The web of belief approach: The case with Newton’s physics and relativity

This will not involve many science facts as the discussion is wholly philosophical in nature. This is an epistemological, not scientific essay, it just happens to use some facts of science.

I want to show the value of thinking of things as inconsistent sets of propositions (or whatever truth carrier you like, but I like propositions) or at least implausible sets of propositions (when at least one inference is inductive (or non-deductive, if you like that term better)).

Consider this set of propositions:

  1. Newton’s physics is correct.
  2. Things are in a such and such way at time t1.
  3. That Newton’s physics is correct and things are in a such and such way at time t1, implies that things will happen in such and such way at time t2.
  4. A study found that such and such did not happen at time t2.
  5. The study is correct.
  6. That the study is correct implies that such and such did not happen at time t2.

This set is plainly inconsistent; it cannot be true. At least one proposition in this set is false. Suppose we are around the time when Einstein introduced his relativity theories. At that time physicists had pretty good reason to believe (1) (among others: good explanatory power, lots of empiric confirmation), and I’m sure some people called physicists who did not stop believing in Newton’s physics even when some studies found results that are contrary to the predictions of Newton’s physics given some antecedent state of affairs dogmatic. I’m fairly sure such a claim of dogmatism is often thrown around in similar cases.

My point is that it is unwise to claim someone is being dogmatic quickly. For there are many things other than some widely accepted theory that could be wrong (in this case (1)). We could be wrong about the antecedent states of affairs (in this case (2)), or wrong about what the theory predicts (in this case (3)) given that state of affairs; perhaps the scientist that make the prediction from the theory made a calculation error. Something similar applies the the study that ‘challenges’ the accepted theory (in this case (5)). So there are many things that could be wrong without the accepted theory being false. It is wise to consider that before calling people that are being epistemically conservative for dogmatic.

The method of putting the relevant propositions in an inconsistent set forces us to be made aware of some perhaps not normally discussed propositions without which the set would be consistent (or not-implausible). Usually in a moderately complex case such as the one with Newton’s physics, a set of propositions that form as inconsistent set (or implausible) will contain 5-10 propositions. In more complex cases, the sets can be much longer (such as very complex cases involving the impossibility of an infinite past which involves temporal and modal logic). In general, the more propositions we can find that together forms an inconsistent set (or implausible), the better overview, and the easier to is to make a justified decision about which proposition(s) to stop believing in in the case that one actually believes all of them. If we are to avoid inconsistent beliefs (=inconsistent objects of beliefs), then we should think of the many potentially epistemically justified ways there are to deal with a such inconsistent set.

In the above case, rejecting (4) would probably not be a wise decision, neither would it be to reject (6). If there is only one study and it is not exceptionally well done, then rejecting (5) is probably not a bad decision to begin with. If more studies (by competent scientists) confirm the first study, then sooner or later we should begin wondering if not our beliefs would have better coherence were we to reject the theory (1). But before we do that we should consider other alternatives such as (2) and (3). It would not be good if we rejected some theory and later found it that we had no grounds to do that because we were wrong about what the antecedent state of affair was (2).

This way of solving problems (which usually involve an inconsistency of we add together the relevant propositions to a set), is applicable to every topic that I have thought of. It is especially useful to very complex situations where it is hard to get an overview and it seems hard to settle on a specific solution (that is, hard to find out which proposition is the epistemically most justified to deny).

What does “begging the question” mean?

Introduction

Abstract

In this essay I attempt to clarify what it means to say that an argument begs the question. One may think that it is a fairly straightforward matter but my analysis reveals that it isn’t so.

Shorthands

“BTQ” means begging the question, or begs the question whichever is grammatically correct on the context.

The phrase “begs the question” in english

The phrase “begs the question” has at least two meanings in english. The first and perhaps most common meaning is that of raising an important question. As it is written on FallacyFiles.org:

The phrase “begs the question” has come to be used to mean “raises the question” or “suggests the question”, as in “that begs the question” followed by the question supposedly begged. The following headlines are examples:

        • Warm Weather Begs the Question:
          To Water or Not to Water Yard Plants

        • Latest Internet Fracas Begs the Question:
          Who’s Driving the Internet Bus?

        • Hot Holiday Begs Big Question:
          Can the Party Continue?

This is a confusing usage which is apparently based upon a literal misreading of the phrase “begs the question”. It should be avoided, and must be distinguished from its use to refer to the fallacy.”1

The second meaning of “beg the question” is in the informal logical fallacy of begging the question. It is this meaning that this essay attempts to clarify.

Proposed definitions

So what does it mean to say that an argument BTQ? There are surprisingly many different answers from good sources. Below I quote many of the different definitions given, some by authorities and some not.

