PLM Reviews

  Introduction This was an interesting paper by Luca Incurvati and I enjoyed reading it quite a bit. We read this paper as part of our weekly philosophy of maths reading group at the University of Vienna. My thanks, in alphabetical order, to Julie Lauvsland, Benjamin Marschall and Simon Weisgerber. In particular, thanks to Julie for suggesting the paper. This is, though, the first paper I've reviewed where I've generally disagreed with the author. It's not that I necessarily disagree with all the conclusions, but I think there responses that Incurvati doesn't consider and alternative arguments that are important. I'm also unconvinced by Incurvati's positive proposal. Now one quasi-objection I have is that the paper takes place from a Platonist/realist perspective. I think that's wrong from the start and is bound to lead to confusion when we worry about which axioms or claims about sets are really  correct and why. I think we should choose our concept of &quo

  Introduction Mary Leng's recent paper "an i for an i, a Truth for a Truth" is, in my opinion, a strong one. We read this paper as part of our weekly philosophy of maths reading group at the University of Vienna. My thanks, in alphabetical order, to Julie Lauvsland, Benjamin Marschall and Simon Weisgerber for an interesting discussion on the paper. The paper was my suggestion and I was excited to read it both because of its relevance to my work and because I was fortunate enough to be briefly taught by Mary during by BA at York. The paper, I'm glad to say, didn't disappoint and I would certainly recommend it. The paper responds to an objection raised by both Shapiro and Burgess to "algebraic" interpretations of mathematical statements. The idea behind algebraic interpretations is not to take mathematical statements at face value, but to ameliorate them in some way that will potentially make them nominalistically acceptable. A nominalist, for those unawa

Introduction This was an exciting paper to read, as it was the first as part of a new reading group on the Philosophy of Maths at the University of Vienna. My thanks to Benjamin Marschall both for organising the group and suggesting the paper. I look forward to reviewing many of the papers that we'll read in this group. Present this week, in alphabetical order, was Julie Lauvsland, Benjamin Marschall, myself and Georg Schiemer. In the paper, Warren advances the claim that it is possible for us to reason infinitely. What does this mean? A working definition is that inferences are a kind of mental or cognitive act connecting a series of premises to a conclusion. Oxford's dictionary of philosophy says something similar stating: "Any process of drawing a conclusion from a set of premises may be called a process of reasoning." An inference might be a good (valid) inference or it might be a bad (invalid) one. Typically, though, inferences are finite in the sense that one i