Fictionalism. ( For those interested.)

[Joker]

Fictionalism is a methodological theory in philosophy that suggests that statements of a certain sort should not be taken to be literally true, but merely a useful fiction. Two important strands of fictionalism are modal fictionalism (which states that facts about what might have been the case or what must necessarily be the case are merely fictions) and mathematical fictionalism, which states that talk of numbers and other mathematical objects is nothing more than a convenience for doing science.

Fictionalism consists in at least the following three theses:

Claims made within the domain of discourse are taken to be truth-apt; that is, true or false.
The domain of discourse is to be interpreted at face value–not reduced to meaning something else.
The aim of discourse in any given domain is not truth, but some other virtue(s)(e.g., simplicity, explanatory scope).

Balaguer, Mark (1998). Platonism and Anti-Platonism in Mathematics. Oxford Oxfordshire: Oxford University Press. ISBN 9780195143980.
Kalderon, Mark (2005). Moral Fictionalism. Oxford: Clarendon Press. ISBN 9780199275977.

en.wikipedia.org/wiki/Fictionalism

Mathmatical Fictionalism

Fictionalism was introduced in 1980 when Hartry Field published Science Without Numbers, which rejected and in fact reversed Quine’s indispensability argument. Where Quine suggested that mathematics was indispensable for our best scientific theories, and therefore should be accepted as a body of truths talking about independently existing entities, Field suggested that mathematics was dispensable, and therefore should be considered as a body of falsehoods not talking about anything real. He did this by giving a complete axiomatization of Newtonian mechanics that didn’t reference numbers or functions at all. He started with the “betweenness” of Hilbert’s axioms to characterize space without coordinatizing it, and then added extra relations between points to do the work formerly done by vector fields. Hilbert’s geometry is mathematical, because it talks about abstract points, but in Field’s theory, these points are the concrete points of physical space, so no special mathematical objects at all are needed.

Having shown how to do science without using mathematics, he proceeded to rehabilitate mathematics as a kind of useful fiction. He showed that mathematical physics is a conservative extension of his non-mathematical physics (that is, every physical fact provable in mathematical physics is already provable from his system), so that the mathematics is a reliable process whose physical applications are all true, even though its own statements are false. Thus, when doing mathematics, we can see ourselves as telling a sort of story, talking as if numbers existed. For Field, a statement like “2 + 2 = 4” is just as false as “Sherlock Holmes lived at 221B Baker Street” — but both are true according to the relevant fictions.

By this account, there are no metaphysical or epistemological problems special to mathematics. The only worries left are the general worries about non-mathematical physics, and about fiction in general. Field’s approach has been very influential, but is widely rejected. This is in part because of the requirement of strong fragments of second-order logic to carry out his reduction, and because the statement of conservativity seems to require quantification over abstract models or deductions. Another objection is that it is not clear how one could have certain results in science, such as quantum theory or the periodic table, without mathematics. If what distinguishes one element from another is precisely the number of electrons, neutrons and protons, how does one distinguish between elements without a concept of number?

en.wikipedia.org/wiki/Philosophy … ctionalism

[Mr_Reasonable]

I like modal realism better. Fiction sucks. We need a smiley that spits.

[IrvingWashington]

You get fictionalism about moral statements too, which Joker would probably like, given these guys are saying the same things he’s constantly banging on about.

[Joker]

@Smears

I like modal realism better. Fiction sucks. We need a smiley that spits.

What is modal realism?

[Joker]

@IrvingWashington

You get fictionalism about moral statements too, which Joker would probably like, given these guys are saying the same things he’s constantly banging on about.

Do you have a grudge against the understanding of fictionalism?

[IrvingWashington]

What? No. Where would you get that from? I was just saying its a view some philosophers hold about moral statements, which you might be interested in. Richard Joyce holds this view, from what I remember. You should check him out.

[Joker]

@IrvingWashington

What? No. Where would you get that from? I was just saying its a view some philosophers hold about moral statements, which you might be interested in. Richard Joyce holds this view, from what I remember. You should check him out.

Oh I misunderstood you. Actually you are right I am interested in such things as that basically has been my reading material the past month.

But I am not just interested in moral fictionalism as mathmatical fictionalism also seems interesting to me too.