FallacyFiles.org

In an article entitled “Begging the Question” FallacyFiles.org writes:

“The phrase “begging the question”, or “petitio principii” in Latin, refers to the “question” in a formal debate—that is, the issue being debated. In such a debate, one side may ask the other side to concede certain points in order to speed up the proceedings. To “beg” the question is to ask that the very point at issue be conceded, which is of course illegitimate. “2

And:

“Any form of argument in which the conclusion occurs as one of the premisses, or a chain of arguments in which the final conclusion is a premiss of one of the earlier arguments in the chain. More generally, an argument begs the question when it assumes any controversial point not conceded by the other side.”3

Notice how vague the one mentioned in the first paragraph is. To the defense of FallacyFiles.org, we may note that that paragraph is entitled “Etymology”, and is perhaps not meant to actually explain clearly what it means to BTQ but only to explain how the etymology relates to the meaning of the term.

The second paragraph is entitled “Exposition” and is clearly meant to explain the meaning of the term. However the paragraph features two independent definitions, a strict (which is a disjunction) and a general (or rather, broad) one.

butterfliesandwheels.com

In the article entitled “Bad Moves: Begging the question” butterfliesandwheels.com writes:

“Begging the question – assuming what needs to be argued for [...]”4

skepdic.com aka. The Skeptic’s Dictionary

In an article entitled “begging the question” it is written on skepdic.com:

“Begging the question is what one does in an argument when one assumes what one claims to be proving.”5

And a bit later:

“If one’s premises entail one’s conclusion, and one’s premises are questionable, one is said to beg the question.”6

Notice that these two definitions are not at all identical. Examples will show this later.

Wikipedia.org

In an article entitled “Begging the question” it is written on Wikipedia.org:

“The fallacy of petitio principii, or “begging the question”, is committed “when a proposition which requires proof is assumed without proof.”[3] More specifically, petitio principii refers to arguing for a conclusion that has already been assumed in the premise. The fallacy may be committed in various ways.

When the fallacy of begging the question is committed in a single step, it is sometimes called a hysteron proteron,[4] as in the statement “Opium induces sleep because it has a soporific quality”.[5] Such fallacies may not be immediately obvious in English because the English language has so many synonyms; one way to beg the question is to make a statement first in concrete terms, then in abstract ones, or vice-versa.[5] Another is to “bring forth a proposition expressed in words of Saxon origin, and give as a reason for it the very same proposition stated in words of Norman origin”,[6] as in this example: “To allow every man an unbounded freedom of speech must always be, on the whole advantageous to the State, for it is highly conducive to the interests of the community that each individual should enjoy a liberty perfectly unlimited of expressing his sentiments.”[7]

When the fallacy of begging the question is committed in more than one step, it is sometimes referred to as circulus in probando or reasoning in a circle[4] but incorrectly if we look at the definition Aristotle gave us in Prior Analytics.[1]

“Begging the question” can also refer to making an argument in which the premise “is different from the conclusion … but is controversial or questionable for the same reasons that typically might lead someone to question the conclusion.”[8]”7

And:

“In informal situations, the term begging the question is often used in place of circular argument. In the formal context however, begging the question holds a different meaning.[1] In its shortest form, circular reasoning is the basing of two conclusions by means of which there is demonstrated a reversed premise of the first argument. Begging the question does not require any such reversal.

Begging the question is similar to the Fallacy of many questions: a fallacy of technique that results from presenting evidence in support of a conclusion that is less likely to be accepted than merely asserting the conclusion. A specific form of this is reducing an assertion to an instance of a more general assertion which is no more known to be true than the more specific assertion:

* All intentional acts of killing human beings are morally wrong.

* The death penalty is an intentional act of killing a human being.

* Therefore the death penalty is wrong.

If the first premise is accepted as an axiom within some moral system or code, this reasoning is a cogent argument against the death penalty. If not, it is in fact a weaker argument than a mere assertion that the death penalty is wrong, since the first premise is stronger than the conclusion.”8

New York Times

In an article entitled “ON LANGUAGE; Take My Question Please!” it is written in New York Times:

“”This sentence fragment uses ‘begs the question,’ ” he writes, ”in the sense of a question that begs to be asked, usually because it is obvious to all. However, I am plagued by my logic course of some years ago, which taught me that begging the question is nothing of the kind. Rather, begging the question is a logically invalid form of argument that uses the point to be proven as part of the argument for its proof.”

Amen. Readers have been protesting this misuse of a term about a concept set down by Aristotle, a student of Plato Cacheris, in his book on logic written about 350 B.C. (Here comes mail on B.C.E.) His Greek term en archei aiteisthai was translated by the Romans as petitio principii, and rendered into English in 1581 as begging the question. In whatever language, it described the fallacy known as ”the assumption at the outset.”

In his 1988 book, ”Thinking Logically,” Prof. James Freeman explains: ”An argument begs the question when the conclusion, in the same or different words, or a statement presupposing the conclusion, is introduced as a premise. The case for the conclusion ultimately depends on accepting the conclusion itself.””9

Notice how it says that it is an invalid form of argument. But surely any argument that commits the strict fallacy of BTQ, that is, the conclusion is identical to a premise, is a valid argument. Why? Valid arguments are precisely those arguments where the premises logically imply the conclusion. Since any proposition implies itself [P⇒P], then any argument that BTQ in the strict sense is valid.

nizkor.org

In an article entitled “Fallacy: Begging the Question” it is written on nizkor.org:

“Begging the Question is a fallacy in which the premises include the claim that the conclusion is true or (directly or indirectly) assume that the conclusion is true. This sort of “reasoning” typically has the following form.

