1Introduction

What do we mean by "software"?

What is the essence of "software"?

The dictionary definitions of "software"12 are too narrow and do not capture the essence of software.

We need an ontology; we need to define and relate these terms: hardware, software, computer, machine, calculator, program, code, language, programmable, error, mistake, bug, fault, malfunction.

[1]

2The word "software"

What can we infer from the etymology and syntax of "software"?

The word "software" appeared no later than Tukey 1958,3 and by it he meant the same thing that most people mean by "software" in 2019, that is, the intangible-but-vital part of computers. Thus, in order for a computer to be useful, both its hardware and its software must be useful.

What is the difference between a softwareless computer and an empty box?

The word "hardware" appeared no later than the 15th century in which it meant "small metal goods". The phrase "hardware store" appeared no later than 1789.4

The word "software" is a mass noun, which is uncountable.

When a non-native speaker writes "a software", he usually means to write "a program" instead.

Uncountable nouns do not have to be abstract nouns. If we can list something, then it is described by a countable noun. There are abstract countable nouns, such as "invitation", "friend", "failure", and "achievement". There are concrete uncountable nouns, such as "water".

Some abstract things are countable, and some concrete things are uncountable. By "uncountable", we mean "impractical to count".

What can we infer from how "software" is used in English?

Semantics of mass nouns [2].

English sometimes hampers thought. We simply accept this syntactic idiosyncrasy as the cost of using English. Let us move on to more important semantic issues.

3Software from Platonism perspective

Software is to hardware as choreography is to dancers. Indeed choreographies are software. Choreographies without dancers are dead ideas. Dancers without choreographies are useless matter.

The dancers are the hardware, the choreography is the software, and the entire performance is the running computer.

I'll be a Platonist here.

A drawing in dance notation5 on a sheet of paper is a representation of several closely-related choreographies. The drawing is not itself a choreography. The choreographies described by that notation are abstract objects with eternal existence in idea space. If the sheet is destroyed, the choreographies persist; for example, the choreographies may be represented in the memories of dancers. Even if there are no people to discover them, the choreographies still exists in idea space.

A drawing cannot practically describe exactly one choreography, because there will always be a slightly different choreography in which the practical means of drawing does not have sufficient fidelity/resolution to describe the difference. For example, suppose that choreography Y is the same as choreography X but with the hand shifted 1 micrometer to the right. It is practically impossible to distinguish X and Y, because it is practically impossible to perceptibly move the hand with micrometer precision.

Thus there be the question: Are ideas discovered or invented? If I invent a word to mean something new, the concept that I mean with that word already exists in idea space. Thus, a Platonist would say that words are invented and concepts are discovered. Thus, for example, when Newton invented calculus, he invented words and notations for concepts that have always existed but not yet known by many people. The concept of derivatives has always existed, but the word "derivative" did not exist before humans existed.

How do we test Platonism? Is it even falsifiable?

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The choreography is the software. The dancer is the hardware.

The recipe is the software. The paper is a representation of the recipe, but not the recipe itself. You can tell the recipe to your friend, without paper. The cook is the hardware.

The music score is the software. The performers are the hardware.

The law is the software. People in government is the hardware.

Software is choreography of hardware. Software is an arrangement.

4The teleology of software

What is software for? What is the purpose of software?

The definition of "chair" is a mixture of ontology and teleology: Ontologically, a chair is something with a back rest. Teleologically, a chair is for humans to sit. Thus, a chair is something that has a back rest and can be used by humans to sit. All those aspects are essential: If any of those aspects is missing, then the object is not a chair.

5The mereology of computers: hardware and software

"Software" and "hardware" are disjoint categories: If something is software, it is not hardware; if something is hardware, it is not software.

A computer is the sum of its hardware and its software. A computer consists of its hardware, its software, and nothing else.

Thus, by the lone unqualified word "software" on its own, we actually mean "the software part of all computers". Thus "software" is like "water": By saying "water exists", we actually mean "there exists an object that has the properties of water".

But software is not purely abstract: It is stored in hardware as an arrangement of materials. But is that software or a representation of software?

What other things can be analyzed as a sum of hardware and software? Laws, choreographies, recipes.

A software house is a company that makes software.

Why "hardware store" but "software house"? A software house is more like a blacksmith's workshop than a hardware store: Things can be made-to-order in a blacksmith's workshop but not in a hardware store. Like "production house" for movies.

Hardware bridges software and reality.

A piece of hardware is a concrete object that can be controlled by an abstract object (a piece of software).