[realunoriginal]

Interesting post Joker, but do you really think philosophy or ILP needs more -ists and -isms?? Hehe.

[Joker]

@realunoriginal

Interesting post Joker, but do you really think philosophy or ILP needs more -ists and -isms?? Hehe.

Sure. Deconstruction is inevitable with larger more complex ratios.

[IrvingWashington]

The one thing I never got with moral Fictionalism is why anybody would think it could ever work.

As somebody who has studied a lot of mathematical physics, its as real as words are. Whether thats quite what these guys are saying, I’m not sure.

[north]

@Joker

Fictionalism is a methodological theory in philosophy that suggests that statements of a certain sort should not be taken to be literally true, but merely a useful fiction. Two important strands of fictionalism are modal fictionalism (which states that facts about what might have been the case or what must necessarily be the case are merely fictions) and mathematical fictionalism, which states that talk of numbers and other mathematical objects is nothing more than a convenience for doing science.

Fictionalism consists in at least the following three theses:

Claims made within the domain of discourse are taken to be truth-apt; that is, true or false.
The domain of discourse is to be interpreted at face value–not reduced to meaning something else.
The aim of discourse in any given domain is not truth, but some other virtue(s)(e.g., simplicity, explanatory scope).

Balaguer, Mark (1998). Platonism and Anti-Platonism in Mathematics. Oxford Oxfordshire: Oxford University Press. ISBN 9780195143980.
Kalderon, Mark (2005). Moral Fictionalism. Oxford: Clarendon Press. ISBN 9780199275977.

en.wikipedia.org/wiki/Fictionalism

Mathmatical Fictionalism

Fictionalism was introduced in 1980 when Hartry Field published Science Without Numbers, which rejected and in fact reversed Quine’s indispensability argument. Where Quine suggested that mathematics was indispensable for our best scientific theories, and therefore should be accepted as a body of truths talking about independently existing entities, Field suggested that mathematics was dispensable, and therefore should be considered as a body of falsehoods not talking about anything real. He did this by giving a complete axiomatization of Newtonian mechanics that didn’t reference numbers or functions at all. He started with the “betweenness” of Hilbert’s axioms to characterize space without coordinatizing it, and then added extra relations between points to do the work formerly done by vector fields. Hilbert’s geometry is mathematical, because it talks about abstract points, but in Field’s theory, these points are the concrete points of physical space, so no special mathematical objects at all are needed.

Having shown how to do science without using mathematics, he proceeded to rehabilitate mathematics as a kind of useful fiction. He showed that mathematical physics is a conservative extension of his non-mathematical physics (that is, every physical fact provable in mathematical physics is already provable from his system), so that the mathematics is a reliable process whose physical applications are all true, even though its own statements are false. Thus, when doing mathematics, we can see ourselves as telling a sort of story, talking as if numbers existed. For Field, a statement like “2 + 2 = 4” is just as false as “Sherlock Holmes lived at 221B Baker Street” — but both are true according to the relevant fictions.

By this account, there are no metaphysical or epistemological problems special to mathematics. The only worries left are the general worries about non-mathematical physics, and about fiction in general. Field’s approach has been very influential, but is widely rejected. This is in part because of the requirement of strong fragments of second-order logic to carry out his reduction, and because the statement of conservativity seems to require quantification over abstract models or deductions. Another objection is that it is not clear how one could have certain results in science, such as quantum theory or the periodic table, without mathematics. If what distinguishes one element from another is precisely the number of electrons, neutrons and protons, how does one distinguish between elements without a concept of number?

en.wikipedia.org/wiki/Philosophy … ctionalism

while I think mathematics can basicly make any mathematical equation true ;

I realize at the same time that without mathematics we wouldn’t have built the space shuttle , the refrigerator or the phone without it .

thus for this thread a paradox

[IrvingWashington]

Look, maths can’t make ‘any’ equation true, in the same way that the word ‘hat’ can’t (properly) be used to mean just anything. Its all about conventions. Maths is a language, simple as that. There is no paradox, at least no paradox beyond being able to refer to any object we wish as a hat. What equations you can use, what algebraic manipulations you can make etc are as well defined (actually, better, but its a matter of degree) as what makes a sentence grammatically correct.