1. Premises in which the truth of the conclusion is claimed or the truth of the conclusion is assumed (either directly or indirectly).

2. Claim C (the conclusion) is true.

This sort of “reasoning” is fallacious because simply assuming that the conclusion is true (directly or indirectly) in the premises does not constitute evidence for that conclusion. Obviously, simply assuming a claim is true does not serve as evidence for that claim. This is especially clear in particularly blatant cases: “X is true. The evidence for this claim is that X is true.”

Some cases of question begging are fairly blatant, while others can be extremely subtle.”10

The Cambridge Dictionary of Philosophy

In an article entitled “Circular Reasoning” Robert Audi writes:

“circular reasoning, reasoning that, when traced backward from its conclusion, returns to that starting point, as one returns to a starting point when tracing a circle. The discussion of this topic by Richard Whatley (1787–1863) in his Logic (1826) sets a high standard of clarity and penetration. Logic textbooks often quote the following example from Whatley:

To allow every man an unbounded freedom of speech must always be, on the whole, advantageous to the State; for it is highly conducive to the interests of the Community, that each individual should enjoy a liberty perfectly unlimited, of expressing his sentiments.

This passage illustrates how circular reasoning is less obvious in a language, such as English, that, in Whatley’s words, is “abounding in synonymous expressions, which have no resemblance in sound, and no connection in etymology.” The premise and conclusion do not consist of just the same words in the same order, nor can logical or grammatical principles transform one into the other. Rather, they have the same propositional content: they say the same thing in different words. That is why appealing to one of them to provide reason for believing the other amounts to giving something as a reason for itself. Circular reasoning is often said to beg the question. ‘Begging the question’ and petitio principii are translations of a phrase in Aristotle connected with a game of formal disputation played in antiquity but not in recent times. The meanings of ‘question’ and ‘begging’ do not in any clear way determine the meaning of ‘question begging’. There is no simple argument form that all and only circular arguments have. It is not logic, in Whatley’s example above, that determines the identity of content between the premise and the conclusion. Some theorists propose rather more complicated formal or syntactic accounts of circularity. Others believe that any account of circular reasoning must refer to the beliefs of those who reason. Whether or not the following argument about articles in this dictionary is circular depends on why the first premise should be accepted:

(1) The article on inference contains no split infinitives.

(2) The other articles contain no split infinitives.

Therefore, (3) No article contains split infinitives.

Consider two cases. Case I: Although (2) supports (1) inductively, both (1) and (2) have solid outside support independent of any prior acceptance of (3). This reasoning is not circular. Case II: Someone who advances the argument accepts (1) or (2) or both, only because he believes (3). Such reasoning is circular, even though neither premise expresses just the same proposition as the conclusion. The question remains controversial whether, in explaining circularity, we should refer to the beliefs of individual reasoners or only to the surrounding circumstances. One purpose of reasoning is to increase the degree of reasonable confidence that one has in the truth of a conclusion. Presuming the truth of a conclusion in support of a premise thwarts this purpose, because the initial degree of reasonable confidence in the premise cannot then exceed the initial degree of reasonable confidence in the conclusion.”11

What can we gather from this?

There is consensus about a strict definition of BTQ which is identical to circular logic. This is defined as: An argument is circular iff one of the premises is identical to the conclusion.

There is no consensus about a broad definition of BTQ. At best this is some intuitive notion. Further analysis could try to find a meaning appropriate for this broad sense. That task I will take up in a forthcoming essay.

Notes

1www.fallacyfiles.org/begquest.html. See also Gary Curtis, “Please Stop Begging that Question You’re Raising”, The Editorial Eye, 2/2007

2Ibid.

3Ibid.

6Ibid.

8Ibid.

9www.nytimes.com/1998/07/26/magazine/on-language-take-my-question-please.html ON LANGUAGE; Take “My Question Please!”, By William Safire, Published: Sunday, July 26, 1998

11Robert Audi, The Cambridge Dictionary of Philosophy, Second edition, p. 177

An examination of randomness in Heroes of Newerth

An examination of randomness in Heroes of Newerth

———–

First published June 12, 2010.

Revised 30 July, 2010.

Introduction

In this essay I will examine the different kinds of randomness involved in Heroes of Newerth (=HON). Later I suggest some ways to reduce or remove the effects of randomness on gameplay.

Randomness affected elements

Randomness adds a luck factor to a game. A player is lucky, if a random element comes out in his favor. The randomness that I am talking about in this essay is the kind that is uncontrollable by players. I am not talking about any other kinds of randomness. For instance, as when a player teleports to safety because the players of the other team lost sight of him in the woods. Often, such players are called lucky. I am not interested in that kind of luck in this essay.

