My Writings - or some of them anyway

Here you can read or download [and so, not read, typically] most of the texts I've written for presentation to other people over the last three decades.

Texts in chronological order (backwards).

  1. A Users' Guide to RNM [not yet done]
  2. The Surveyability of Long Proofs 
  3. Mediated Fallacies    
  4. Pernicious Logical Metaphors
  5. Argumentum Ad Nauseam     {currently being tidied up}    
  6. In Praise of Sophistry and Rhetoric
  7. Why God knows No Mathematics       
  8. Mathematics, Not Metaphor!     
  9. Some Limits on Philosophy     
  10. Arguments of the Third Kind     
  11. The Truth     
  12. Acts of Argumentation: Beyond Spoken Dialog     
  13. Review of Walton's ​Arguments from Ignorance   
  14. Sexed Reason     
  15. The Seven Values of Mathematics     
  16. Drugs in Sport ­ - Why Not ?     
  17. Diagrams and Reasoning     
  18. Fallacies : There Are and There Aren't 
  19. There is No Fallacy of Arguing from Authority    
  20. Fallacy Irrationality Mistake     
  21. Failings of Reason     
  22. Mathematics ­- Semantics or Semiotics ? [Or, Ontological Nonchalance]   
  23. Fallacies in Reasoning, Dialogs and Texts   
  24. The Real Begriffsschrift     
  25.  Mathematical Knowledge: back to Kant?     
  26. Potato Logic     
  27. The Logic of Postmodernism     
  28. Presenting Mathematical Information      
  29. Why I Should Not Be Giving This Talk     
  30. Logic is a Branch of Rhetoric
  31. Paragraphy     
  32. Philosophy and Chaos     
  33. Mathematical Praxis     
  34. Du Travail Mathematique     
  35. Comment Decrire les Mathematiques?     
  36. Intuitionistic Reasoning     
  37. Strict Finitism and Necessity     
  38.  Nietzsche's Eternal Return     
  39. The Role of Notation in Mathematics {RNM}     {Not Yet Available - Real Soon Now!}
  40. Vague Talk     
  41. Speech Act and Text Act     
  42. Writing and Mathematics     
  43. Multiplying Entities     
  44. Reason and Evolution
  45. The Tootle Solution
  46. The Symbolic Calculus for Measures
  47. The Eckmann-­Hilton Theory of Spectral Sequences     
  48. ..............in progress ..........  :
  49. Recollecting Rhetoric 
  50. Number Magic 
  51. Is Formal Logic of any Value in Evaluating Argumentation? 
  52. Notes on Lavine 
  53.    - and numerous others

 

 

NB this page is being expanded  to include short outlines of each text, and an overview of their interconnections - once  they have mostly been cleaned up and made available -  A Users' Guide to My Writings [not yet available]

There are two main threads running through this work.One is philosophy of mathematics, and the other is (informal) logic, particularly fallacies. There is a specific historical connection which is explained in the text UGRNM, but mostly they can be (mostly) followed independently.

The connection is through my PhD thesis of 1988, The Role of Notation in Mathematics, which is [soon-to-be] available for download below. If you are interested to read that - NB 450 pages! - probably you would be wise to look at the Users' guide to RNM first, which gives an overview, some amendments, and a retrospective/second edition/supplement thirty years on. The original RNM is [over-] long due to some digressions; its third part can be significantly improved; and the rise of CMSs such as Mathematica deserves considerable dicsussion to extend and qualify some of the claims in RNM.

These pieces were mostly written​ for presentation to conferences and seminars (theses aside [RNM,SCM, RE, EHTSS]). Some [SLP, PLM, TINFOAFA...] are in print. All the versions here have been [mostly lightly] edited, mostly fixing typos and clarifications.

 

Texts in chronological order (backwards).

[2018]                               the Users' Guide to RNM [not yet done]

 

==============

 

[2008]                               The Surveyability of Long Proofs            

This paper was my contribution to an issue of Foundations of Science about argumentation and mathematics. Here's the abstract:

The specific characteristics of mathematical argumentation all depend
on the centrality that writing has in the practice of mathematics, but blindness to
this fact is near universal. What follows concerns just one of those characteristics,
justification by proof. There is a prevalent view that long proofs pose a problem for
the thesis that mathematical knowledge is justified by proof. I argue that there is
no such problem: in fact, virtually all the justifications of mathematical knowledge
are ‘long proofs’, but because these real justifications are distributed in the written
archive of mathematics, proofs remain surveyable, hence good.

 

==============

[2006]                                         Mediated Fallacies    
         

This paper was presented to the ISSA conference and is in the printed proceedings.

My main claims are that there exist fallacies which are dependent on the medium of expression, for which I shall argue by example, that in consequence there are many new fallacies over time (though many things traditionally called fallacies are no such thing) and that accordingly an acceptable “theory” of fallacy will require the construction of what I call The Book of Objections.

 

==============

[2006/2010]                                Pernicious Logical Metaphors 

Thii paper was given to a conference on Logic and Rhetoric at Cambridge University in 2006 and published in Logique et Analyse - but not until 2010.

