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1. If I am currently dreaming then all of my current experiences are actually dream experiences.
When you dream, you only have dream experiences.
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2. Dream experiences are not good guides to how the external world actually is.
I can dream something, but this doesn't mean this is actually happening to me. Because there is no necessary connection between my dreams and what is really happening at that time, my dreams are not good guides to know how the external world truly is.
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3. Anything that I can experience while I am awake I can experience while I am asleep and dreaming.
(from 1 and 2) There is no experience that I could only have while awake.
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4. So, the experiences I am having right now could be a dream experience, for all I know. (So, I cannot tell whether what I am experiencing now is a dream experience or a waking experience.)
(From 3) Every experience I can have while awake I can equally have while dreaming, my current experiences could either be waking or dreaming experiences. So right now, I can't tell which it is.
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5. So, I never know whether I am awake or asleep and dreaming.
(from 3 and 4) By 3, the claim in 4 is true of every moment. So, at the moment, I do not know whether I am having a wakeful experience of a dreaming one.
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6. I must know that I am not dreaming in order to know anything about a world external to my mind on the basis of my sense experiences.
This sets a criteria or condition for knowing anything. From 1 and 2, we know dreaming experiences aren't good at providing us with knowledge about the external world. To trust our senses, we need to know that these are not dreams.
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7. So, I cannot know anything about an external world on the basis on my sense experiences.
(From 5 and 6) The condition from premise 6 can never be met due to, premise 5, never having the knowledge of whether or not I am awake.
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