Randomness affected elements in HON

In this section I will document all elements of HON that are affected by randomness. I may have missed some. If I did, please notify me.

Hero abilities

In this section I will document the randomness elements in the abilities of heroes. I will do that by mentioning the hero name in headline 3 (in bold). The ability name in headline 4 (in italic). I will then copy (if possible) the description of the skill from the official homepage. Sometimes I will omit irrelevant parts of the description. All text that is copied or almost copied is placed in an indentation one level to the right. Text not placed in a such indentation are my comments on the copied text which is usually clarification or notes about whether something is random or not.

Swiftblade

Counter Attack

Extensive training in melee combat has allowed Swiftblade to perfect the art of countering enemy attacks, granting a chance that he will retaliate every time an enemy hero attacks him.

On Attack

15 / 20 / 25 / 30% chance to counter-attack if attacker is an enemy hero.

“On attack” should be understood as “when attacked”.

Way of the Sword

Swiftblade’s unsurpassed skill at the sword has made him a master of hitting where it hurts, giving him a chance to critically strike opponents with each attack.

10 / 18 / 26 / 36% chance to do 2x damage.

Swift Slashes

Swiftblade attacks random nearby targets with such speed that he appears to teleport to them. Targets are randomly chosen, yet it is possible to teleport to the same target multiple times.

Teleports self to random targets 3 / 5 / 8 times, dealing 150 to 250 Physical damage to each target. Applies Swift Slashes to self for duration of activation.

Moon Queen

Multi-strike

The Moon Queen’s skill with her Luna Shuriken allows her to bounce it from her primary target to hit additional foes.

Activation

When toggled on, attacks on Hero targets will only bounce to other visible enemy heroes.

On Attack

Attack bounces up to 1 / 2 / 3 / 4 times to enemy units and buildings. Deals 35% less damage per bounce.

I’m not sure whether this feature is random or not, but it may be. I’m guessing that it works in either of these two ways: 1. The shurikens bounce to a random target within a set radius, 2. It bounces automatically to the nearest target in a set radius.

Moon Finale

Casts 4 / 7 / 10 Moon Beams on random targets in radius. Maximum of 4 hits per target. Moon beams deal 300 damage per hit.

Wildsoul

Summon Beardulon

Wildsoul summons his pet bear, Beardulon

Activation

Summons Beardulon at target location. Beardulon cannot be summoned if he is currently active.

Beardulon has the ability to carry items.

-Increasing the level of the ability grants Beardulon more health and armor

-Level 1, Beardulon learns the Return ability

-Level 3, Beardulon learns the Entangling Claws ability.

-Level 4, Beardulon learns the Demolish and Magic Resist abilities.

There is a cooldown of 5 seconds on the Entangling Claws ability. It is not documented what the % chance of entangling an enemy is.

Zephyr

Wind Shield

Zephyr uses his control of the wind to create a protective barrier around himself, increasing his evasion and speeding him up. The barrier also has a chance to redirect incoming projectile based attacks back at the attacker.

Activation

Applies Wind Shield to self for 10 / 15 / 20 / 25 seconds.

On Attack

Applies Wind Shield to self for 3 seconds when Zephyr lands an attack

This ability contains Evasion properties. Evasion properties do not stack. Instead, you will automatically use the Evasion from the item or ability that grants you the highest chance to evade.

Wind Shield Effects

6 / 9 / 12 / 15% Melee Evasion

10% Movement Speed

6 / 9 / 12 / 15% chance to redirect projectile based attacks back at the attacker.

Chronos

Rewind

Chronos steps back through time when damaged, giving him a chance to undo damage taken quickly.

On Damage

10 / 15 / 20 / 25% chance to heal damage taken. Heal occurs at a rate of 25% of maximum health per second.

Scout

Disarm

The Scout’s mastery of close range combat allows him to occasionally disarm an opponent, then take advantage of the opening with a devastating attack.

On Attack

10 / 15 / 20 / 25% chance to disarm opponent for 1 seconds and deal a 1.25 / 1.5 / 1.75 / 2.0x critical strike.

Once disarmed, opponents cannot be disarmed again by the scout for 2 seconds.

Valkyrie

Call of the Valkyrie

Valkyrie calls forth several Battle Maidens to damage nearby enemies.

Activation

Deals 75 / 150 / 225 / 300 Magic damage to targets in radius around self.

Deals an additional 37.5 / 75 / 112.5 / 150 Magic damage to one random target in a 200 radius.

Blacksmith

Chaotic Flames

Fireball:

– When cast, has a {25,40,50}% chance to impact at least twice, {0,20,25}% chance to impact at least three times, {0,0,12.5}% chance to impact four times.

Frenzy:

– When cast, has a {25,40,50}% chance to cast twice, {0,20,25}% chance to cast three times, {0,0,12.5}% chance to cast four times.

