If my interpretation is correct, Kant argued in the Critique of pure reason and Prolegomena that:

> 
> The existence of an external world guarantees that we can intuit, conceive, etc internally.
> 
> 
> 

This argument bears that "transcendental" essence in it. 

Now my question is:
Does the Brain-in-a-Vat thought experiment undermines Kant's transcendental argument above? in what way?

I have read [this entry in the SEP](http://plato.stanford.edu/entries/realism-sem-challenge/), but it doesn't get me any further for the question I had.
['https://philosophy.stackexchange.com/questions/7603', 'https://philosophy.stackexchange.com', 'https://philosophy.stackexchange.com/users/1671/']
> 
> The existence of an external world guarantees that we can intuit,
>  conceive, etc internally. Does the Brain-in-a-Vat thought experiment
>  undermines Kant's transcendental argument above?
> 
> 
> 

I think your central question is “Does external exist, and we conceive internally, if we are a brain in the vat?
Answer: If we apply the Occam's razor the question is pointless.The maps are not the territory.

Suppose a Bizarre Brain, BB, that is, the computer of the "brain in the vat" skepticism, the brain of the Descartes' devil that deceives us, a permanently dreaming brain, or the solipsistic brain that create the "universe" for itself or for us. If the BB makes her mind the object of scientific study, it will find that it behaves with the same complexity as the universe described by a Common Sense Brain, CSB. Thus what CSB calls "the universe", the BB calls "one's own mind." Understood this way, the distinction between CSB and BB collapses and amounts to different ways of describing the same thing: a massively complex process that causes all the BB's experiences. Presumably having made the case that the BB scientist is actually a CSB scientist, the BB applies Occam's Razor, and suggests to the BB scientist to prefer the CSB's standard external “reality” over something like a BB's "reality". This is because the standard "reality" fits all the data available to the scientist, and on the skeptic's hypothesis is impossible to find differences, rendering superfluous the other more complicated possibilities.

Unobservables such as atomic particles, the force of gravity, and the quantum physics, are useful representation models. "The brain in the Vat" skepticism and the solipsism are interpretations or models too. Any language which provide a practical way of thinking and make sense about natural laws, a common mind-independent world, must provide a way of expressing common true inductive inferences about this world, or a description that relates representation to prediction. What varies are the models and interpretations, but if they are to be true, what they predict does not change. There is no more an objective basis for choosing one theory/representation over another than there is for preferring the Fahrenheit to the Celsius scale for temperature ascriptions. In an interpretation, it is prediction that remains invariant between different, but equally adequate, theories or representations.

If too many of speakers utterances are false, then the link between what speakers say and the world is severed; and the enterprise of interpretation each other halts. Too much error in statements about the world is not an option if speakers are going to translate each other. Therefore prediction is objective in the sense that most of what speakers say about the world are truths about the world. This is an assumption an translator makes because the only path into the world speakers share are the events in the world that cause them to hold those sentences true. Models translation need essentially inter-subjectivity.The maps are not the territory. It is pointless to say "the mountain is disobeying the map".

Central ideas of David Deutsch and David Davidson
Kant was reacting to two positions - the wholly idealistic philosophy of Berkeley - which is a very rough equivalent to the 'brain in a vat' thought experiment which is more akin to classical solipsism - in which everything is mind and objective reality disappears, and the radical scepticism of Hume which totally undermined the basis for empirical science - essentially the idea of causality. 

The phenomenal world as we know it and sense it immediately is structured by the the intuition giving it space & time to be presented to the intellectual & reasoning faculties of the mind - the understanding. (Think of a photograph, it is actually flat, but the mind projects an illusion of space; think of reading a novel, we give the illusion of time to the protagonists in it, a (narrative) time that is entirely separate from the flow of time we are as we are reading it).

The world in-itself (noumena) is never accessible - but it exists - otherwise we won't see its representation as phenomena. 

So Kant finds a middle ground where mind & intuition meet reality and each is immanent in the other. This allows science to happen, as it must; and leaves solipsism still fighting a lost battle.