The British logician Peter Geach wrote that “facts” found their way into literature by the end of the 19th century via the fashion journal “Strand Magazine”. In former times one could do without them. Facts spread very quickly after that, like a disease (Geach used another word). He calls them the wrong attempt to reduce hyothetical statements to categorical ones. (P. Geach, Oxford 1972, p 121ff).
Here are some more arguments that might be interesting:
Some authors say facts are the same as true assertions (R. Brandom, J.L. Austin), others deny this (e.g. A.J. Ayer) because there are more than one possible true assertions for one fact.
For some authors facts are the truth makers for assertions.
The following Ph.D. thesis may prove helpful in answering this question:
D. Subramanian, A theory of justified reformulations, Ph.D. thesis, Stanford University, 1989:
http://www.dtic.mil/dtic/tr/fulltext/u2/a210153.pdf
See Section 3.6.5 (starting on page 69) Properties of proofs in the WI_1 calculus.
James,
Thank you for your indication of this very interesting thesis about reformulation of problems in order to make them manageable for an automated treatment by computers.
Irrelevance-logic: as far as I read the thesis up until now it is partly about inferences from stronger to weaker and from weaker to stronger claims such as
“is a father” > “is an ancestor”
but not vice versa. In cases like that we may say that there is no additional information (fact) when we know that somebody is a father and then say that he is also an ancestor. – Then we should not say that there is a fact that makes a father be an ancestor. I hope I got that right.
It would be interesting to hear about present work that makes computers deal with problems like this. There is the well-known book from Robert Brandom discussing inferences in the light of the weaker/stronger-problem.
Facts: if there is any fact that makes e.g. a father be an ancestor than it should be a fact about our language use. In the corresponding case of an ancestor being a father it would be a question (resp. a fact) of biology, or we could say it is a contingent fact of life that this individual was born a man or a woman.
Irrelevance: there seems another definition of irrelevance for a computational system in the thesis mentioned by you on pp 103-104 saying that a fact is irrelevant when it is already in the system. This would then be a completely different point of view:
When we try this definition of a fact: a fact is, what makes a difference – then this definition will not be appropriate in the sense of the thesis: because something that is already in the system (and therefore is called irrelevant) can still make a difference, is it not?
The mentioned Herbrand bases seem to be interesting for the distinction finite/infinite interpretations and therefore for the question, if there are infinitely many possible sentences (see that other thread https://www.researchgate.net/post/Are_there_infinitely_many_possible_sentences_in_a_natural_language?_tpcectx=profile_questions).
Thank you. James.
Cheers,
Martin.
The question for this thread takes us in some interesting directions.
It is possible to argue that we do need causes as well as facts, at least from my point of view. My starting point is a theorem that has a proof. A theorem with a proof is something that is factual, something that we can accept, something that gives us a starting point. The antecedent of a proved theorem can either be an axiom (e.g., sets A and B remote from each other give rise to a set C that contains B and a set D is remote from B and that contains A (Efremovich's axiom)) or a previous theorem that has been proved or a conjecture that has not been proved. An antecedent of a new theorem would be considered the cause of the new theorem.
This means, depending on our perspective, a theorem can have both a causal character if it is the antecedent of another theorem and also a factual character that we accept. So, anywhere in a chain of theorems,
T0 => T1 => … => Ti => … => Tn
T0, for example, has a causal character if it leads to theorem T1. And theorem T0 has a factual character, if T0 has a proof. Strangely enough, T0 will not have a causal character, if it is does not lead to a new theorem. And the antecedents of theorem T0 have a causal character, since the hypothetical antecedents led to theorem T0. And the same can be said about every other theorem in the chain T0 => … => Tn.
From this perspective, a fact known to us (already in the "system") is relevant, not irrelevant. Do you agree?