Glacius

Glacial Downpour

Glacius showers the area around him with shards of ice. The shards will randomly strike around Glacius, slowing the attack and movement speed of nearby enemies and dealing intense damage to them.

Activation

Spawns an Ice Shard every 0.1 seconds at a random location within radius for 4 seconds or until ability is cancelled. Applies Glacial Freeze to targets within a 200 radius of where an Ice Shard impacts and damages them for 105 / 170 / 250 Magic damage.

Voodoo Jester

Acid Cocktail

Voodoo Jester throws a wretched mix of cursed chemicals at an enemy, stunning them and nearby units one after the other.

Activation

Deals 75 / 100 / 125 / 150 Magic damage and stuns target for 1.5 second on heroes and 5 seconds on creeps. Bounces 2 / 4 / 6 / 8 times. Bounces deal no damage to heroes and stun for 1 second.

It seems that the target for the next bounce is chosen randomly within some radius.

Torturer

Impalement

The Torturer constantly summons many blades around him for a duration, impaling random enemies and structures near him.

Activation

Deals 9.375 / 18.75 / 28.125 / 37.5 Physical damage to a random target in radius every 0.25 seconds for 8 seconds, for a total of 300 / 600 / 900 / 1200 Physical damage.

Plague Rider

Plague Carrier

The Plague Rider lets loose a Plague Carrier towards an enemy. The Carrier deals damage to the target it lands on before traveling to another nearby target. Any enemy near someone hit becomes Infected.

Activation

Deals 280 / 370 / 460 damage to the target, bouncing to another enemy within 600 units. Bounces 7 times.

The target is apparently chosen randomly within the radius.

War Beast

Summon Hellhounds

War Beast Summons forth Hellhounds from the underworld to attack his enemies.

Activation

Summons 2 Hellhounds for 55 seconds.

Hellhounds have 400 / 475 / 550 / 625 Health, deal 17 / 27 / 34 / 43 to 18 / 30 / 40 / 49 Physical damage per attack, and have an attack cooldown time of 1.25 seconds. Their attacks have a 0 / 30 / 30 / 30% chance to do 1.5x normal damage.

Pharoh

Hellfire

Pharaoh conjures plumes of fire around him for a short duration, hitting random nearby enemy targets, damaging each and stunning them briefly.

Activation

For 10 seconds, impacts a random target in radius every 0.75 seconds, dealing 10 / 30 / 50 / 70 Magic damage and stunning them for 0.1 seconds.

Legionnaire

Whirling Blade

The Legionnaire’s skill with a Battle Axe is unrivaled. Every time he is attacked, he has a small chance to perform a Whirling Blade maneuver, which damages all nearby enemies.

On Attack

17% chance to damage enemies in 300 radius for 100 / 125 / 150 / 175 when attacked.

“On Attack” should be understood as when attacked.

Rampage

Horned Strike

There is a chance Rampage’s rhino unleashes a devastating Horned Strike when he begins an attack, doing bonus damage and pushing then enemy backwards.

On Attack

17% chance on attack to stun and push back the target 140 / 180 / 220 / 260 units over 0.95 / 1.15 / 1.35 / 1.55 seconds, dealing 25 / 50 / 75 / 100 bonus Magic damage.

Pestilence

Gore

Pestilence gains a chance to stab an enemy unit with his frontal horn when attacking, causing them to take some additional damage and be stunned briefly.

On Attack

10 / 15 / 20 / 25% chance to deal 40 / 50 / 60 / 70 bonus Magic damage to target and stun for 1 second.

Maliken

Possession

Maliken allows himself to become possessed, transforming him into a full daemon temporarily. While in this form, Maliken’s attack becomes ranged and he attacks faster.

Activation

Applies Possessed to self for 30 seconds. Applies Feared to enemy heroes in a 400 radius for 0.75 / 1.25 / 2 seconds.

Possessed Effects

+20 / 40 / 60 Armor for the first 2 seconds, decreasing to +0 armor over the next 5 seconds.\n\nAttack Type changes to Ranged, with a range of 550.\n\nAttacks splash to nearby units.\n^y50 / 75 / 100%^* Splash in a 75 AOE\n^y35 / 50 / 65%^* Splash in a 200 AOE\n^y20 / 25 / 30%^* Splash in a 350 AOE

Feared

40% Movement Speed

Perplexed

Silenced

Disarmed

Lose character control, running around in fear

As far as I can tell. The movement caused by Feared is random.

Runes

A rune spawns every two minutes at a randomly chosen location from two possible. The type of rune spawned is random but is one of the following: Regeneration, Double-Damage, Illusion, Invisibility or Haste.