Software is an arrangement of matter (hardware) that makes the hardware useful. But must software have any purpose?

Examples of programming: Designing mechanical linkages. We arrange matter so that it does something we want.

6What can/cannot be done to software?

Software can be copied, but not moved like a concrete object such as a car.

7What is software?

Software is an arrangement of matter (hardware).

Software is executable abstract object?

Software is program, documents, configuration, and so on.

Software is abstract object.

Software is executable mathematics.

Software is an idea.

  • Which ICSE paper said this?
    • Law is software.
    • Process is software.
    • Recipe is software.
  • What is software?

The source code is not the software. Don't commit reification fallacy.

Examples of software?

Programs, laws, choreographies, and recipes are software.

Minds are software?

Software has existed for millenniums, although not called "software".6

8The dualistic nature of machines; the machine-program dualism; the hardware-software dualism

The hardware is the body. The software is the mind.

Are bits software itself, or are bits a representation (embodiment) of software?

A running machine embodies the software it is running?

9Computer vs running computer

A computer has software, but is the computer running?

Software and electricity; running computers vs non-running computers

The operation of a computer requires an energy source.

A computer that is not turned has the potential to compute, in the same way a seed has the potential to grow.

An assignment statement can be modeled by a state endofunction.

10Philosophy?

https://www.perforce.com/blog/modern-software-engineering-meets-philosophy

https://mystudentvoices.com/is-the-programmer-the-new-philosopher-or-software-the-new-philosophy-6c0cbea5b8d2

https://conferences.oreilly.com/software-architecture/sa-ny-2016/public/schedule/detail/50859

https://www.sws.cs.ru.nl/

11Hardness: pure hardware, pure software, and mixtures

If a computer is a mixture of hardware and software, then it makes sense to ask next: How much of it is hardware, and how much of it is software?

We define the hardness of a system as the proportion of it that is hardware.

An example of a pure-hardware system is a mechanical linkage or a salt crystal.

An example of a pure-software system is a mathematical equation or an algorithm.

An example of a mixed hardware-software system is a computer running a program.

If 2 unit of pure hardware is mixed with 8 unit of pure software, then the result should be a 10-unit 20%-hardness system.

The question is: What is that unit?

Does upgrading the hardware of a computer increase its hardness, because upgrading hardware implies adding hardware mass?

Mass is a unit of hardware.

Formula length is a unit of software.

12Computer science terms?

12.1Tools and machines

(I need to find the words to say this, and rewrite this more clearly.)

A machine is an automatic tool: it is a tool that runs by itself; it has its own behavior.

A hammer doesn't have its own behaviors. A car has its own behaviors. A computer has its own behaviors.

12.2What does it mean for a machine to compute a real number?

Computation is approximate expression normalization. To compute a real number is to calculate some of its digits. To compute an arithmetic expression is to evaluate it (to reduce it into a value), often approximately. For example: 1/7 is an expression, and .142 is a value that is the 3 most significant digits of the result of evaluating that expression.

Why do we feel that 1.412 is more evaluated than \(\sqrt{2}\)? Why do we feel that 1.412 is a normal form? Because it is physically easier for us to locate 1.412 on the real number line than to locate \(\sqrt{2}\). Thus to compute a real number is to locate it on the real number line. This justifies the geometric interpretation of real numbers.

We can partially evaluate an expression, such as from 1+2-1 to 3-1.

See also:

Don't conflate a real-number expression and a real number. A real-number expression evaluates to a real number. A real-number expression is not a real number.

Let \(E(\Real)\) be the set of all real-number expressions.

Let \(f:E(\Real)\to\Real\) be the evaluation function.

Questions:

  • What is the machine computing when I'm typing this document?
  • There are several ways of defining the real numbers. Which one should we use for the philosophy of mind and computation, and why?

Algebraic-geometric definition: A real number is a point in the totally-ordered set of points in one-dimensional Euclidean geometry; the real numbers form a field.

Addition also has a geometric meaning: it is the set of points on the plane \(\{(x,y,z) ~\vert~ x+y=z\}\).

12.3Algorithm, machine, describability, computability

We assume that these are primitive concepts: algorithm, machine. By "machine", we mean a computing machine.

An algorithm describes what a machine computes.

An algorithm is an executable description: a string in a formal language in a formal system. A description has finite length. By "executable", we mean that an algorithm has a machine model. We always define an algorithm with respect to a machine.

Thus not every real number is describable, because there are fewer strings in that formal language than there are real numbers.

Thus not every real number is computable, because computability requires describability.

Remember that a formal system is a formal language and a set of inference rules.