Dear Jim,
This is going to get interesting. Sorry that I took so much time. Up until now my thoughts are not well organized. I collect some of them and write them down. First a few questions:
Should we take antecedence and consequence as cause and effect? – Is the first axiom an “unmoved mover”? – Are all axioms (independently from each other, as they should be) unmoved movers? –
Do you agree that numbers have no causal powers? – Do formulas have causal powers? - Do you agree that even natural laws don’t have causal powers? – Is it right that only individual cases have to do with powers – but that causality is best described by generalizations about types of events?
Numbers: that they have no causal powers is – in my opinion – showed by the possibility to use different numbers to describe the same fact – in relation to litres or gallons, inch or centimeters, Fahrenheit or Celsius etc. we will have different numbers to describe the same fact.
A certain individual mass attracts another individual mass – but both do neither appear in a formula, nor in a law.
It would be a lot of work to write about causality – only two short points everybody knows: Hume located it in regularity between types of events – Kant made it the foundation of our concept of time.
Facts: most authors see them as true propositions or as the truthmakers for assertions. There are differences that may be important later, but I think it is sufficient for a start.
Here are some more points for the coming discussion:
There are no facts in a calculation – no facts that make a calculation true.
What I am interested in is the so-called “non-factualism”.
Let me stop for now. Maybe you would like to intervene at this point.
Best Regards,
Martin.
Dear Martin,
I agree that after taking a closer look at facts vs. causes, this rich ground with lots of fascinating paths to follow. I am reminded of what Thomas Carlyle wrote in his Sartor Resartus:
Many a scene that looks desert and rock-bound from a distance will unfold itself, when visited, into rare valleys.
http://www2.hn.psu.edu/faculty/jmanis/carlyle/sartorresartus.pdf
http://www.kouroo.info/kouroo/Carlyle/SARTOR/Sartor_III.pdf
I have to leave to take care of some chores but will return to join in the discussion about unmoved movers and other things you have mentioned.
Jim,
Thanks for the link. The “unmoved mover” is not a serious option for me. I just stumbled upon causality in relation to axioms. I assume that formulas have no causal powers. So the u. m. was kind of a joke.
@Martin: Should we take antecedence and consequence as cause and effect? – Is the first axiom an “unmoved mover”? – Are all axioms (independently from each other, as they should be) unmoved movers?
In terms of antecedence in the context of theorems, we can bring into the discussion the notion of a basis. In general, objects in a system are generated by a basis. In a given system, the concepts in a given theorem represent a combination of the concepts (definitions, axioms, lemmas, theorems) that came before the theorem is given. You can see this, if you look at the proof of a theorem. Proofs hearken back to valid concepts that make it possible to show (argue) that the assertion in a theorem follows from what we know to be true.
So a theorem can viewed as an effect of what came before it, its antecedents.
A famous example of this interplay between antecedents giving rise to a theorem can be found in the presentation of geometry in Euclid's Elements. Apparently, borrowed quite a bit from the works of his predecessors. We know this from Proclus (410-485 A.D.), who wrote a commentary on Euclid's Book. Proclus is important because the original works by the forerunners of Euclid, Archimedes and Apollonius are lost.
For example, Proclus refers to Eudemis, student of Aristotle, in crediting the Pythagoreans with the discovery of Theorem I.32 (Proclus reproduces the proof given by Eudemis). Here is Theorem I.32:
Theorem I.32 In any triangle, if one of the sides is produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles.
Theorem I.32 is Aristotle's favourite illustration when he wishes to refer to some truth generally acknowledged.
From this, I would say that any axiom springs from a perception of the significance of what has been found by other mathematicians. I doubt if any axiom can be viewed as an unmoved mover. But then that is a difficult question that you have asked. Perhaps you had some insights in mind in posing your question.
Dear Martin,
I just now found a downloadable copy of Euclid's Elements with Sir Thomas L. Heath's commentary:
http://www.aaaban.com/books/In%20English%20History%20and%20Philosophy%20of%20Science/Heath%20-%20Thirteen%20Books%20of%20Euclid%27s%20Elements%202e%20Unabridged%20-%20Vol.%201%20-%20Books%20I-II%20%28Cambridge,%201968%29.pdf
Heath's remarks about Proclus, I.32 and the Pythagoreans can be found on p. 36. It is amazing that this valuable book is now freely available to everyone. The pdf version of this book is easier to read than my paper copy, which is 55 years old.