Neutral creep spawns

Neutral creeps spawn in the forest at 0:30 and afterwards at every whole minute (= at xx:00). The creeps spawn in camps located in the woods at each side of the river in the middle. There is an easy camp, two moderate camps, two hard camps in each team’s large forest. There is also an ancients camp on the other side of the road. Each spawn has a number of different creeps that can spawn there with varying difficulty. Some slow, some disspell buffs, some has poisonous attacks, some stun, some are more numerous than others, some do more damage than others and some are magic immune. Many heroes have problems (especially Zephyr and Tempest) killing the magic immune creeps and they are often avoided in the early game. Some heroes (Zephyr and Legionnaire) benefit from there being many creeps at a spawn location.

Damage intervals

All heroes, all creeps, and all towers (but maybe not the well/tar pit) do damage chosen from some interval. The exact damage is seemingly chosen at random in the interval. Sometimes this matters more than others. Especially in the case of last-hitting it matters a lot as one often fails to get a last hit if one gets a low damage number on the interval.

Damage intervals are common to many games. Some games, however, feature ways to reduce the randomness introduced by such intervals. Team Fortress 2, for instance, has a server-side variable where one can disable the intervals and use instead a fixed number on all hits.

Game modes

Banning modes

One might think which heroes are banned is a randomness factor, but it is not. It is controllable by players though, of course, only a single player.

Draft modes

Which heroes are selected for the game is randomly chosen.

Force random

Obviously the heroes are here selected at random.

Items

In this section I will document randomness elements in items. I will do that by copying the relevant description text from the official homepage. Item names are in type 3 headlines (in bold). The copied description is placed in an indentation one level to the right as in the Hero Abilities section. Any text below the text in the indentation are my comments.

Iron Buckler

60% chance to block 20 attack damage. Only 10 damage is blocked for ranged heroes.

Halberd

On attack. 15% chance to deal 40 physical damage to target.

Snake Bracelet

25% evasion.

Helm of the Black Legion

70% chance to block 40 attack damage.

Riftshards

10% chance for 1.8 / 2 / 2.2 / 2.4x critical strike.

Savage Mace

On attack. 35% chance to deal 100 physical damage to target and stun for 0.1 seconds.

Wingbow

30% evasion.

Brutalizer

25 / 10 (for melee / range) chance to stun for 1.4 seconds.

Thunderclaw

20% chance to cast Chain Lightning on target and two additional targets on attack. Deals 150 magic damage.

Additional targets are seemingly chosen randomly within a radius.

Charged Hammer

20% chance to cast Chain Lightning on target and two additional targets on attack. Deals 200 magic damage.

On activation casts Charged Up on target. When attacked with Charged Up on self, one has 20% chance to do 200 magic damage to the attacker and two nearby targets.

As with above, the additional targets seem to be chosen randomly within a radius.

Other randomness elements

Kongor

Kongor has a bash ability.

Uphill attacking

Attacking a target uphill gives a 20% chance to miss.

Discussion of how to change randomness factors into non-random factors

There are mainly two kind of randomness abilities: First, skills that has a % chance to activate on a single target per hit/attack; single target abilities. Second, skills that target a random target in some radius; random target abilities.

Single target randomness abilities

One way to change critical hits based solely on chance (based on some % to get a critical hit) into a non-random element, is to remove the % part and set a necessary and sufficient condition to get the effect. Two examples of this. First, in a recent patch, Chronos’s bash ability (Time Freeze/Curse of Ages) was changed from having a chance to bash the opponent to bashing every 4 hits.

0.1.66:

[...]

Time Freeze reworked: now Curse of Ages

-Steals 1/2/3/4 agility per hit, debuff lasts 10 seconds.

-The 4th consecutive hit on a target stuns it for 1 second during which Curse can no longer add charges to the target or build towards a stun.

-Does not stack with Brutalizer.

-Every action allies take while in Chronosphere is slowed by 90% (MS, AS, CS). This value changes to 80% with Staff of the Master. (source)

Second, Night Hound’s critical hit ability (Backstab) has the condition that it only works when Night Hound is attacking a target from behind. This is unlike the similar hero, Scout, ‘s critical ability (Disarm).

Interesting conditions for abilities are:

    Activate if and only if (iff):

  • Target has a higher/lower average/min/max damage than self
  • Target is higher/lower/equal in level to self
  • Target has more/less current/max hp/mp than self
  • Target is facing you
  • Target has recently attacked a teammate of your

One more examples of such conditions in use. Target is not near any ally is used in Sand Wraith’s critical ability (Deserted).

Random target abilities

A way to change these is to introduce some condition for how they target players. Examples are:

  • The nearest/farthest player
  • The player with the most/less current hp/mp
  • The player with the most/less max hp/mp

If we think of Plague Rider’s ultimate (Plague Carrier) these will have different effects:

  • Targeting the nearest player will cause the ultimate to bounce faster and longer. The opposite effect for the farthest player.
  • If targeting the most current hp, then it will result in less kills from the ultimate, however the team will take more damage in total (supposing that any damage that is in excess is reduced to 0). If the most hp, then it will result in more kills. Clever positioning can make the ultimate stop before hitting 7 times.
  • If targeting the most max hp, then it will result in bouncing a lot between high hp heroes (say, two str heroes) making this ultimate easier to counter with good positioning. If targeting the less max hp, it will result in bouncing between agi/int heroes more, scoring more kills. Giving these heroes magic armor (which does not give more max hp) then will result in a more ineffective ultimate (in total damage done after armor reduction). It will be easier countering this ultimate with clever item builds (the two lowest max hp get Headdress/Idol).