I claim that there are pernicious logical metaphors. My primary example is 'logical
construction', but I will also discuss some other, related ones. Such metaphors
both derive from and foster a distorted and aggrandized conception of logic and a
distorted and unhistorical conception of rhetoric. They are pernicious because
they have these effects, which ramify into philosophy more generally. These
metaphors distort how logic is conceived, and thus they distort conceptions of
practices with logical components, particularly epistemology and mathematics.
An understanding of the role of metaphor informed by classical rhetoric can make
the use of such metaphors less pernicious.

==============

2005  Argumentum Ad Nauseam     {currently being tidied up}     

 

==============

 


[2005]                            In Praise of Sophistry and Rhetoric

The paper was written for a non-professional audience [yes it was delivered orally] and so it has no citations or bibliography. But anyone can easliy track down the references and allusions by searching the rest of these texts!

'Rhetoric' is nowadays synonymous with 'mere rhetoric', 'sophistry' with 'xxxxing sophistry'. This is the triumph of one side in an old argument which Plato started, between philosophy on one side, and sophistry and rhetoric on the other. But there is really more merit in the other side, and in the long view the recent denigration of sophistry and rhetoric may prove a brief interruption to the secular attitudes. I will try to explain the nature and status of the disputes, and to show why current attitudes are wrong.

==============

 

coming real soon now ..............................

2003  why God knows no mathematics       
2001  mathematics, not metaphor!     
2000  some limits on philosophy     
          arguments of the third kind     
1999  the truth     
1998  acts of argumentation: beyond spoken dialog     
         review of walton's ​Arguments from ignorance   
         sexed reason     
1997 the seven values of mathematics     
         drugs in sport ­ why not ?     
1996 diagrams and reasoning     
         fallacies : there are and there aren't 

   
[1995]                               There is No Fallacy of Arguing from Authority     
 

This paper was written for and published in Informal Logic.

I argue that there is no fallacy of argument from authority. I first show the weakness
of the case for there being such a fallacy: text-book presentations are confused, alleged
examples are not genuinely exemplary, reasons given for its alleged fallaciousness are not
convincing. Then I analyse arguing from authority as a complex speech act. R~iecting the
popular but unjustified category of the "part-time fallacy", I show that bad arguments which
appeal to authority are defective through breach of some felicity condition on argument as a
speech act, not through employing a bad principle of inference.

 

coming real soon now ..............................

       Fallacy Irrationality Mistake     
         failings of reason     
1994 mathematics ­- semantics or semiotics ? /ontological nonchalance    
         fallacies in reasoning, dialogs and texts   
1993 the real Begriffsschrift     
         mathematical knowledge: back to Kant?     
1992 potato logic     
         the logic of postmodernism     
         presenting mathematical information      
1991 why I should not be giving this talk     


 [1991]                                     Logic is a Branch of Rhetoric

Written for and given to the first Australian conference on Reasoning; published in its proceedings.   

My case is that logic is a branch of rhetoric, and better seen so.

First, I argue that Rhetoric is not what people commonly think. Rather than mere persiflage, it is the rigorous study of means of persuasion. Its present bad reputation deserves both explanation and contestation. Next, I argue that since Rhetoric is the study of what makes texts persuasive, and since persuasion relies on three modes, inference authority and emotion, while Logic is the study of only one of these, namely what makes inference good, therefore, Logic is only one of three branches of rhetoric. I go on to refute the obvious riposte that two rhetorical modes, the appeals to authority and emotion, are illegitimate. On the contrary they are both legitimate and necessary. Finally I argue for the value of recognising logic to be only a branch of rhetoric. The previous arguments show that not all "fallacies" are bad arguments, so fallacy is not a purely logical concept and rhetoric gives us a better account of bad reasoning than can logic alone. Since persuasive worth depends on the author and audience as well  as text, and not every reasoning tries to win assent to propositions, rhetoric which recognises these things, gives a fuller account of good reasoning than can logic alone. Therefore, rhetoric gives a better account of both good and bad reasoning than can logic alone, and logic is better seen as a branch of rhetoric.

A different way to overview this text is to read the Conspectus on the first page.

coming real soon now ..............................

 
1990 paragraphy     
        philosophy and chaos     
1989 mathematical praxis     
        du travail mathematique     
        comment decrire les mathematiques?     
        intuitionistic Reasoning     
1988 strict finitism and necessity     
        Nietzsche's eternal return     
        the role of notation in mathematics {RNM}     {Not Yet Available - Real Soon Now!}
1987vague Talk     
        speech act and text act     
1986 writing and mathematics     
1985 multiplying entities     
 
1978 reason and evolution

 

not philosophy: 

   
1977 the tootle solution

1984 the symbolic calculus for measure 

      
1976 the Eckmann­Hilton theory of spectral sequences     
 
 =======================================
in progress ...
recollecting rhetoric 
number magic 
is formal logic of any value in evaluating argumentation? 
notes on lavine 
   - and numerous others

 

 

 

Published on  August 31st, 2018