Dear Jim
You profess a lot confidence in me. I do not really have any substantial ideas in mind according to an unmoved mover or the role of axioms as an unmoved mover.
As to causality I wanted to defend a line where mathematical forms, formulas, equations etc. do not have any causal powers.- Of course they can be very influential when perceived by other theoreticians. But that would be an “indirect” form of causality for me – I don’t know if I can make this clearer: we often see in discussions that someone says that “in a broader sense” things have to do with each other. I hope I’ll find some examples. Good old “dialectic” was a case of that. My strategy – if I have any – is to stress the differences.
In order to keep you a bit busy, let me indicate Hartry Field as a very interesting author on the philosophy of mathematics. He wrote “Science without numbers” – a fascinating book. In short:
Numbers do not exist – sentences about non-existent objects are neither true nor false – we need something else to make them true – otherwise we could have no proofs – solution: proportions of proportions (or ratios of ratios?) – e.g. the diff. btw. the first two values is bigger than that btw. the second.two…an so on - he claims that he fixed a lot of physics up to General (not Special) Relativity with it.
I wonder what you will have to say to that. Have fun!
Dear Martin,
Many thanks for pointing out Harry Field's Science Without Numbers, Princeton University Press, 1980. A copy of this book can be downloaded from
http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Field%20-%20SWN%20selections.pdf
The heart of the matter in Field's approach is nominalism, which Field explains succinctly and cogently, starting in his Prelimanary Remarks, beginning on page 1.
Indirectly, Field is weighing in against Platonism and the Platonic view that numbers are entities. I think most mathematicians would agree that numbers, functions, sets and similar structures are abstractions that we use to model phenomena in nature.
There is a lot more to this story, which you ably have pointed out.
The last posts were about causality – let me try to contribute something about facts. My question was about facts: if we do need them at all. Here is just
A tricky case for facts (I posted this somewhere else before)
Imagine there is a village where the inhabitants hate cherries and never eat them. The village is located within a county. The inhabitants of this county love cherries. Now imagine that the county is located in a larger region where cherries are detested. This region is part of a country where cherries are the favorite fruit. This country is part of a continent where cherries are not loved…
Imagine you are an inhabitant of that village. Is it a fact that you are a member of a society which likes cherries or a member of a society which doesn’t like them?
This is my “easy version” of Alvin Goldmans example of “barn facades” (perfect forgeries) and the discussion of this issue in Brandom. Related problem: > reference classes.
Dear Martin,
It seems that facts and truths appear to be considered synonymous. For example, as a member of the imaginary village, imagine the Mayor of the village remarking to his loyal followers:
The water table is low. His followers agreed.
There is a cherry blossom on that tree. HIs followers looked, saw the blossom and agreed.
This goes back to Frege's view of the world:
http://www2.warwick.ac.uk/fac/soc/philosophy/people/faculty/longworth/research/travis_austin_draft_16_8.pdf
Perhaps you will agree that we can distinguish between a fact (e.g., low water table and cherry blossom) and an assertion about a fact. Facts can lead to truthful assertions. After observing a fact and stating a truthful observation (another fact), we are led to the conclusion that facts have a causal character.
Dear Jim,
I fully agree that facts and truths should be treated in the sense of redundancy theory but not as being synonymous.. I took a look at your link and find an inconsistency in the points I. to VI. (p.1): it is not so that we only can know truths about sensory data. We can know logical truths. The fault lies in the equation of sensory experience (of concreta) and the totality of possible knowledge.
Let me find the stuff, I will ad something that I posted before in another thread. It is about different views on facts: facts = true assertions, facts = truth makers of assertions etc. – and some counter arguments to these claims.
Do you think that there can be a fact "instead of" another fact? Where should the "instead of" be located when we have
A instead of B
Will it belong to A or to B? Or to none of them?
- Badges
- Science method
- Similar topics
- Philosophy