Runes spawns

Instead of having rune types random, one could have them spawn in sequences. Instead of having rune spawn locations random, one could have a new spawn each time at alternating locations. This is easily done for runes in a way that is easy to remember because there are five different runes that spawn every 2 minutes. Players merely have to remember the last digit to know which rune will spawn. Assuming that: 1. that bot is the first location, 2. that the sequence is Double-Damage/Illusions/Regeneration/Invisibility/Haste, then it would go like this:

Location Time (in minutes) Rune
Bot 0 Double-Damage
Top 2 Illusions
Bot 4 Regeneration
Top 6 Invisibility
Bot 8 Haste
Top 10 Double-Damage
Bot 12 Illusions
Top 14 Regeneration
Bot 16 Invisibility
Top 18 Haste

To avoid the the spawns repeating, one could make rune spawns depend on some condition. An interesting condition is that it spawns the place where all the players are the closest to at average. This means that players could have the rune spawn near them by clever positioning.

For instance, suppose that in the 13th minute, 4 players on a team are out ganking and have run out of mana. They notice that in 30 seconds, a regeneration rune will spawn (because the last digit is 4), so they all go to the nearby rune spot. By being so close to the spot, the reduce the average range to that rune spawn area a lot, thereby increasing the chance (seen from their perspective, it’s not a randomness factor in the relevant sense, the reason for the probability is that they don’t know where the entire other team is) that the rune will spawn there.

Creep spawns

Similar to the sequence idea with runes above, creeps could spawn in such sequences, or the special type of creep could spawn for each 10 minute interval. For instance, by having the weakest creeps spawn in the first 10 minutes of the game. This would remove the randomness factor of getting lucky with the creep spawns as, for instance, Zephyr (in which where you want the group of 5 weak enemies, not the group of 3 with a slow debuff).

Uphill attacking

One way to remove the randomness here is to decrease the damage done uphill instead of having a 20% chance to miss. In the big perspective, this will result in the same amount of damage, so there will still be a penalty by attacking uphill but it is no longer random and can be taken into account by skilled players. For instance, when a player is last-hitting uphill, a good tactic is to wait a bit longer before attacking the creep since one’s attacks will do less damage.

The contagiosity of meaninglessness – formalised for propositional logic

In an earlier essay I mentioned that that meaninglessness is contagious with respect to sentences. One can pretty easily formulate the principle in normal english – if a sentence is meaningless, then so is any more complex sentence of which it is a part of. To get a proper, formal formulation of this we may simply think of the rules in logic systems used to form well-formed formulas (=wff’s) and then formulate some similar principles for the meaninglessness of sentences. Here’s what I have in mind:

Negation. For all sentences, iff it is not the case that a sentence is meaningful, then it is not the case that the negation of that sentence is meaningful.

(∀S)(¬M(S)↔¬M(¬S)

Conjunction part. For all sentences, if it is not the case that a sentence is meaningful, then for all sentences, it is not the case that the conjunction of that sentence with another sentence is meaningful.

(∀S)(¬M(S)→(∀Z)¬M(S∧Z)1

Disjunction part. For all sentences, if it is not the case that a sentence is meaningful, then for all sentences, it is not the case that the disjunction of that sentence with another sentence is meaningful.

(∀S)(¬M(S)→(∀Z)¬M(S∨Z)

Implication/conditional part. For all sentences, if it is not the case that a sentence is meaningful, then for all sentences, it is not the case that the implication of the first sentence to the second is meaningful, and it is not the case that the implication of the second sentence to the first is meaningful.

(∀S)(¬M(S)→(∀Z)¬M(S→Z)∧¬M(Z→S))

Bi-implication/bi-conditional part. For all sentences, if it is not the case that a sentence is meaningful, then for all sentences, it is not the case that the bi-implication of the first sentence to the second is meaningful, and it is not the case that the bi-implication of the second sentence to the first is meaningful.

(∀S)(¬M(S)→(∀Z)¬M(S↔Z)∧¬M(Z↔S))

This should cover propositional logic. It is left to the reader can invent the relevant principles for modal logics and predicate logic.

Notes

1Notice here that the bi-conditional version is false because it could be the other conjunct that is meaningless instead. However, at least one of them is meaningless.

Sentence theories of truth, meaningless sentences and untrue sentences

By sentence theory I just mean a theory of truth carriers that implies that some sentences are true or some are false. Not necessarily a monist sentence theory (=theory that implies that sentences are the only kind of truth carriers) or a theory of sentences as primary truth carriers (=theory that implies that sentences are the primary truth carriers). For more about these terms, see my earlier writings on the subject.