An algorithm is a string in a formal language \(L\). We model a machine as a formal system whose language is \(L\). The machine is not the formal system. The thing is not the model.

What does it mean for a machine to compute a real number?

Suppose that \(Y(T) \in \Real\) is the output of the algorithm \(A\) if we let the algorithm run for duration \(T \in \Nat\).

The algorithm \(A\) computes the limit of the approximation sequence \( \langle Y(t) \rangle_{t \in \Nat} \). Thus "\(A\) computes real number \(R\)" means that the limit of that sequence is \(R\).

More explicitly, we say "the algorithm \(A\) computes the real number \(R\)" to mean: for every approximation error \(E > 0\) that we are willing to have, there exists a duration \(T \in \Nat\) such that \(\abs{Y(T) - R} < E\). Informally, the algorithm can always take more time to satisfy ever-diminishing (but still positive) approximation error.

A real number \(R\) is computable iff there is an algorithm that computes \(R\).

There are as many natural numbers as there are algorithms. Therefore not every real number is computable, because there are fewer natural numbers than real numbers.

See also:

12.4What it means for an algorithm to compute a function

The algorithm \(A\) computes the function \(f : A \to B\) iff for every input \(x \in A\), the algorithm outputs \(f(x)\).

12.5Machine, algorithm, embodiment, computation

A machine embodies an algorithm. A machine computes what the algorithm computes.

"To program a machine to compute X" is to arrange the machine to compute X, for example: rewire the machine, load another set of punch cards, write a program in a text editor, etc.

12.6TODO Move this somewhere else: Hierarchy of machines

12.7What is a tool?

Philosophically, a tool is something that extends the user's self (the set of all things that the user can control). But this raises the question: Where is the boundary between two selves?

Economically, a tool is something that increases productivity (output per input).

Teleologically, a tool is something made by man for a specific purpose: A tool makes something easier (or even possible at all).

12.8Should we define one's "self" as the set of all things he can control?

There are lots of parts of one's own body that one cannot fully control, such as his heart, his breathing muscles, his reflexes, etc.

13Language issues in philosophy

Language is more about communication/utility than truth.

13.1The common conflation of something and its representation

Draw a car, and ask someone what it is, and he will probably answer "a car", although, pedantically, it is incorrect, and the correct answer is "the drawing of a car". However, we communicate not to be correct, but to be useful. Thus, in everyday communication, we conflate things and their representations: we often say "X" to mean "a representation of X".

The positions of levers and switches are not software, but a representation of software. The magnetic fields in a hard disk is not data, but a representation of data. Changing the concrete representation of an abstract object affects the represented abstract object.

13.2Words: Invented or discovered?

Neologisms7 prove that words can be invented, such as "grok", "quark", "bromance", and "brexit". But words can also be discovered. For example, Heinlein invented "grok"8, but I discovered it through someone who has read his writing.

But what do we mean by saying that a word exists? If we say that words are invented, then words are not abstract objects in idea space? But a word is not a concrete object, and thus it must be an abstract object. But must it? What if we declare three categories of being instead: concrete objects, abstract objects, and names? Or, can abstract objects be invented?

Plato's Forms are abstract objects, but they are eternal.

Can abstract objects be non-eternal?

Does an idea exist if there is no one to think of it?

But a concept has to be named before it can be thought about and communicated. The name is invented, but the concept is discovered. Thus one job of philosophers is to pick names for concepts that may be important but cannot yet be communicated.

14Bibliography

[1] Gruner, S. 2011. Problems for a philosophy of software engineering. Minds and Machines. 21, 2 (2011), 275–299. url: <https://www.cin.ufpe.br/~ksb/Problems_for_a_Philosophy_of_Software_Engineering.pdf>.

[2] Nicolas, D. 2018. The logic of mass expressions. The stanford encyclopedia of philosophy. E.N. Zalta, ed. https://plato.stanford.edu/archives/win2018/entries/logic-massexpress/; Metaphysics Research Lab, Stanford University.

  1. https://en.wiktionary.org/wiki/software↩

  2. https://www.dictionary.com/browse/software↩

  3. http://www.historyofinformation.com/detail.php?entryid=936↩

  4. https://www.etymonline.com/word/hardware?ref=etymonline_crossreference↩

  5. https://en.wikipedia.org/wiki/Dance_notation↩

  6. https://en.wikipedia.org/wiki/History_of_software↩

  7. https://en.wikipedia.org/wiki/Neologism↩

  8. https://www.etymonline.com/search?q=grok↩