centered on specific actions. This view on neural representations puts 'Molyneux's Problem' in a new light. Unisensory signals are fused into multisensory motor representations unified by an action, but since Molyneux does not suggest any action, his 'problem' may be better viewed as an ill-posed question—at least from a neuroscientific perspective.....