Ordinal, nominal data type. what type of data is True/false matrix? (Level of measurement)         cat1    cat2    cat3    cat4
topic1  1        1         1    1
topic2  1        0         1    1
topic3  1        0         1    1
topic4  1        0         1    0

This data table means:
When a topic belongs to category, the data entry will be 1. 
If the topic doesn't belong to certain category, then the data entry will be 0.
What kind of level measurement is this? Ordinal scale, nominal scale, ratio scale, or  interval scale?
Thank You 
 A: This is probably nominal data (also known as categorical data - knowing that would have eliminated the need to ask the question, I suspect!)
You can also make an argument for counting it as ordinal data, if there is some sense of ordering to whether the theme is included in the category or not, eg if Category 1 is 'Good/Bad' or Category 2 is 'High/Low', as pointed out in the answer below.
How can you tell what your data is in general?


*

*If you can't sensibly order the data, it is nominal/categorical (eg "What nationality are you?" "What is your eye color?")

*If you can order the data but it doesn't make sense to add or subtract data points from each other, or multiply by a constant factor, it is ordinal data (eg "Do you strongly agree/agree/disagree/strongly disagree that kittens are cute?" "Rate this brand of peanut butter on a scale of 1 to 5")

*If you can order the data and it makes sense to add and subtract it, and multiply by a constant factor, but there isn't any sensible meaning assigned to a value of zero, it is interval data (eg "What is your IQ?" "What is the temperature outside in Celsius/Fahrenheit?")

*If the data can be ordered and you can add and subtract the data points together to get meaningful results, and there is a meaning to a zero value, then it is ratio data (eg "How tall are you?" "How much do you weigh?" "What is the temperature outside in Kelvin?")
A: The answer actually depends on what the categories are. If the categories you are referring to are, for example, positive/negative for some disease (or some other type of presence/absence response), then analysts can, and often do, view the data as ordinal. In particular, logistic or probit regression models can be equivalently conceived of as being generated from unobserved continuous variables (with a logistic or normal distribution in the two cases, respectively) that are thresholded at 0, which is inherently viewing the binary responses as ordinal.  
On the other hand, many examples of binary data are clearly nominal, as Chris Taylor pointed out above. 
