# From Data to Semantic Information

## Abstract

**:**

## 1. Introduction

## 2. The Standard definition of information

#### An Analysis of the Standard Definition of Information

## 3. Alethic neutrality

## 4. Nine bad reasons to think that false information is a type of semantic information

_{1}, e.g. “there will be only one guest for dinner”, and a true but too vacuous FI

_{2}, e.g. “there will be less than a thousand guests for dinner”. What this shows is not (i) that false information is an alethically qualified type of genuine information, but that (ii) false information can still be pragmatically interesting (in the technical sense of the expression, see section two), because sources of information are usually supposed to be truth-oriented or truth-tracking by default (i.e. if they are mistaken, they are initially supposed to be so only accidentally and minimally), and that (iii) logically, an analysis of the information content of σ must take into account the level of approximation of σ to its reference, both when σ is true and when it is false.

## 5. Two good reasons to believe that false information is pseudo-information

## 6. The standard definition of information revised

- σ consists of n data (d), for n ≥ 1;
- the data are well-formed (wfd);
- the wfd are meaningful (mwfd = δ);
- the δ are truthful.

## 7. Conclusion: summary of results and future developments

## Appendix

_{1},…δ

_{n}}

- P.1
- ∀x H(x) ≥ 0
- P.2
- ∀x ∀y (I(x, y) → (H(x) + H(y) = H(x, y))) (additive principle)
- P.3
- ∀x ∀y (R(y, x) ↔ (H(x) + H(y) = H(x))) (general redundancy principle)
- P.4
- ∀x ∀y (x = y → R(x, y) ∨ R(y, x)) (token redundancy principle)
- P.5
- ∀x ((x = σ) → (H(x) > 0))

- I.i.
- |= ∀x (T(x) → (H(x) = 0 → ¬ (x = σ)))

- I.ii.
- |= ∀x (¬ T(x) → (H(x) > 0))

- I.1.
- (T(x) ∧ T(y)) → H(x, y) = 0
- I.2.
- (T(x) ∧ F(y)) → H(x, y) = H(y) > 0
- I.3.
- (T(x) ∧ t/f(y)) → H(x, y) = H(y) > 0
- I.4.
- (F(x) ∧ F(y) ∧ x ≠ y) → H(x, y) = 2H(x)
- I.5.
- (F(x) ∧ F(y) ∧ x = y) → H(x, y) = H(x) > 0
- I.6.
- (F(x) ∧ t/f(y)) → (0 < H(x) < H(x, y) > H(y) > 0)
- I.7.
- (t/f(x) ∧ t/f(y) x ≠ y) → (0 < H(x) < H(x, y) > H(y) > 0)
- I.8.
- (t/f(x) ∧ t/f(y) ∧ x = y) → H(x, y) = H(x) > 0

_{1}, m

_{2}, … m

_{n}, then from M.1 it follows that:

- I.9.
- S → H(m
_{1}) ≤ H(m_{2}) ≤ …H(m_{n}) - I.10.
- ∀m
_{x}∈ S ((x < y) → (P (H(m_{y}) > H(m_{x})) > P (H(m_{y}) = H (m_{x}))))

- R.1
- ¬ (S → H(m
_{1}) ≤ H(m_{2}) ≤ H(m_{3})…) - R.2.a
- ∀m ∈ S ((x < y) → (P (H(m
_{y}) > H(m_{x})) < P (H(m_{y}) ≤ H (m_{x})))) (weaker) - R.2.b
- ∀m ∈ S ((x < y) → (P (H(m
_{y}) ≥ H(m_{x})) < P (H(m_{y}) < H (m_{x})))) (stronger)

- II.i.
- |= ∀x ((T(x) ∨ F(x)) → (H(x) = 0 → ¬ (x = σ))

- II.ii.
- II.ii. |= ∀x (t/f(x) → (H(x) > 0))

- II.1.
- (T(x) ∧ T(y)) → H(x, y) = 0
- II.2.
- (T(x) ∧ F(y)) → H(x, y) = 0
- II.3.
- (T(x) ∧ t/f(y)) → H(x, y) = H(y) > 0
- II.4.
- (F(x) ∧ F(y)) → H(x, y) = 0
- II.5.
- (F(x) ∧ t/f(y)) → H(x, y) = H(y) > 0
- II.6.
- F((t/f(x) ∧ t/f(y)) → (H(x) + H(y) = 0) (consistency condition)
- II.7.
- (¬ F((t/f(x) ∧ t/f(y)) ∧ x = y )) → H(x, y) = H(x) > 0
- II.8.
- (¬ F((t/f(x) ∧ t/f(y)) ∧ x ≠ y )) → (0 < H(x) < H(x, y) > H(y) > 0)

