Avoiding reification: Heuristic effectiveness of mathematics and the prediction of the Ω−Ω− particle

• The prediction of the omega minus particle is thoroughly discussed.
• A new reconstruction for the prediction is presented.
• The new reconstruction is based on mathematical heuristic effectiveness.
• A new account for mathematical heuristic effectiveness is proposed.

According to Steiner (1998), in contemporary physics new important discoveries are often obtained by means of strategies which rely on purely formal   mathematical considerations. In such discoveries, mathematics seems to have a peculiar and controversial role, which apparently cannot be accounted for by means of standard methodological criteria. M. Gell-Mann and Y. Ne׳eman׳s prediction of the Ω−Ω− particle is usually considered a typical example of application of this kind of strategy. According to Bangu (2008), this prediction is apparently based on the employment of a highly controversial principle—what he calls the “reification principle”. Bangu himself takes this principle to be methodologically unjustifiable, but still indispensable to make the prediction logically sound. In the present paper I will offer a new reconstruction of the reasoning that led to this prediction. By means of this reconstruction, I will show that we do not need to postulate any “reificatory” role of mathematics in contemporary physics and I will contextually clarify the representative and heuristic role of mathematics in science.