Anyway, I read the newest post on my favorite logic blog (Blog&~Blog). It dealt with the sentences which I have given incredibly clever names (in footnotes):

For all sentences, if it is not the case that it is meaningful, then it is not the case that it is true.

NMNT.1 (∀S)(¬M(S)→T(S))

For all sentences, if it is not the case that it is meaningful, then it is not the case that it is false.

NMNF.2 (∀S)(¬M(S)→F(S))

With the obvious interpretation keys.

This seems like plausible sentences to many when faced with sentences such as the Chomsky:

C. Colorless green ideas sleep furiously.

Which Ben, btw, got wrong as he forgot the first word.

Let’s also agree that:

1. It is not the case that C is meaningful.

¬M(C)

However, this along with some other sentences is inconsistent (=implies a contradiction). First sentence bivalence:

SB.3 For all sentences, it is either true or it is false.

(∀S)(T(S)∨F(S))

The contradiction is easy to derive here:

2. ¬T(C) [from 1, NMNT, MP]

3. ¬F(C) [from 1, NMNF, MP]

4. T(C) [from 3, SB, DS]

5. T(C) ∧¬T(C) [from 2, 4, conj.]

Contradiction! So this doesn’t work. Here I told Ben (author of the blog) that I would drop SB.4 However that apparently doesn’t work either.

Say hi to the T-schema, or the semantic theory of truth:

TS1. For all sentences, iff it is true, then it is the case.

(∀S)(T(S)↔S)

TS2. For all sentences, iff it is false, then it is not the case.

(∀S)(F(S)↔¬S)

Now these are obvious to most people. Not something is that plausible to deny unless the alternatives are really bad. However from these one can get their contra-positional versions:

TS1-CP. For all sentences, iff it is not the case, then it is not the case that it is true.

(∀S)(¬S↔¬T(S))

TS2-CP. For all sentences, iff it is not the case that it is not the case, then it is not the case that it is false.

(∀S)(¬¬S↔¬F(S))

And from these, we can derive their converses (and we can do that because these are bi-conditionals that can be conversed without problems). Do the same for TS1 and TS2:

TS1-CP-C. For all sentences, iff it is not the case that it is true, then it is not the case.

(∀S)(¬T(S)↔¬S)

TS2-CP-C. For all sentences, iff it is not the case that it is false, then it is not the case that it is not the case

(∀S)(¬F(S)↔¬¬S)

TS1-C. For all sentences, iff it is the case, then it is true.

(∀S)(S↔T(S))

TS2-C. For all sentences, iff it is not the case, then it is false.

(∀S)(¬S↔F(S))

And these actually need to be simplified too before I can use them, but I’m too lazy to do that, so I’ll just add a simp. step. No big deal.

Now:

6. ¬C [from 2, TS1-CP-C, simp., MP]

7. F(C) [from 6, TS2-C, simp., MP]

8. F(C)∧¬F(C) [from 3, 7, conj.]

Contradiction. And I didn’t need to use double negation to get it though one could do that too with TS2-CP-C, and of course I didn’t use SB either. It seems to me that this is terrible and the best way out of the contradiction is to deny NMNT and NMNF, and believe instead that sentences like C cannot even meaningfully be said to be true or false, nor can they meaningfully be said to be not true or not false. Any complex sentence with a meaningless part is itself meaningless.5

There is a tendency for people to conflate denial of properties with the denial of the meaningful application of these properties to things. This seems to be the case here too. So instead of saying things like:

Meaningless sentences are not true.

Cars are not true.

We should say things like:

Meaningless sentences cannot meaningfully be said to be true.

Cars cannot meaningfully be said to be not true.

Maybe some people sometimes, confusingly, use the first versions as a shorthand for the second. If they do and really mean what the second ones mean, then they should use them.

In a web of beliefs approach one could set up an inconsistent set of sentences and see which one is the least plausible. I figure that my readers can do that in their heads without I needing to write it out in this case. Maybe the readers will agree with me that NMNT and NMNF are the least plausible ones in the set.

Notes

1Not meaningful not true.

2Not meaningful not false.

3Sentence bivalence.

4Because, seen as a set of inconsistent sentences, this one is the least plausible to me.

5One can formulate clever sentences for this principle. I’ll do that in another essay quickly to follow this one.

Less activity

This is not because I am not actively writing anything. It is because I am working on a very large (for me) project – a reform proposal to the danish orthography. Currently the draft is about 40 pages and it is not done yet. It is written in danish and I do not expect to translate it into english. I will post it on my sister (brother?) blog when it’s done.

A dissimilarity between “believe” and “know”

I noticed a small dissimilarity between the two words. As I have pointed out numerous times in the past, the phrase “I don’t believe that p” is ambiguous between belief in not-p and lack of belief in p. However the similar phrase for knowledge, “I don’t know that p” is not similarly ambiguous. It is however ambiguous in another way; between lack of belief in p and in not-p, and lack of knowledge that p.