For binary classifiers (that output Negative or Positive), there are four types of outcomes:
True Positive -> The classifier reports positive and is correct.
False Positive -> The classifier reports positive but is wrong.
True Negative -> The classifier reports negative and is correct.
False Negative -> The classifier reports negative and is wrong.
40% false positives (fp) out of all responses does not tell you much about the other responses. But all together they sum up to 100%. Also: it does not automatically tell you how it will perform in the future. Also, the result is always relative to the true label distribution: If you tested it on 60 positive and 40 negative labels, 40% false positives means, that it misclassified 100% of the negatives, since there are only 100 instances and the positives cannot be classified as false positives, they need to come from the negatives. Since the percentage is always relative to the whole population, 40% of 100 are 40 which leaves no negatives that are classified as true negatives.
So you need all 4 types of outcomes and also the label ratios of the test set to judge your result.
TP + TN + FP + FN = 1.0
TP + TN = Rate of correctly classified over both outcomes, positive and negative classes.
FP / TP = Error rate for positives to be missclassified. Since you are missing the TP, you cannot say how many positives would be missclassified.
Maybe something that could also help to understand: Think about a classifier that always predicts positive, no matter what. What would be your TP, TN, FP, FN be for the two following cases:
a) You give it 60% positive and 40% negative instances.
b) You give it 99% positive and 1% negative instances.
! a) TP = 60%, TN = 0%, FP = 40%, FN = 0%
! b) TP = 99%, TN = 0%, FP = 1%, FN = 0%