Theoretically, under positivist paradigm, it is “essential” to follow probability sampling because of three key reasons:

(a) Objectivity: a random sample prevents researchers from choosing their own personal choice of samples, keeping the research and the researcher independent of each other (b) control: probability sampling method prevents influencing the results arising out of sampling method, and (c) generalizability: results based on probability sampling may be generalizable to the population. Since positivist paradigm talks about being objective and scientific in knowing the truth, the probability sampling is expected to align with the philosophy of the positivist paradigm.

Now please look back at the word “essential”, meaning that it is theoretically an ideal proposition and usually expected. There could be certain situational constraints where researchers may not be able to maintain such an ideal sampling process. Therefore, they must clearly mention any violation of such positivist’s requirement. It may significantly lower the research value, and many journals would (most likely) decline to publish due to non-probability sampling process, unless there has been no option for the researcher and the findings have been really worth sharing.  

However, this is not to say that violations are not accepted at all. Some authors (Ref. 1) noted that many published studies actually followed non-probability sampling in cross-cultural psychological research (where probability sampling would have been ideal for the sake of generalizability and comparison of multiple samples from different cultures). Some authors (e.g., Ref. 2) argued that despite there are evidences that non-probability sampling was adopted by some researchers, positivists should use probability sampling for the purpose of generalizability. Therefore, the researcher has to decide whether there are extreme difficulties in conducting a probability sampling or not, and justify non-probability sampling (if adopted) in conducting a survey, in my humble opinion.

(1) Visser, P. S., Krosnick, J. A., & Lavrakas, P. J. (2000). Survey research.

(2) Chirkov, V. (2015). Fundamentals of Research on Culture and Psychology: Theory and Methods. Taylor & Francis.

I personally think your professor's stance is too strong. In particular, if you were doing purely descriptive work, then you would only make the claim that your observations applied to the topics that you studied. From there, you could make predictions that if others studied the equivalent materials, they would see the same things. But that is not the same as generalizing numeric values to a larger, unseen population, from measurements in a smaller sample.

For example, physicists do not study random samples of electrons and biologists do not study random samples of red blood cells. 

I don't see why not

This is an issue of dispute between scholars. I witnessed two examiners in one dissertation defense with a challenging dispute about this issue. 

I'm thinking in terms of the original "logical positivists," which can be rather different from what social scientists mean when talk rather loosely about "positivism."

Thanks All, any suggestions ? as i have to use quantitative data which will be collected by non probability sampling and SEM ll be used for analysis.

I saw a general summary of positivism which divides it into about six assumptions:

-  There are universal laws of human behaviour that the social scientist always tries to discover and understand.

- Human behaviour can be understood by theorising about how it works. Hypotheses are tested using rigorous methods and techniques - usually, we use statistical techniques - and hypotheses are rejected or accepted. Hypotheses which are not falsified become knowledge which, together with other knowledge, forms the body of current scientific knowledge.

- The best science allows for the repetition of experiments which, in turn, may refine our knowledge.

- Measurement is the cornerstone of the scientific method. When you cannot measure the phenomenon in question the scientific nature of the object under study is called into question.

- The scientist is a disinterested observer of the phenomenon of interest. Observation does not affect the object of study and subjectivity cannot contaminate the correctness of the observations.

- The world is an objective reality ready to reveal its mysteries to the skilled and methodical scientist.

But positivism has its origins in Comte's thinking and his attempt to justify the use of methods used in the natural sciences when analysing social phenomena. I think Margaret Mead's work is a classic example of positivistic thinking when the method used is, supposedly, non-positivistic (ethnography). Having pre-conceived ideas that you are determined to prove at all costs seems to me the bedrock of positivism and what you say about something is taken as being objective fact. Unfortunately, practically all of what passes for science nowadays is positivistic and practically the only way to get anything published is to produce something with "significant" results.

In a nutshell, Muhammad, your lecturer is wrong. You should ask him for a clear definition of non-positivistic thinking.

Yes, I use it