In industrial engineering, forecasting is one of the key tools we used in making production decision. My question is, does forecasting only involves mathematical tool such as (correlation) or does it also involves philosophical logic?
There are philosophical assumptions involved since you are assuming that current events will somehow influence the future behavior of the predicted phenomenon.There is also an assumption that one variable somehow influences another. Such behavior can be subject to some causal model that is subject to philosophical debate.
Wow, you spotted a crucial point. In my experience now during coronavirus pandemic we must focus on the application side of forecasting which includes definitely math, and philosophical logic as well. I do not know which feature is more important, rather I argue they are related to one another:
1) CDC (2020). "Cases, Data & Surveillance: COVID-19 Forecasting: Background Information- Why COVID-19 Forecasting Is Important" Centers for Disease Control and Prevention National Center for Immunization and Respiratory Diseases (NCIRD), Division of Viral Diseases, U.S. Department of Health & Human Services August 8, 2020, Available at: https://www.cdc.gov/coronavirus/2019-ncov/cases-updates/forecasting.html