- III.i
- |= ∀x ((T(x) ∨ F(x) ∨ f(x)) → ((H(x) = 0) → ¬ (x = σ)))

- III.ii
- |= ∀x (t(x) → (H(x) > 0))

- III.1.
- (T(x) ∧ T(y)) → H(x, y) = 0
- III.2.
- (T(x) ∧ F(y)) → H(x, y) = 0
- III.3.
- (T(x) ∧ f(y)) → H(x, y) = 0
- III.4.
- (T(x) ∧ t(y)) → H(x, y) = H(y) > 0
- III.5.
- (F(x) ∧ F(y)) → H(x, y) = 0
- III.6.
- (F(x) ∧ f(y)) → H(x, y) = 0
- III.7.
- (F(x) ∧ t(y)) → H(x, y) = H(y) > 0
- III.8.
- (f(x) ∧ f(y)) → H(x, y) = 0
- III.9.
- (f(x) ∧ t(y)) → H(x, y) = H(y) > 0
- III.10.
- (t(x) ∧ t(y)) ∧ x = y) → H(x, y) = H(x) > 0
- III.11.
- (t(x) ∧ t(y)) ∧ x ≠ y) → (0 < H(x) < H(x, y) > H(y) > 0)

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## Notes

^{4}This technical term is used here to mean, weakly, “coming upon something subsequently, as an extraneous addition”. The term is not used with the stronger meaning according to which “if a set of properties x supervenes on another set of properties y, this means that there is no variation with respect to x without a variation with respect to y”. I am grateful to Philipp Keller for having prompted me to add this clarification.^{5}There are many plausible contexts in which a stipulation (“let the value of x = 3” or “suppose we discover the bones of a unicorn”), an invitation (“you are cordially invited to the college party”), an order (“close the window!”), an instruction (“to open the box turn the key”), a game move (“1.e2-e4 c7-c5” at the beginning of a chess game) may be correctly qualified as kinds of information. These and other similar, non-declarative meanings of “information” (e.g. to refer to a music file or to a digital painting) are not discussed in this paper, where objective semantic information is taken to have a declarative or factual value i.e. it is suppose to be correctly qualifiable alethically.^{6}Syntactic information is studied by the Mathematical Theory of Communication, also known as Communication Theory or Information Theory. I have opted for MTC in order to avoid any possible confusion. For an introduction to MTC see chapter five in [24].^{7}See [3]. A pragmatic theory of information addresses the question of how much information a certain message carries for a subject S in a given doxastic state and within a specific informational environment.^{9}This is in line with common practice in AI, Computer Science and ICT (information and communication technology), where the expression “information resources” is used to refer to objective semantic information in different formats, e.g. printed or digital texts, sound or multimedia files, graphics, maps, tabular data etc. [33].^{10}Interested information is a technical expression. The pragmatic theory of interested information is crucial in Decision Theory, where a standard quantitative axiom states that, in an ideal context and ceteris paribus, the more informative σ is to S, the more S ought to be rationally willing to pay to find out whether σ is true [56].^{12}A similar position has been defended more recently in physics by [28], whose work is based on a Platonist perspective.^{13}Note that the conjunction of FI and TI presupposes two theses that are usually uncontroversial: (i) that information is strictly connected with, and can be discussed in terms of alethic concepts; and (ii) that any theory of truth should treat alethic values or concepts symmetrically.^{14}I am grateful to Timothy Colburn and Philipp Keller for having pointed out this other possible source of confusion.^{15}I am very grateful to Frederick R Adams, Ian C. Dengler, Roger Brownsword, Timothy Colburn, James Fetzer, Ken Herold, Bernard Katz, Philipp Keller, Janet D Sisson, and J. L. Speranza for their valuable suggestions on previous drafts of this paper. A more polished version was used by Anthonie W. M. Meijers and his students in a series of lectures about the philosophical aspects of information at the Delft University of Technology, The Netherlands, and I am very grateful to him and those who attended the lectures for their detailed comments.

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**MDPI and ACS Style**

Floridi, L. From Data to Semantic Information. *Entropy* **2003**, *5*, 125-145.
https://doi.org/10.3390/e5020125

**AMA Style**

Floridi L. From Data to Semantic Information. *Entropy*. 2003; 5(2):125-145.
https://doi.org/10.3390/e5020125

**Chicago/Turabian Style**

Floridi, Luciano. 2003. "From Data to Semantic Information" *Entropy* 5, no. 2: 125-145.
https://doi.org/10.3390/e5020125