We can make space shuttles work because we start with physical phenomena, then describe these phenomena in the language of maths. What this means is we create a model of the situation. The model isn’t the situation in the same way as a description of a space shuttle isn’t a space shuttle. Space shuttles fly because we’ve got a good language going with maths. Mathematical equations aren’t real objects, they describe parts of our model, which isn’t a physical thing.

I hope I’ve got my point across.

[north]

@IrvingWashington

Look, maths can’t make ‘any’ equation true, in the same way that the word ‘hat’ can’t (properly) be used to mean just anything. Its all about conventions. Maths is a language, simple as that. There is no paradox, at least no paradox beyond being able to refer to any object we wish as a hat. What equations you can use, what algebraic manipulations you can make etc are as well defined (actually, better, but its a matter of degree) as what makes a sentence grammatically correct.

perhaps but in physics there ad-hocs to make the equation work

We can make space shuttles work because we start with physical phenomena, then describe these phenomena in the language of maths. What this means is we create a model of the situation. The model isn’t the situation in the same way as a description of a space shuttle isn’t a space shuttle. Space shuttles fly because we’ve got a good language going with maths. Mathematical equations aren’t real objects, they describe parts of our model, which isn’t a physical thing.

I disagree

mathematical equations aren’t real objects in-themselves but they describe real parts of a model which is a physical thing .such as the aerodynamics of flight or the electronic circuts of the shuttle

I hope I’ve got my point across.

not yet

[IrvingWashington]

How can a model be a physical thing? The actual material electronic circuits are physical, but thats not a model, How the circuit operates, as in the actual electronic processes, our description of that is a model Its non-physical. There is a difference between a physical phenomenon and the modelling of it. The physical phenomenon is massive objects falling, the model is gravitation. One is a physical thing, the other a model. Physical theories are like interpretations of reality.

Maths is ad hoc in a sense. In the same sense that language is. We create new words, re-arrange sentences, change grammatical rules over time. But its not ad hoc in the sense that anything goes. The maths used in physics is, again, as ad hoc as a natural language. If you want to introduce some new mathematics, well, thats fine, as long as what you introduce has physical significance (helps with talking about our models) and doesn’t contradict other parts of the language; in the same way that using the same word to refer to contradictory properties would be bad practice in a natural language.

[north]

@IrvingWashington

How can a model be a physical thing?

by being based on the physical aspects of a thing as we understand it

true it can still be a " model " but it is not competely devoid of the physical knowledge we have

The actual material electronic circuits are physical,

yes

but thats not a model, How the circuit operates, as in the actual electronic processes, our description of that is a model Its non-physical.

but it is physical . its based on the physical though . electrons

There is a difference between a physical phenomenon and the modelling of it. The physical phenomenon is massive objects falling, the model is gravitation. One is a physical thing, the other a model. Physical theories are like interpretations of reality.

sure 

and gravitation as a physical thing has yet to be proven . as in gravitational wave or gravitons

Maths is ad hoc in a sense.

its not so much that it math is in itself an ad-hoc but that certain aspects to the equation are added to , to make it work

In the same sense that language is. We create new words, re-arrange sentences, change grammatical rules over time. But its not ad hoc in the sense that anything goes. The maths used in physics is, again, as ad hoc as a natural language.

you can’t compare spoken or writen language to the language of mathematics

true mathematics is " like " a spoken and writen language but mathematics , at least physical mathematics , especially physical mathematics can be changed or manipulated to account for some physical thing which has not been observed or encountered.

If you want to introduce some new mathematics, well, thats fine, as long as what you introduce has physical significance (helps with talking about our models) and doesn’t contradict other parts of the language; in the same way that using the same word to refer to contradictory properties would be bad practice in a natural language.

this is exactly what I mean by ad-hoc mathematics .

true the part of the mathematical equation that is added , doesn’t contradict the other parts of the mathematical language , as it couldn’t really , otherwise it couldn’t be added . what I’m trying to point out is that , what is added doesn’t necessarily mean that it has any real aspect to its self , other than mathematically

[IrvingWashington]

Of course it doesn’t have any real aspect in itself, thats exactly what I was saying! In the same way as ‘hat’ isn’t real. Do you think ‘ad hoc’ is a good phrase for this? After all, mathematicians don;t just pluck new expressions out of thin air. They need to mean something physically,