
To not further obfuscate the issue we should probably put "intelligence" aside. There are lots of "intelligent" folks with "intelligent" plans and broke. We could get into the whole emotional intelligence discussion, but then we're off on a serious tangent. That would be more of a philosophical description of afford rather than a financial one.
I'll put this one forward with the full knowledge that it's full of holes, but expands a bit on "ability to buy"
- Afford: The ability to buy ____ without becoming further indebted (this one would at least meet Chip's "pay cash" approach without financial shenanigans - that is, borrowing to have cash on hand)
or a much more stringent definition
- Afford: The ability to buy ___ without becoming further indebted or reducing your
a. existing savings
b. existing expenses
c. existing assets?
d. net worth?
Hmmm....any purchase you make or avoid moves your net worth along a number line. I only care where that number is as it affects my happiness, now and in the future.
I purchase things that I believe will improve my overall happiness/wellbeing. If having the money in "savings" will make me more happy (confidence in the present, and avoiding hunger in the future

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On another note. Since someone mentioned gold. I don't feel comfortable unless a portion of my portfolio is in tangible assets, which for me means gold and real estate.
Gold preserves wealth. It's real; it's not paper. It can't be easily manipulated, and if things go to hell (unlikely) gold will hold it's value. Fiat currency, stock certificates and bonds will always be useful for kindling however.
Owning real estate (or at least renting from the government) also gives a certain level of comfort.
Other than that, spend less than you earn.